Example 7.23 from Elementary Algebra, 7.2 Factor Quadratic Trinomials with Leading Coefficient 1

Factor Quadratic Trinomials with Leading Coefficient 1: example 7.23

Factor: $q^{2} - 2 q - 15$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{matrix} q^{2} - 2 q - 15 \\ Factors will be two binomials with first terms q . & (q) (q) \\ You can use 3, −5 as the last terms of the & (q + 3) (q - 5) \\ binomials. \end{matrix}$

Factors of $−15$ Sum of factors

$1, −15$ $1 + (−15) = −14$

$−1, 15$ $−1 + 15 = 14$

$3, −5$ $3 + (−5) = −2 *$

$−3, 5$ $−3 + 5 = 2$

Check.

$(q + 3) (q - 5)$

$q^{2} - 5 q + 3 q - 15$

$q^{2} - 2 q - 15 ✓$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor: $r^{2} - 3 r - 40$ .

How did it go?