factor -7x³ + 21x² + 3x - 9 by grouping. what is the resulting expression? (3 - 7x)(x² - 3) (7x - 3)(3 + x²)…

Explanation:

Step1: Group the terms

$(-7x^{3}+21x^{2})+(3x - 9)$

Step2: Factor out the greatest - common factor from each group

From the first group $-7x^{3}+21x^{2}$, the GCF is $-7x^{2}$, so $-7x^{3}+21x^{2}=-7x^{2}(x - 3)$. From the second group $3x - 9$, the GCF is 3, so $3x - 9=3(x - 3)$. The expression becomes $-7x^{2}(x - 3)+3(x - 3)$.

Step3: Factor out the common binomial factor

Factor out $(x - 3)$: $(x - 3)(-7x^{2}+3)=(3 - 7x^{2})(x - 3)$

Answer:

C. $(3 - 7x^{2})(x - 3)$