Hi Jared,
Factor the polynomial completely.
5x^3 y+25x^2y+5xy
Ok, let's start with the coefficients for each term in this expression.
1st term 5x^3 coefficient is 5
second term 25x^2y coefficient is 25
third term 5xy coefficient is 5
The question you need to ask yourself: What is the greatest factor that goes into each of these numbers?
coefficient is 5 factors 5 and 1
coefficient is 25 factors 5, 5 , 1
coefficient is 5 factors 5 and 1
So you can factor out 5 since it is common to all three terms in the expression:
5x^3 y+25x^2y+5xy = 5 (x^3 y+5x^2y+xy)
Is there anything else that is a common factor in all three terms of the expression? Yes, x's
1st term x^3y there are three x's x, x, x
second term 5x^2y there are two x's x, x
third term xy there is one x x
So there is one x common to all three terms, therefore one x can be factored out:
5x^3 y+25x^2y+5xy = 5 (x^3 y+5x^2y+xy)
= 5x (x^2y + 5xy + y)
Is there anything else that there is a common factor in all three terms of the expression? yes, y's
1st term x^2y there are two y's y, y
second term 5xy there are one y y
third term y there is one y y
Looking at the three terms, there is one y that is common to all three terms, so the y can be factored out.
5x^3 y+25x^2y+5xy = 5 (x^3 y+5x^2y+xy)
= 5x (x^2y + 5xy + y)
= 5xy (x^2 + 5x + 1) now the expression is fully factored.
I hope that you now have a better understanding of the process.
THINK MATH!!
