Factor............

Question

5x^3y-75xy^2

Answer 1

Here, you can factor out a GCF.  The GCF of the polynomial is a product of the GCF of the coefficients and the GCF of the variables.  Let's first look at the coefficients, 5 and -75.  The GCF of these two numbers is 5.  Now, look at the variables, x being the first.  There's an x³ in the first term and an x in the second term.  The largest factor we can take out from these is x.  Next, there's a y in the first term and a y² in the second term, so the GCF is just y because you cannot factor out anything larger than a single y.  Now, simply combine the GCF of the coefficients and the two variables:

 

5 · x · y = 5xy

 

5xy(x² - 15y)