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

The answer is C. (x2 + 5)(3x2 – 2)

Answer 2

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

Explanation:

The polynomial is first correctly stated as follows

`3x^(4) - 2x^(2) + 15x^(2) - 10`

This is rearranged, grouped and solved as follows:

`3x^(4) + 15x^(2) - 2x^(2) - 10`

`(3x^(4) + 15x^(2)) - (2x^(2) + 10)`

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

Factorizing the common factors
`(x^(2) + 5)`, we have the product of the factored form of the polynomial as follows:

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

That is the third option in the question if rewritten in the correct form.