SOLUTION: Please show me how to do this. Thank you in advance for your help. Factor completely: x3 – 26x2 + 48x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please show me how to do this. Thank you in advance for your help. Factor completely: x3 – 26x2 + 48x       Log On


   

Question 110815: Please show me how to do this. Thank you in advance for your help.
Factor completely:
x3 – 26x2 + 48x
Found 2 solutions by MathLover1, Earlsdon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3–26%2Ax%5E2+ 48%2Ax……….factor out common factor x
= x%28+x%5E2+-+26x+%2B+48%29………now replace -+26x with the two numbers that multiply to 48 and add to -26, which are: -2 and -24)

= x%28+x%5E2+-+2x+-+24x+%2B+48%29………inside parentheses group the first two terms together and the last two terms together like this: %28+x%5E2+-+2x%29+%2B+%28-+24x+%2B+48%29
Then we will have:
= x%28%28+x%5E2+-+2x%29+%2B+%28-+24x+%2B+48%29%29……… Factor a 1x out of the first group and factor a -24 out of the second group.
= x%281x%28+x+-+2%29+-+24%28x+-+2%29%29……… now since we have a common term x+%96+2 we can combine the two terms
= x%28+x+-+2%29+%28x+-+24%29………
So the quadratic x%5E3 – 26%2Ax%5E2 ++48%2Ax factors to x%28+x+-+2%29+%28x+-+24%29

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
x%5E3-26x%5E2%2B48x First, factor an x.
x%28x%5E2-26x%2B48%29 Now factor the trinomial x%5E2-26x%2B48.
You know that the factors will be of the form: %28x%2Bm%29%28x%2Bn%29 where: m%2An+=+48 and m%2Bn+=+-26, so what are the possibilities?
If m = -2 and n = -24, then m%2An+=+48 and m%2Bn+=+-26, so the factors of the trinomial are: %28x-2%29%28x-24%29, and the factors of the original expression are:
x%5E3-26x%5E2%2B48x+=+x%28x-2%29%28x-24%29