# How do you factor 8x^2+18x+9?

May 2, 2015

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 8 \cdot 9 = 72$
AND
${N}_{1} + {N}_{2} = b = 18$

After trying out a few numbers we get ${N}_{1} = 12$ and ${N}_{2} = 6$

$12 \cdot 6 = 72$, and $12 + 6 = 18$

$8 {x}^{2} + 18 x + 9 = 8 {x}^{2} + 12 x + 6 x + 9$

$= 4 x \left(2 x + 3\right) + 3 \left(2 x + 3\right)$

$2 x + 3$ is a common factor to each of the terms

 =color(green)( (2x+3)(4x+3)
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