Question

Factor the polynomial 3x4 – 2x2 + 15x2 – 10 by grouping. Which product is the factored form of the polynomial? (–x2 – 5)(3x2 + 2) (x2 – 2)(3x2 + 5) (x2 + 5)(3x2 – 2) (3x2 – 5)(x2 + 2)

Answer 1

Answer:

$(x^2+5)(3x^2-2)$

Step-by-step explanation:

The polynomial is

$3x^4-2x^2+15x^2-10$

You can group the first and third term and the second and last term

$3x^4+15x^2-2x^2-10$

Factorize each pair

$3x^4+15x^2-2x^2-10$

$3x^2(x^2+5)-2(x^2+5)$

Finally, you can factor the $(x^2+5)$ and obtain

$(x^2+5)(3x^2-2)$

Then, the answer is (x2 + 5)(3x2 – 2)

Answer 2

Answer:

(3x² - 2)(x² + 5)

Step-by-step explanation:

Given

3$x^{4}$ - 2x² + 15x² - 10

Factor the first/second and third/fourth terms

= x²(3x² - 2) + 5(3x² - 2) ← factor out (3x² - 2) from each term

= (3x² - 2)(x² + 5)