factor the polynomial $3x^{4}-2x^{2}+15x^{2}-10$ by grouping. which product is the factored form of the…

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

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

Answer

Answer:

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

Explanation:

Step1: Group the terms

$3x^{4}-2x^{2}+15x^{2}-10=(3x^{4}-2x^{2})+(15x^{2}-10)$

Step2: Factor out GCF from each group

From $3x^{4}-2x^{2}$, GCF is $x^{2}$, so $3x^{4}-2x^{2}=x^{2}(3x^{2}-2)$. From $15x^{2}-10$, GCF is $5$, so $15x^{2}-10 = 5(3x^{2}-2)$.

Step3: Factor out common binomial factor

$x^{2}(3x^{2}-2)+5(3x^{2}-2)=(x^{2}+5)(3x^{2}-2)$