Week 9 – GCF of Polynomials

This week in Math 10 we learned how to find the greatest common factor of a polynomial. Finding the GCF of a polynomial is very similar to finding the GCF of two numbers. In this question the like terms have not been combined yet, so we have to do that first. Once we’ve combined the like terms we end up with ( $-4xy^3$ ) + ( $6x^3$ $y$ ) + ( $6x^2y^2$ ). To find the GCF you have to first find the GCF of the coefficients which in this case is $2$ . Then we take the lowest exponents out of all terms which in this case is $x$ to the power of one and $y$ to the power of one and that is the GCF. To go a step further we put in brackets the coefficients and exponents we need to multiply to get our combined like terms. To do this we calculate what, when multiplied by $2xy$ will equal ( $-4xy^3$ ) + ( $6x^3y$ ) + ( $6x^2y^2$ ). We end up with ( $-2y^3$ + $3x^2$ + $3x^3$ + $3xy$ ) and then we put $2xy$ in front of the bracket to get our final answer which is: $2xy$ ( $-2y^3$ + $3x^2$ + $3xy$ )