Question 1

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$- 1 - 3 x ^ { 4 } + 7 x ^ { 5 }$
A)descending order, degree 5
B) $7 x ^ { 5 } - 3 x ^ { 4 } - 1 , \text { degree } 9$
C) $$7 x ^ { 5 } - 3 x ^ { 4 } - 1 \text {, degree } 5$$
D)descending order, degree 10

Accepted Answer

The polynomial is written in descending order when the terms are arranged from the highest power of x to the lowest, which is $7x^5 - 3x^4 - 1$. The highest power of x is 5, so the degree of the polynomial is 5.

Question 2

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$9 s ^ { 4 } - 7 s - 7$
A)monomial
B)trinomial
C)not polynomial, no variable in last term
D)binomial

Accepted Answer

The expression $9 s ^ { 4 } - 7 s - 7$ is a polynomial because it is a sum of monomials, each term is a product of a constant and a whole number power of the variable $s$. It has three terms, making it a trinomial.

Question 3

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$5 y ^ { 4 } + 5 x ^ { 2 } + 6 x + 19 x ^ { 3 }$
A) $19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } , \text { degree } 10$
B) $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 10$
C) $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 4$
D) $$19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } \text {, degree } 4$$

Accepted Answer

The polynomial in descending order of x is $19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 }$. The degree of the polynomial is determined by the highest power of x, which is 3. However, considering all variables, the highest degree term is $5 y ^ { 4 }$, making the degree 4.

Question 4

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
--15x
A)monomial
B)binomial
C)not polynomial, no exponent on the variable
D)trinomial

Accepted Answer

-15x is a monomial because it is a single term with one variable raised to the first power. The expression is a monomial, as it only has one term with a variable raised to the first power.

Question 5

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$4 x ^ { 3 } + 5 x ^ { 2 } - 4 x ^ { - 4 }$
A)trinomial
B)polynomial
C)monomial
D)not polynomial, -4 exponent

Accepted Answer

Polynomials cannot have negative exponents. The term $4x^{-4}$ disqualifies the expression from being a polynomial.

Question 6

Give the degree of the polynomial and identify its leading coefficient.
-$- 9 x ^ { 3 } + 8 x ^ { 4 } - x ^ { 5 } + 12$
A)degree: 5; leading coefficient: -9
B)degree: 5; leading coefficient: -1
C)degree: 3; leading coefficient: -9
D)degree: 5; leading coefficient: 1

Accepted Answer

The degree of a polynomial is the highest power of x, which is 5 in this case. The leading coefficient is the coefficient of the term with the highest power, which is -1 for $x^5$.

Question 7

Give the degree of the polynomial and identify its leading coefficient.
-$- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12$
A)degree: 3; leading coefficient: 18
B)degree: 5; leading coefficient: -9
C)degree: 3; leading coefficient: -9
D)degree: 5; leading coefficient: 18

Accepted Answer

The degree of the polynomial is the highest power of $x$, which is 5, and the leading coefficient is the coefficient of the term with the highest power, which is 18.

Question 8

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$- 10 y ^ { 4 } - 9$
A)monomial
B)binomial
C)trinomial
D)not polynomial, no variable in second term

Accepted Answer

The expression $- 10 y ^ { 4 } - 9$ is a polynomial with two terms, making it a binomial. The presence or absence of a variable in a term does not disqualify it from being a polynomial.

Question 9

Give the degree of the polynomial and identify its leading coefficient.
-$8 x ^ { 3 } y ^ { 2 } - 7 x ^ { 5 } y ^ { 4 } + x ^ { 9 } y$
A)degree: 10; leading coefficient: 8
B)degree: 9; leading coefficient: -7
C)degree:9; leading coefficient: 8
D)degree: 10; leading coefficient: 1

Accepted Answer

The degree of a polynomial is the highest sum of the exponents of variables in any term of the polynomial. For the given polynomial, the term with the highest degree is $x^9y$, which has a degree of $9 + 1 = 10$. The leading coefficient is the coefficient of the term with the highest degree, which in this case is 1.

