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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q. 397 (page 899)

Factor Trinomials Using the 鈥渁c鈥� Method.
In the following exercises, factor.
$2 x^{2} + 9 x + 4$

Short Answer

Expert verified

$2 x^{2} + 9 x + 4 = (2 x + 1) (x + 4)$

Step by step solution

01

Step 1. Given information

We have been given a trinomial $2 x^{2} + 9 x + 4$ .

We have to factor it Using the 鈥渁c鈥� Method.

02

Step 2. Find the product ac

$2 x^{2} + 9 x + 4 a = 2 c = 4 a c = 2 (4) = 8$

03

Step 3. Find two numbers m and n that m⋅n=a⋅c and m+n=b

We have to find m and n such that:

$m 鈰� n = 8 and m + n = 9$

Therefore, we get:

$m = 8 n = 1$

04

Step 4. Split the middle term using m and n and then factor by grouping.

$2 x^{2} + 9 x + 4 = 2 x^{2} + 8 x + x + 4 = 2 x (x + 4) + 1 (x + 4) = (2 x + 1) (x + 4)$

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