Question

factor $-7x^3 + 21x^2 + 3x - 9$ by grouping. what is the resulting expression?
○ $(3 - 7x)(x^2 - 3)$
○ $(7x - 3)(3 + x^2)$
○ $(3 - 7x^2)(x - 3)$
○ $(7x^2 - 3)(3 + x)$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(-7x^3 + 21x^2) + (3x - 9)$

Step2: Factor out GCF from each group

Factor out $-7x^2$ from the first group and $3$ from the second group: $-7x^2(x - 3) + 3(x - 3)$

Step3: Factor out common binomial factor

Factor out $(x - 3)$: $(3 - 7x^2)(x - 3)$ (we can rewrite $-7x^2(x - 3)+3(x - 3)$ as $(3 - 7x^2)(x - 3)$ by factoring out the common $(x - 3)$ and rearranging the signs appropriately)

Answer:

C. $(3 - 7x^2)(x - 3)$ (assuming the options are labeled A, B, C, D with C being $(3 - 7x^2)(x - 3)$)