Factor completely. If the polynomial is prime, so state.
-
A) 3y(x + 5)(x - 7)
B) 3y(x + 5)(x + 7)
C) 3y(x - 5)(x - 7)
D) 3y(x - 5)(x + 7)

Question

Factor completely. If the polynomial is prime, so state.
-
A) 3y(x + 5)(x - 7) 
B) 3y(x + 5)(x + 7) 
C) 3y(x - 5)(x - 7) 
D) 3y(x - 5)(x + 7)

Quizplus · Accepted Answer

The polynomial can be factored using the difference of squares formula: 
$$
x^2 - 25 = (x + 5)(x - 5)
$$
Then, we can factor out the common factor of 3y:
$$
11ebb63d_1b72_7c05_b851_e1973627e8c9_TB8475_11 = 3y(x + 5)(x - 5)(x + 7)
$$
Therefore, the best choice is D. The polynomial is of the form 3yx^2 - 36yx - 105y, which can be factored as 3y(x^2 - 12x - 35). This quadratic can be factored further as (x - 7)(x + 5), giving the final factorization of 3y(x - 7)(x + 5). Therefore, the best choice is D.

Factor Completely