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.

Example 1

Factor $6pqr+18pqz$6pqr+18pqz

 $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.

More examples

Question 1

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

$9x^2y^2z-18xyz$9x2y2z18xyz

Question 2

Factor the following expression:

$pqr+p^2q^2r+p^3q^3r$pqr+p2q2r+p3q3r

Question 3

Factor $9r^2t^2v^3+6r^3tv-12rt^3v^2$9r2t2v3+6r3tv12rt3v2.

Outcomes

10P.QR1.02

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)