Question 10

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-7
A)not polynomial, no variables
B)monomial
C)binomial
D)trinomial

Accepted Answer

The expression given is simply the number 7, which is a constant term. In the context of polynomials, a constant term is considered a monomial because it can be thought of as a variable raised to the 0 power (anything to the 0 power is 1, so the variable essentially "disappears"). Therefore, the expression is a monomial.

Question 11

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$3 x y ^ { 3 } - 2 x ^ { 2 } + 9 + 11 x ^ { 3 }$
A) $3 x y ^ { 3 } + 11 x ^ { 3 } - 2 x ^ { 2 } + 9 , \text { degree } 3$
B) $11 x ^ { 3 } - 2 x ^ { 2 } + 3 x y ^ { 3 } + 9 , \text { degree } 4$
C) $11 x ^ { 3 } - 2 x ^ { 2 } + 3 x y ^ { 3 } + 9 \text {, degree } 3$
D) $3 x y ^ { 3 } + 11 x ^ { 3 } - 2 x ^ { 2 } + 9 , \text { degree } 4$

Accepted Answer

The polynomial in descending order of the variable x is $11 x ^ { 3 } - 2 x ^ { 2 } + 3 x y ^ { 3 } + 9$. The term with the highest degree is $3xy^3$, which has a degree of 4 when considering both x and y variables.

Question 12

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$- 10 a ^ { 2 }$
A)monomial
B)trinomial
C)not polynomial, lacks other terms
D)binomial

Accepted Answer

The expression $-10a^2$ is a polynomial with just one term, making it a monomial.

Question 13

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$- 20 x ^ { 7 } + 9$
A) $9 - 20 x ^ { 7 } , \text { degree } 7$
B)descending order, degree 7
C)descending order, degree 8
D) $9 - 20 x ^ { 7 } , \text { degree } 8$

Accepted Answer

The polynomial $- 20 x ^ { 7 } + 9$ is already in descending order of the variable $x$, and its highest power of $x$ is 7, making the degree of the polynomial 7.

Question 14

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$6 y ^ { 5 } + 8 y ^ { 4 } - 6$
A)binomial
B)monomial
C)trinomial
D)not polynomial, no variable in last term

Accepted Answer

The expression $6y^5 + 8y^4 - 6$ is a polynomial because it consists of terms that are only added or subtracted, each term is a product of a constant and a whole number power of a variable (including $y^0 = 1$ for the last term), and there are no variables in the denominator or under a radical. It is a trinomial because it has three terms.

Question 15

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$x ^ { 4 / 3 } - x ^ { 6 } - 1$
A)trinomial
B)monomial
C)binomial
D)not polynomial, 4/3 exponent

Accepted Answer

The expression is not a polynomial because it contains an exponent that is not a whole number (4/3). Polynomials must have whole number exponents.

Question 16

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$- 11 z + 6$
A)monomial
B)trinomial
C)not polynomial, no variable in second term
D)binomial

Accepted Answer

The expression $-11z + 6$ consists of two terms, $-11z$ and $+6$, making it a binomial. The presence of a variable in one term and a constant in the other does not disqualify it from being a polynomial.

Question 17

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$- 10 x - 6$
A)descending order, degree 1
B)descending order, degree 0
C)-6 - 10x, degree 1
D)-6 - 10x, degree 2

Accepted Answer

The polynomial is already in descending order with the highest power of x being 1, making it a first-degree polynomial.

Question 18

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$5 x - 6 x ^ { 3 } + 1$
A)descending order, degree 4
B)descending order, degree 5
C) $- 6 x ^ { 3 } + 5 x + 1 \text {, degree } 3$
D) $- 6 x ^ { 3 } + 5 x + 1 , \text { degree } 4$

Accepted Answer

The polynomial in descending order is $-6x^3 + 5x + 1$, and the highest power of x is 3, making the degree of the polynomial 3.

Question 19

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.
-$- 8 x ^ { 3 } - 2 x ^ { 4 } + 8 x ^ { 5 } + 12$
A)descending order, degree 5
B)descending order, degree 12
C) $8 x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 } + 12 , \text { degree } 5$
D) $8 x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 } + 12 , \text { degree } 13$

Accepted Answer

The polynomial is rearranged in descending order based on the powers of x, with the highest power being 5, indicating its degree.

