Factoring | welcome-to-quadratic

Common Factoring

When factoring a polynomial, the first thing we want to do is to find a correct factoring stratagy. Lets use the guess and check method. We have to make sure that our equation is in standard form.

Let's lake a look at the standard form equation: ax²+bx+c. If values a, b and c have a value that is common you would factor it out. Place the number you factored out of the equation a, b and c outside the bracket.

Now find the factors of a and c and put it in this equation: ( _+_ )( _+_ )

Keep on guessing and checking until you get the right two numbers in the above equation.

To check your answer all you need to do is to multiply the two binomials so that you get the original polynomial. Let this example help you out.

We now have a factored form equation.

Ex: 2x²+4x+8

You would then factor this to: 2(x²+2+4)

Now factor whats in the bracket: 2(x+2)(x+2)

Simple Trinomials

To identify a simple trinomal, the coefficient of a has to be 1 so it would only be x².

If the standard form equation is x² then simply use the guess and check method to factor down the equation.

Example: x²+x6+8

=x(x+4)(x+2)

Complex Trinomials

To identify a complex trinomal, the coefficient of a has to be greatter than 1 and cannot have a common factor.

Next, use the guess and check method to factor down the equation but only this time we would need to list the multiples of a and c and out it into the equation lIke so:

3x²+7x+2

(x + 2) (3x + 1)

To make sure check you answer so that it looks like the original standard form equation.

Perfect Squares

To identify a perfect square standard form equation both a and c must be squares.

Sqaure root a and c and to find b all you need to do is: 2(√a)(√c)

To put it into factored form, simply: (√a+√c)(√a+√c)

(√a+√c)²

Example: ax²+bx+c

=36x²+ __ + 16

a=√36 c=√16

a=6 c=4

Now: b= 2(6)(4)

b= 48

Final: (6x+4)²

Difference of Squraes

To identify a difference of squares standard form equation b needs to be 0. In order for that to happen, both a and c have to be squares, however this time c is negative.

Then, square root a and c. put a and c into the factored form equation but make sure that in the binomials one c is negative and the other is positive thus, b will cancel out and be 0.