Question

Factor the following expression.

Answer 1

10x^5 + 5x^3 - 14x^2 - 7

= 5x^3(2x^2 + 1) - 7(2x^2 + 1)

= (5x^3 - 7)(2x^2 + 1)

Answer is D

(5x^3 - 7)(2x^2 + 1)

Answer 2

Answer:

D.

Step-by-step explanation:

Let's use common factor gruping terms. We have that we have a common factor between the two left terms and another common factor between the two right terms. Then,

for the two left terms we take the common divisor, in this case 5 and the x with the minimun exponent, that is 5x^3.

for the two right terms we take the common divisor, in this case -7 and the x with the minimun exponent, in this case the -7 has no x so we don't include it in the common factor.

$10x^5 + 5x^3 - 14x^2 - 7 = 5x^3(2x^2+1)-7(2x^2+1)$

Now, we use common factor again, this time the common factor will be $2x^2+1$:

$10x^5 + 5x^3 - 14x^2 - 7 = 5x^3(2x^2+1)-7(2x^2+1)= (2x^2+1)(5x^3-7)$.

Then, the answer is D.