Week 5 – Factoring Polynomials

Factoring is writing an expression in simpler form (UNLESS STATED IT’S NOT SOLVING ). To factor polynomials there are a few steps to take:

C-common (GCF)
D-differences of squares (BINOMIALS!)
P-pattern? (TRINOMIALS)
E-easy ( $1x^2$ )
U-ugly ( $ax^2$ )

Binomial exp.

$4x^2$ -16$

What’s common? 4

4 ( $x^2-4$ )

Is it a difference of squares (Binomial)? Yes

4(x-2)(x+2)

(x-a)(x+a) is a conjugates because if you foil it the middle terms will cancel so that you can have a binomial.

= $x^2 -a^2$ (this only works if you are subtracting) $x^2$ -49 = (x-7)(x+7)

Trinomial exp.

$3x^2 -9x +6$

What’s common? 3

$3(x^2 -3x+2)$

Is it a difference of square? No

Does it have a pattern? Yes

$x^2$ , x, #

Easy? Yes

$3(x^2 -3x+2)$

Now you figure out _x_=2 but also _+_=-3

-1x-2=2 and -1+-2=-3

3(x-1)(x-2)

Ugly Factoring exp.

$3x^2 +7x+4$

Anything common? NO

Difference of squares?Binomial? NO

Pattern? Yes

Is it easy? No

So you have to do ugly factoring aka box method!

You take the first term and the last term and put them in a box

$3x^2$ | #

# | +4

Then you multiply them $3x^2 x4= 12x^2$

Then you find all the factors the would equal $12x^2$

1x-12x
2x-6x
3x-4x

Out of these factors pick the one that when added together equal term b.

7x=4x+3x

Then add these into the box,

$3x^2 | +4x$

+3x | +4

Then find what’s common for the top row, bottom row, left column and right column.

Top row: 1x
Bottom row: +1

=(1x+1)

Left column: 3x
Right column: +4

=(3x+4)

(1x+1)(3x+4) would be the factored version of $3x^2+7x+4$

Toria Stewart

Riverside Rapids

Week 5 – Factoring Polynomials

Leave a Reply Cancel reply