Question

factor the polynomial (3x^4 - 2x^2 + 15x^2 - 10) by grouping. which product is the factored form of the polynomial? (\bigcirc (-x^2 - 5)(3x^2 + 2)) (\bigcirc (x^2 - 2)(3x^2 + 5)) (\bigcirc (x^2 + 5)(3x^2 - 2)) (\bigcirc (3x^2 - 5)(x^2 + 2))

Explanation:

Step1: Group polynomial terms

Group first two and last two terms:
$(3x^4 - 2x^2) + (15x^2 - 10)$

Step2: Factor out GCF from each group

Factor $x^2$ from first group, 5 from second:
$x^2(3x^2 - 2) + 5(3x^2 - 2)$

Step3: Factor out common binomial

Factor $(3x^2 - 2)$ from both terms:
$(x^2 + 5)(3x^2 - 2)$

Step4: Match to options

Compare with given choices.

Answer:

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