Example 7.19 from Elementary Algebra, 7.2 Factor Quadratic Trinomials with Leading Coefficient 1

Factor Quadratic Trinomials with Leading Coefficient 1: example 7.19

Factor: $y^{2} + 17 y + 60$ .

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
$\begin{matrix} y^{2} + 17 y + 60 \\ Write the factors as two binomials with first terms y . & (y) (y) \end{matrix}$

Find two numbers that multiply to 60 and add to 17.

Factors of $4 + 15 = 19$ Sum of factors

$1, 60$ $1 + 60 = 61$

$2, 30$ $2 + 30 = 32$

$3, 20$ $3 + 20 = 23$

$4, 15$ $4 + 15 = 19$

$5, 12$ $5 + 12 = 17 *$

$6, 10$ $6 + 10 = 16$

$\begin{matrix} Use 5 and 12 as the last terms. & (y + 5) (y + 12) \\ Check. \\ (y + 5) (y + 12) \\ (y^{2} + 12 y + 5 y + 60) \\ (y^{2} + 17 y + 60) ✓ \end{matrix}$

Your turn

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

Factor: $x^{2} + 19 x + 60$ .

How did it go?