Ontario 10 Applied (MFM2P)

Factor algebraic expressions

Lesson

We've previously learnt how to factor both algebraic and numeric terms from expressions. Now we are going to look at expressions where the greatest common factor (GCF) may consist of more than one variable, or even a linear factor. Let's look at some examples below.

Factor $6pqr+18pqz$6`p``q``r`+18`p``q``z`

$6p^2qr+18pqz$6p2qr+18pqz |
$=$= | $6\left(p^2qr+3pqz\right)$6(p2qr+3pqz) Take out the highest numerical factor |

$=$= | $6pq\left(pr+3z\right)$6pq(pr+3z) Take out the highest common powers of each variable |

Since there was a $q$`q` present in both terms, as well as a single power of $p$`p`, we were able to pull both of these out of the expression as factors.

Factor the following expression by taking out the highest common factor:

$9x^2y^2z-18xyz$9`x`2`y`2`z`−18`x``y``z`

Factor the following expression:

$pqr+p^2q^2r+p^3q^3r$`p``q``r`+`p`2`q`2`r`+`p`3`q`3`r`

Factor $9r^2t^2v^3+6r^3tv-12rt^3v^2$9`r`2`t`2`v`3+6`r`3`t``v`−12`r``t`3`v`2.

Factor binomials (e.g., 4x^2 + 8x) and trinomials (e.g., 3x^2 + 9x – 15) involving one variable up to degree two, by determining a common factor using a variety of tools and strategies (e.g., patterning)