factor 6x^4 - 5x^2 + 12x^2 - 10 by grouping. what is the resulting expression?\n(6x + 5)(x^2 - 2)\n(6x…

Answer:

D. $(6x^{2}-5)(x^{2}+2)$

Explanation:

Step1: Combine like - terms

$6x^{4}-5x^{2}+12x^{2}-10=6x^{4}+7x^{2}-10$

Step2: Group the terms

Group the first two and the last two terms: $(6x^{4}-5x^{2})+(12x^{2}-10)$

Step3: Factor out the GCF from each group

From the first group $6x^{4}-5x^{2}$, the GCF is $x^{2}$, so we get $x^{2}(6x^{2}-5)$. From the second group $12x^{2}-10$, the GCF is 2, so we get $2(6x^{2}-5)$.

Step4: Factor out the common binomial factor

The common binomial factor is $(6x^{2}-5)$. So, $x^{2}(6x^{2}-5)+2(6x^{2}-5)=(6x^{2}-5)(x^{2}+2)$