Question

warm-up
use factoring to rewrite this polynomial expression.
drag each factor to the correct location on the equation. each factor can be used more than once, but not all factors will be used.
$x^3 + 5x^2 - 9x - 45 = (\quad)(\quad)(\quad)$
$x - 3$ $x - 5$ $x + 3$ $x + 5$ $x + 9$ $x - 9$ $x + 1$ $x - 1$

Explanation:

Step1: Group terms

Group the first two terms and the last two terms: $(x^3 + 5x^2) + (-9x - 45)$

Step2: Factor out GCF from each group

Factor out $x^2$ from the first group and $-9$ from the second group: $x^2(x + 5) - 9(x + 5)$

Step3: Factor out common binomial

Factor out $(x + 5)$: $(x + 5)(x^2 - 9)$

Step4: Factor difference of squares

Factor $x^2 - 9$ as a difference of squares: $(x + 5)(x - 3)(x + 3)$

Answer:

$(x + 5)(x - 3)(x + 3)$