Question

Factor completely:$8x^2-18x+9$.

Short answer

The factors for$8x^2-18x+9$are,$\left(2x-3\right)\left(4x-3\right)$.

Step-by-step solution

Step 1. Given information

$8x^2-18x+9$.

We need to find the factors for the given expression.

Step 2. Let us use the trial and error method to find the factors.

$8x^2-18x+9$

Possible Factors	Product
$\left(2x-3\right)\left(4x-3\right)$	$8x^2-18x+9$
$\left(8x-3\right)\left(x-3\right)$	$8x^2-3x-15$
$\left(x-9\right)\left(8x-1\right)$	$8x^2-73x+9$
$\left(8x-9\right)\left(x-1\right)$	$8x^2-17x+9$
$\left(4x-9\right)\left(2x-1\right)$	$8x^2+14x+9$
$\left(2x-9\right)(4x-1)$	$8x^2-38x+9$

From the table, the obtained factors are, $\left(2x-3\right)\left(4x-3\right)$.

Step 3. Let us check the answer.

Multiply the obtained factors.

$$\begin{gathered} \left(2x-3\right)\left(4x-3\right)=\left(2x.4x\right)+\left(2x.\left(-3\right)\right)+\left(\left(-3\right).4x\right)+\left(\left(-3\right).\left(-3\right)\right) \\ =8x^2-6x-12x+9 \\ =8x^2-18x+9 \end{gathered}$$

which is correct.