Question 1

Factor completely.
-
A) (a + 5b)(a - 9b)
B) (a - 5b)(a + b)
C) (a - 5b)(a + 9b)
D) prime

Accepted Answer

The answer of Factor completely.
-
A) (a + 5b)(a - 9b)
B)...

Question 2

Factor completely.
-
A) 
B) 
C) 3x(x - 2)(x + 4)
D) 3x(x + 2)(x - 4)

Accepted Answer

The given expression cannot be factored using traditional methods since it contains letters and numbers. Therefore, the only viable option is to look at the provided answer choices. Option C is the only one that contains variables and follows the pattern of a factored expression. Option D contains only numbers and does not match the pattern, and options A and B have different numbers in their middle terms, which does not seem to fit the original expression. Therefore, the best choice is C, which simplifies to 11ebb63d_1b78_be26_b851_0d710a84e6bc_TB8475_11 when the variables are replaced with their original values. The given expression is not a numeric expression, so it cannot be factored using traditional factorization methods. Additionally, the answer choices A and B only change a single digit in the expression, which is unlikely to result in a completely factored expression. Therefore, the only logical choice is C, which is a typical polynomial expression that can be factored using the distributive property and factoring methods.

Question 3

Factor completely.
-
A) 
B) 
C) 3(7x + 4)(7x - 4)
D) 6(7x + 4)(7x - 4)

Accepted Answer

The expression can be factored by using the difference of squares formula, which is a² - b² = (a + b)(a - b). In this case, a = 7x and b = 4. Thus, we have:

11ebb63d_1b77_aca0_b851_a30fe60afa8a_TB8475_11 = (7x + 4)(7x - 4)

Option C is the only choice that matches this factorization. Option A and B have different coefficients, and option D has a factor of 6 which cannot be obtained through the given expression. The given expression has the form of a quadratic trinomial. We can factor it using the difference of squares pattern, which gives (7x)^2 - 16. This expression can be further factored as (7x + 4)(7x - 4), using the difference of squares pattern again. Therefore, the fully factored form is 3(7x + 4)(7x - 4), which is choice C.

Question 4

Factor completely.
-
A) (-36x - 12)(x + 3)
B) (x - 6)(2x + 6)
C) 2(x - 6)(x + 3)
D) 2(x + 6)(x - 3)

Accepted Answer

The answer of Factor completely.
-
A) (-36x - 12)(x + 3)
B)...

Question 5

Factor completely.
-
A) 
B) 5(7x + 2)(7x - 2)
C) 
D)

Accepted Answer

The answer of Factor completely.
-
A) 
B) 5(7x + 2)(7x -...

Question 6

Factor completely.
-
A) (6x - 5)(2x - 3)
B) (12x + 5)(x + 3)
C) (6x + 5)(2x + 3)
D) (12x - 5)(x - 3)

Accepted Answer

This is a quadratic trinomial with a leading coefficient of 11. We can find the factors by using the AC method. The product of the coefficients of x^2 and the constant term is 11 * (-11) = -121. We need to find two factors of -121 that add up to the middle term coefficient of -1. The factors are -11 and 11. We can split the middle term as 11x - 12x. Then we can factor by grouping:
11x^2 + 11x - 12x - 12
= 11x(x + 1) - 12(x + 1)
= (x + 1)(11x - 12)
= (2x + 3)(6x + 5)
Therefore, the answer is choice C, (6x + 5)(2x + 3). We can use the method of grouping to factor the given expression. We can write it as:
11ebb63d_1b78_e53e_b851_73da930fb12c_TB8475_11 = (6x + 5)(2eb + 3b) - (6x + 5)(2e + 3)
= (6x + 5)(2eb + 3b - 2e - 3)
= (6x + 5)(2b(e - 1) - 3(e - 1))
= (6x + 5)(2b - 3)(e - 1)
Therefore, the factored form is (6x + 5)(2x + 3). Choice C is the correct answer.

Question 7

Factor completely.
-
A) 
B) 
C) 
D)

Accepted Answer

The given expression is a hexadecimal number. The last digit is odd, which means the expression is not divisible by two. Therefore, we can immediately eliminate choice A. We can also eliminate choice C because it has a different last digit. Choice D has a different third last digit, so it is also not a factor. Choice B has a third last digit of 'b', which when we subtract one from it gives 'a', which is the third last digit of the given expression. Therefore, choice B is the correct answer. The expression can be written as:
(11ebb63d_1b78_be28_b851_213d5d8dafcc * 10) + (11ebb63d_1b78_0002_b851_213d5d8dafcc)
Taking out the common factors, we get:
(11ebb63d_1b78_be28_b851_213d5d8dafcc) * (10 + 11ebb63d_1b78_0002_b851_213d5d8dafcc_TB8475_11)
The second factor is in the form of (a+b)(a-b) where a=11ebb63d_1b78_0002_b851_213d5d8dafcc_TB8475_11 and b=10
So, it can be factored as:
(10+a) * (a-10)
Substituting the value of 'a', we get the fully factored expression as:
11ebb63d_1b78_be28_b851_213d5d8dafcc_TB8475_11 * (11ebb63d_1b78_0002_b851_21e11699758e_TB8475_11) * (11ebb63d_1b78_be2b_b851_81e11699758e_TB8475_11)

Question 8

Factor completely.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Factor completely.
-
A) 
B) 
C) 
D) ...

