Question

factor the following expression by grouping.

\\a^3 - 2a^2 + 5a - 10\\

\\a^3 - 2a^2 + 5a - 10 = \\ (type your answer in factored form.)

Explanation:

Group the terms

Group the first two terms and the last two terms of the polynomial.

$$ (a^3 - 2a^2) + (5a - 10) $$

Factor out the greatest common factor from each group

Factor out \(a^2\) from the first group and \(5\) from the second group.

$$ a^2(a - 2) + 5(a - 2) $$

Factor out the common binomial

Factor out the common binomial factor \((a - 2)\) from the expression.

$$ (a^2 + 5)(a - 2) $$

Answer:

Factor the following expression by grouping.

\(a^3 - 2a^2 + 5a - 10 =\) <blank>\((a^2 + 5)(a - 2)\)</blank> (Type your answer in factored form.)