Question

Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?

Answer 1

Answer: (x² - 5)(x - 7)

Explanation:

Grouping the terms, we have:

(x^3 - 7x^2) + (-5x + 35)

Now, let's factor out the common factors from each pair:

x^2(x - 7) - 5(x - 7)

Notice that we have a common factor of (x - 7) in both terms. We can factor it out:

(x^2 - 5)(x - 7)

Therefore, the resulting expression after factoring by grouping is (x^2 - 5)(x - 7).