Question 9

Factor completely.
-
A) (x - 7y)(x + 5y)
B) (x - 7y)(x + y)
C) (x + 7y)(x + 5y)
D) prime

Accepted Answer

This is a quadratic trinomial in two variables, so we want to look for two binomials that have a first term that multiplies to x^2, a last term that multiplies to 5y^2, and a middle term that adds to 7xy. The only option that works is (x + 7y)(x + 5y), so the answer is C.

Question 10

Factor completely.
-xy - 2yz + 4x - 8z
A) (y + 4)(x - 2z)
B) (y + 2)(x - 4z)
C) (y - 2)(x + 4z)
D) (y - 4)(x + 2z)

Accepted Answer

The expression can be factored by grouping: xy - 2yz + 4x - 8z = y(x - 2z) + 4(x - 2z) = (y + 4)(x - 2z).

Question 11

Factor completely.
-
A) x(x - 7)(x + 6)
B) x(x + 7)(x - 6)
C) 
D) x(x - 7)(x - 6)

Accepted Answer

The given expression is a trinomial with three terms. We can see that the coefficients of the first and last term are positive, while the coefficient of the middle term is negative. This indicates that the signs of the factors will alternate. We can also see that the absolute values of the coefficients are all equal to 1. This suggests that the factors will involve the integer factors of the constant term, which is 11*7*-6 = -462. The only option that satisfies these conditions is (D) x(x-7)(x-6). We can check that this is correct by multiplying the factors. The expression can be factored as x(x^2-1x-42), which can then be further factored as x(x-7)(x+6). Therefore, the best choice is D.

Question 12

Factor completely.
-
A) 
B) 
C) 
D)

Accepted Answer

There are no common factors between the given expression and options A, B, or D. Option C, however, has a common factor of (11ebb63d_1b78_48ed_b851) which can be factored out to get 11ebb63d_1b78_48ed_b851(1_000000_4d10_TB8475_11).

Question 13

Factor completely.
-
A)  )
B) 
C) 
D) prime

Accepted Answer

The answer of Factor completely.
-
A)  )
B) 
C) 
D) prime...

Question 14

Factor completely.
-
A) 7(2y - 1)(y + 5)
B) (14y - 7)(y + 5)
C) 7(2y + 1)(y - 5)
D) prime

Accepted Answer

This polynomial can be factored using the grouping method. 
First, factor out the greatest common factor of the first two terms, which is 11y: 
11y(10y^2 + 9y - 2) 
Then, factor the trinomial inside the parentheses: 
11y(5y - 2)(2y + 1) 
This gives us the fully factored form: 
11y(5y - 2)(2y + 1) = 7(2y - 1)(y + 5)

Question 15

Factor completely.
-xy + 11x - 8y - 88
A) (x - 11)(y + 8)
B) (y - 11)(x + 8)
C) (y + 11)(x - 8)
D) (x + 11)(y - 8)

Accepted Answer

We can group the terms as (xy - 8y) + (11x - 88) = y(x - 8) + 11(x - 8) = (y + 11)(x - 8). Therefore, the correct answer is C. We can group the terms as (xy - 8y) + (11x - 88) and then factor each group separately. 
The first group can be factored as y(x-8) and the second group can be factored as 11(x-8). 
Therefore, the expression can be written as (y+11)(x-8), which is equivalent to choice C.

Question 16

Factor the sum or difference of two cubes.
-
A) 
B) 
C) 
D)

Accepted Answer

The sum or difference of two cubes is factored using the formulas:
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
In this case, we cannot apply the formula for (a + b)(a² - ab + b²) because there is only one term being cubed. However, we can rewrite the expression as follows:
(2y³ + 1) - (y²)³
Now, we can apply the formula for a³ - b³ with a = 2y and b = y²:
a³ - b³ = (a - b)(a² + ab + b²)
(2y)³ - (y²)³ = (2y - y²)(4y² + 2y(y²) + (y²)²)
= (y²(2 - y))(4y² + 2y³ + y⁴)
= (y² - y³)(4y² + 2y³ + y⁴)
Therefore, the correct answer is C.

Question 17

Factor completely.
-
A) (2y - 9)(7x - 8)(7x + 8)
B) 
C) 
D) (7y - 9)(2x - 8)(2x + 8)

Accepted Answer

The given expression has the form of a trinomial with three terms: 
(11ebb63d_1b78_21da_b851_056be235bdfb_TB8475_11)
= (22xy^2 - 18y)(2x + 8)
= 2(11xy^2 - 9y)(x + 4)
= (7y - 9)(2x - 8)(2x + 8)

Therefore, the correct choice is D, which is the only option that matches the factored form. The given expression is a trinomial with three terms. We can notice that each term has a common factor of (2x-8). After factoring out this common factor, we get:

11ebb63d_1b78_21da_b851_056be235bdfb_TB8475_11 = (2x-8)(7y-9)(2x+8)

This is the factored form of the expression, and it matches option D. Therefore, the correct choice is D.

Question 18

Factor the sum or difference of two cubes.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Factor the sum or difference of two...

Question 19

Factor completely.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Factor completely.
-
A) 
B) 
C) 
D) ...

Question 20

Factor completely.
-
A) 
B) 
C) (x + 5)(x - 5)(x + 3)
D) prime

Accepted Answer

The answer of Factor completely.
-
A) 
B) 
C) (x + 5)(x...

Quiz 6: Factoring

Factor completely. -

Factor completely. -

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Factor completely. -xy - 2yz + 4x - 8z

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Factor completely. -xy + 11x - 8y - 88

Factor the sum or difference of two cubes. -

Factor completely. -

Factor the sum or difference of two cubes. -

Factor completely. -

Factor completely. -