Question

Factor completely:$10a^2-17a+6$.

Short answer

The factors for$10a^2-17a+6$are,$\left(5a-6\right)\left(2a-1\right)$.

Step-by-step solution

Step 1. Given information

$10a^2-17a+6$.

We need to find the factors for the given expression.

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

$10a^2-17a+6$

Possible Factors	Product
$\left(5a-6\right)\left(2a-1\right)$	$10a^2-17a+6$
$\left(a-6\right)\left(10a-1\right)$	$10a^2-61a+6$
$\left(a-3\right)\left(10a-2\right)$	Not an option
$\left(2a-6\right)\left(5a-1\right)$	Not an option
$\left(10a-6\right)\left(a-1\right)$	Not an option
$\left(a-2\right)\left(10a-3\right)$	$10a^2-23a+6$

So, the obtained factors are, $\left(5a-6\right)\left(2a-1\right)$.

Step 3. Let us check the answer.

Multiply the factors.

$$\begin{gathered} \left(5a-6\right)\left(2a-1\right)=\left(5a.2a\right)+\left(5a.-1\right)+\left(-6.2a\right)+\left(\left(-6\right).\left(-1\right)\right) \\ =10a^2-5a-12a+6 \\ =10a^2-17a+6 \end{gathered}$$

which is correct.