9/30 – Factoring GCF

Factoring a number means writing it as the product of other numbers. Can the same thing be done to polynomials? Absolutely! Although polynomials may look quite complicated, polynomials represent numbers just like a variable represents a number. One huge idea in algebra is that anything we can do to a number, we can probably do to a polynomial.

Number example: 30 = 5(6)

Polynomial example: 8x^2y^3 - 10x^4y = 2x^2y(4y^2 - 5x^2)

In essence, a polynomial is factored by “extracting” all the factors shared by each of the polynomial’s pieces. The result is an equivalent expression, except this time it’s written as the product of two shorter polynomials. How do we check our work? Use the distributive property. So what’s another name for factoring? The reverse distributive property!