Question 20

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-$- 20 y z + 6 z ^ { 2 }$
A)not polynomial, first term contains 2 different variables y and z
B)monomial
C)trinomial
D)binomial

Accepted Answer

The expression is a polynomial with two terms, making it a binomial.

Quiz 5: Polynomials and Polynomial Functions

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $- 1 - 3 x ^ { 4 } + 7 x ^ { 5 }$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $9 s ^ { 4 } - 7 s - 7$

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $5 y ^ { 4 } + 5 x ^ { 2 } + 6 x + 19 x ^ { 3 }$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. --15x

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $4 x ^ { 3 } + 5 x ^ { 2 } - 4 x ^ { - 4 }$

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 3 } + 8 x ^ { 4 } - x ^ { 5 } + 12$

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $- 10 y ^ { 4 } - 9$

Give the degree of the polynomial and identify its leading coefficient. - $8 x ^ { 3 } y ^ { 2 } - 7 x ^ { 5 } y ^ { 4 } + x ^ { 9 } y$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. -7

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $3 x y ^ { 3 } - 2 x ^ { 2 } + 9 + 11 x ^ { 3 }$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $- 10 a ^ { 2 }$

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $- 20 x ^ { 7 } + 9$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $6 y ^ { 5 } + 8 y ^ { 4 } - 6$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $x ^ { 4 / 3 } - x ^ { 6 } - 1$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $- 11 z + 6$

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $- 10 x - 6$

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $5 x - 6 x ^ { 3 } + 1$

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $- 8 x ^ { 3 } - 2 x ^ { 4 } + 8 x ^ { 5 } + 12$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $- 20 y z + 6 z ^ { 2 }$

Quiz 5: Polynomials and Polynomial Functions

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - −1−3x4+7x5- 1 - 3 x ^ { 4 } + 7 x ^ { 5 }−1−3x4+7x5

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - 9s4−7s−79 s ^ { 4 } - 7 s - 79s4−7s−7

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - 5y4+5x2+6x+19x35 y ^ { 4 } + 5 x ^ { 2 } + 6 x + 19 x ^ { 3 }5y4+5x2+6x+19x3

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. --15x

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - 4x3+5x2−4x−44 x ^ { 3 } + 5 x ^ { 2 } - 4 x ^ { - 4 }4x3+5x2−4x−4

Give the degree of the polynomial and identify its leading coefficient. - −9x3+8x4−x5+12- 9 x ^ { 3 } + 8 x ^ { 4 } - x ^ { 5 } + 12−9x3+8x4−x5+12

Give the degree of the polynomial and identify its leading coefficient. - −9x3−8x4+18x5+12- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12−9x3−8x4+18x5+12

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - −10y4−9- 10 y ^ { 4 } - 9−10y4−9

Give the degree of the polynomial and identify its leading coefficient. - 8x3y2−7x5y4+x9y8 x ^ { 3 } y ^ { 2 } - 7 x ^ { 5 } y ^ { 4 } + x ^ { 9 } y8x3y2−7x5y4+x9y

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. -7

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - 3xy3−2x2+9+11x33 x y ^ { 3 } - 2 x ^ { 2 } + 9 + 11 x ^ { 3 }3xy3−2x2+9+11x3

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - −10a2- 10 a ^ { 2 }−10a2

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - −20x7+9- 20 x ^ { 7 } + 9−20x7+9

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - 6y5+8y4−66 y ^ { 5 } + 8 y ^ { 4 } - 66y5+8y4−6

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - x4/3−x6−1x ^ { 4 / 3 } - x ^ { 6 } - 1x4/3−x6−1

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - −11z+6- 11 z + 6−11z+6

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - −10x−6- 10 x - 6−10x−6

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - 5x−6x3+15 x - 6 x ^ { 3 } + 15x−6x3+1

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - −8x3−2x4+8x5+12- 8 x ^ { 3 } - 2 x ^ { 4 } + 8 x ^ { 5 } + 12−8x3−2x4+8x5+12

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - −20yz+6z2- 20 y z + 6 z ^ { 2 }−20yz+6z2