91Ó°ÊÓ

We have $5q^2-15q-90$.

We will first take out the common factors from the equation. Then we will factorize it by ac method where two numbers are need whose product is equal to the product of first and last term and whose sum is the middle term. Then by writing the equation by splitting the middle term will give us the factors.

We have $5q^2-15q-90$.

Taking $5$common will give,

$5(q^2-3q-18)$.

Now we need to find two numbers whose product is $-18$and sum is $-3$. Negative sum and product show that the number with larger value is negative. The factors of$-18$are-

This shows that two numbers are$3,-6$.

Splitting the middle term gives us,

$$\begin{gathered} =5(q^2-3q-18) \\ =5(q^2+3q-6q-18) \\ =5\left[q(q+3)-6(q+3)\right] \\ =5(q+3)(q-6) \end{gathered}$$

This shows that factors are$5(q-6)(q-3)$.

We will check the solution by simply multiplying the factors. If we get the given equation as the product, our answer is right.

So,

$$\begin{gathered} =5(q-6)(q+3) \\ =(5q-30)(q+3) \\ =5q^2+15q-30q-90 \\ =5q^2-15q-90 \end{gathered}$$

Thus our calculations are right.