## Answers

#### Explanation:

Factoring quadratics:

A quadratic equation in general is defined as:

Example (easy case when A = 1)

The AC Method:

What can we do when the leading coefficient is not 1?

We use an extension of factoring by grouping called the AC method.

Step by Step method for factoring

Step 1. Multiply together AC and list the factors of AC.

Step 2. Find a pair that adds to B. If you can't find such pair the quadratic is a prime and does not factor.

Step 3.

Rewrite the middle term as a sum of terms whose coefficients are the chosen pair.

Step 4. Factor by grouping.

Remember you should always first pull out the GCF.

Examples:

1)

AC = (2)(-25) = -50

the pairs are:

(1,-50), (-1,50), (2,-25), (-2,25), (5,-10) and (-5,10).

We see that: -5 + 10 = 5 hence we choose the pair (-5,10)

We write:

2)

AC = (9)(-30) = -270 => Hint : find the pairs that add to -49 i.e, (-54 , 5):

I hope this helps.