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

(3x² - 2)(x² + 5)

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)

Answer 2

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

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)