Question

factor ( x^3 - 7x^2 - 5x + 35 ) by grouping. what is the resulting expression?
( \bigcirc (x^2 - 7)(x - 5) )
( \bigcirc (x^2 - 7)(x + 5) )
( \bigcirc (x^2 - 5)(x - 7) )
( \bigcirc (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 and $-5$ from the second group: $x^2(x - 7) - 5(x - 7)$

Step3: Factor out the common binomial factor

Factor out $(x - 7)$: $(x^2 - 5)(x - 7)$

Answer:

(x² - 5)(x - 7)