Q. 372

Factor Trinomials of the Form $a x^{2} + b x + c$ ax using the ‘ $a c$ ’ Method
In the following exercises, factor.

$2 x^{2} + 9 x + 4$

Verified

Answer

By using $' a c'$ method, the factors of $2 x^{2} + 9 x + 4$ is $(2 x + 1) (x + 4)$

1Step 1. Given

The trinomial is $2 x^{2} + 9 x + 4$

To find the factors by using $' a c'$ method.

2Step 2. Find the product a c

Find the product $a c$

$a c = 8$

Find two numbers that multiply to $a c$ and add to $b$ .

$(8) (1) = 8$

$8 + 1 = 9$

3Step 3. Split the middle term

$2 x^{2} + 9 x + 4 = 2 x^{2} + 8 x + x + 4$

Factor by grouping

$= 2 x (x + 4) + 1 (x + 4)$

$= (2 x + 1) (x + 4)$

4Step 4. Check the answer

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

$= 2 x^{2} + 9 x + 4$