In order to find the highest common algebraic factor we can use the following steps.
Let's look at an example.
What is the highest common algebraic factor of $2x^2y$2x2y and $6xz$6xz?
Think: We need to look at the numeric coefficient first, then the algebraic variables, and then combine our findings into a solution.
Do: The numerical coefficients are $2$2 and $6$6, so the numerical GCF is $2$2.
The algebraic terms present in the first term are $x$x and $y$y, and those present in the second term are $x$x and $z$z. So $x$x is the only common variable between the two.
The lowest power of $x$x present in either term is $x^1=x$x1=x, so this will be the algebraic component of our highest common algebraic factor.
Solve: Our highest common algebraic factor is $2x$2x.
The same process applies if we are asked to compare $3$3 or more terms, we just need to ensure any common numeric or algebraic variables are common to all terms.
What is the highest common algebraic factor of the terms $9ax$9ax and $8ba$8ba?
What is the highest common algebraic factor of the terms $4bx$4bx and $6by$6by?
What is the highest common algebraic factor of the terms $3a^2mn$3a2mn, $2ya^4x$2ya4x and $5xma^3$5xma3?
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)