Question

factor $x^3 - 4x^2 + 7x - 28$ by grouping. what is the resulting expression?
○ $(x^2 - 4)(x + 7)$
○ $(x^2 + 4)(x - 7)$
○ $(x^2 - 7)(x + 4)$
○ $(x^2 + 7)(x - 4)$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(x^3 - 4x^2) + (7x - 28)$

Step2: Factor out GCF from each group

Factor out $x^2$ from the first group: $x^2(x - 4)$
Factor out $7$ from the second group: $7(x - 4)$
Now the expression is $x^2(x - 4) + 7(x - 4)$

Step3: Factor out the common binomial

Factor out $(x - 4)$: $(x^2 + 7)(x - 4)$

Answer:

D. $(x^2 + 7)(x - 4)$