SOLUTION: I need help factoring out the greatest common factor from a polynomial. The problem is: 5(m-3) - 7(m-3)^2 + 5(m-3)^3. All the examples I've looked at on how to factor out the great

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help factoring out the greatest common factor from a polynomial. The problem is: 5(m-3) - 7(m-3)^2 + 5(m-3)^3. All the examples I've looked at on how to factor out the great      Log On


   

Question 776089: I need help factoring out the greatest common factor from a polynomial. The problem is: 5(m-3) - 7(m-3)^2 + 5(m-3)^3. All the examples I've looked at on how to factor out the greatest common factor have not helped.
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given the polynomial
(1) 5%2A%28m-3%29+-+7%2A%28m-3%29%5E2+%2B+5%2A%28m-3%29%5E3
It has three terms, each has two factors: a constant and the binomial, (m-3). What factor do you think is the same in ALL three terms? Right, it is (m-3). Therefore the ONLY common factor is (m-3). Factoring out this common factor yields
(2) %28m-3%29%2A%285+-+7%2A%28m-3%29+%2B+5%2A%28m-3%29%5E2%29
That's it look no farther!