Question

factor $x^3 - 7x^2 - 5x + 35$ by grouping. what is the resulting expression?
○ $(x^2 - 7)(x - 5)$
○ $(x^2 - 7)(x + 5)$
○ $(x^2 - 5)(x - 7)$
○ $(x^2 + 5)(x - 7)$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(x^3 - 7x^2) + (-5x + 35)$

Step2: Factor out GCF from each group

Factor out $x^2$ from the first group: $x^2(x - 7)$
Factor out $-5$ from the second group: $-5(x - 7)$

Step3: Factor out the common binomial

Now we have $x^2(x - 7) - 5(x - 7)$, factor out $(x - 7)$: $(x^2 - 5)(x - 7)$

Answer:

C. $(x^2 - 5)(x - 7)$