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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)

Verified Answer :

The answer is C. (x2 + 5)(3x2 – 2)

Answer:

\((x^{2} + 5)(3x^{2} - 2)\)

Step-by-step 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.

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