Week 6 – Math 10 – Common polynomial factors

This week in Math 10, I have chosen to talk about common factors in regards to polynomials.

$3x^2+9x-18$

This polynomial can be factored in order to compress it down. This is done using a GCF (Greatest Common Factor). To find a GCF, we first need to expand the polynomial and factor each individual term (numbers separated by + or -) of the polynomial. Factoring being discovering the smallest indivisible numbers that can be found by dividing the number and each of its quotients.

3 $\cdot$ x $\cdot$ x

3 $\cdot$ 3 $\cdot$ x

3 $\cdot$ 2 $\cdot$ 2

Now, we determine which numbers are shared between all of the terms, in this case, only one instance of 3. Now, we divide all the terms of the original polynomial like so.

$\frac{3x^2}{3}$ $\frac{+9x}{3}$ $\frac{-18}{3}$

This factors the polynomial down to…

3( $x^2+3x-6$ )

To verify that we have factored properly, we can distribute the 3 back into the polynomial, like so.

3 $\cdot$ $3x^2$

3 $\cdot$ 3x

3 $\cdot$ (-6)

$3x^2+9x-18$

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Week 6 – Math 10 – Common polynomial factors

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