Question

In the following exercises, factor using the ‘ac’ method$30x^2+105x-60$

Short answer

The factors are$15\left(2x-1\right)\left(x+4\right)$

Step-by-step solution

Step 1. Given Information

The trinomial is $30x^2+105x-60$

Find the factor using 'ac' method.

Step 2. Find GCF

Find GCF and factor it

GCF is 15

S0, $15\left(2x^2+7x-4\right)$

Step 3. Find 'ac'

Compare the trinomial inside the parenthesis with $a{x}^2+bx+c$

So, $a=2,b=7,c=-4$

so, $ac=-8$

Find two number such as their product is role="math" localid="1644581551461" $ac=-8$and their addition is $b=7$

So the numbers are 8 and -1.

Step 4. Split the middle and factor trinomial by grouping

Split the middle term

$15\left(2x^2+8x-x-4\right)$

Factor it by grouping

$15\left(2x\left(x+4\right)-1\left(x+4\right)\right)$

$15\left(x+4\right)\left(2x-1\right)$

Step 5. Check

To check multiply all factors,$15\left(2x-1\right)\left(x+4\right)$

$$\begin{gathered} 15\left(2x^2+7x-4\right) \\ 30x^2+105x-60 \end{gathered}$$