SOLUTION: I'm stuck on these two, could anyone help please? Factor the algebraic expressions completely: 6x^2 - 28x + 16 and x^4 + 2x^3 - 3x - 6 Thank you very much!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm stuck on these two, could anyone help please? Factor the algebraic expressions completely: 6x^2 - 28x + 16 and x^4 + 2x^3 - 3x - 6 Thank you very much!      Log On


   

Question 58340: I'm stuck on these two, could anyone help please?
Factor the algebraic expressions completely:
6x^2 - 28x + 16
and
x^4 + 2x^3 - 3x - 6
Thank you very much!
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the algebraic expressions completely:
There are other method you can use for the first polynomial. I am grouping or using the ac method or using the arch method it's got a lot of names.
6x%5E2-28x%2B16 First factor out the GCF, 2.
2%283x%5E2-14x%2B8%29 2 factors that multiply to give you ac=3*8=24, but add to give you b=-14 are -12 and -2 (-12*-2=24 and -2-12=-14) Replace the middle term with -12x-2x
2%283x%5E2-12x-2x%2B8%29 Group the first two and last two terms
2%28%283x%5E2-12x%29%2B%28-2x%2B8%29%29 Factor out the GCF in each parenthesis.
2%283x%28x-4%29-2%28x-4%29%29 Factor out the x-4
2%28x-4%29%283x-2%29
:
and
:
You have to facto by grouping.
x%5E4%2B2x%5E3-3x-6 Group the first two terms and the last two terms.
%28x%5E4%2B2x%5E3%29%2B%28-3x-6%29 Factor the GCF out of each.
x%5E3%28x%2B2%29-3%28x%2B2%29 Factor (x+2) out of each.
%28x%2B2%29%28x%5E3-3%29
:
Happy Calculating!!!