Example 7.39 from Elementary Algebra, 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1

Factor Quadratic Trinomials with Leading Coefficient Other than 1: example 7.39

Factor: $8 u^{2} - 17 u - 21$ .

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

Is there a greatest common factor? No.
Find $a \cdot c$ .	$a \cdot c$
	$8 (−21)$
	$−168$

Find two numbers that multiply to $−168$ and add to $−17$ . The larger factor must be negative.

Factors of $−168$	Sum of factors
$1, −168$	$1 + (−168) = −167$
$2, −84$	$2 + (−84) = −82$
$3, −56$	$3 + (−56) = −53$
$4, −42$	$4 + (−42) = −38$
$6, −28$	$6 + (−28) = −22$
$7, −24$	$7 + (−24) = −17 *$
$8, −21$	$8 + (−21) = −13$

$\begin{matrix} Split the middle term using 7 u and −24 u . & 8 u^{2} - \underset{↙}{17} \underset{↘}{u} - 21 \\ \underset{⎵}{8 u^{2} + 7 u} \underset{⎵}{−24 u - 21} \\ Factor by grouping. & u (8 u + 7) - 3 (8 u + 7) \\ (8 u + 7) (u - 3) \\ Check by multiplying. \\ (8 u + 7) (u - 3) \\ 8 u^{2} - 24 u + 7 u - 21 \\ 8 u^{2} - 17 u - 21 ✓ \end{matrix}$

Your turn

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

Factor: $20 h^{2} + 13 h - 15$ .

How did it go?