Identify the greatest common factor. Than factor the expression.

Question

x^7-3x^6-3x^5

 

What is the greatest common factor?

 

 

Answer 1

First try to find a common factor for the coefficients. There is no common factor other than 1 and -1 for 1, -3 and -3.

Now find the common factor for the exponential expressions x⁷, x⁶, x⁵. These can each be divided by x, x², x³, x⁴, and x⁵. x⁵ has the largest exponent, so this is the greatest common factor. Now take this common factor "out".

x⁵( ? - ? - ?) = x⁷-3x⁶-3x⁵. We need to find the right expressions to fill in for ?.

Divide each term in the original by the common factor: x⁷/x⁵ = x². 3x⁶/x⁵= 3x. 3x⁵/x⁵ = 3

Take our 3 answers and fill them in for the ? and get x⁵(x²-3x-3).