SOLUTION: Factor completely using integer coefficients: e) x^4+8x^3-2x^2-16x f) 2x^6-20x^4-16x^3+160x j) x^4-x^3-x+1

Question 99741: Factor completely using integer coefficients:
e) x^4+8x^3-2x^2-16x
f) 2x^6-20x^4-16x^3+160x
j) x^4-x^3-x+1
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Factor completely using integer coefficients:
e) First, factor an x.
Now factor the parentheses. I know that my factors here will be two binomials of the form:
where and and , so m = -2 and n = 8. So the parentheses, when factored, look like:
, then the final answer is:

f) First, factor 2x.
Now factor the parentheses. I know my factors here will be two binomials of the form: where: and so and , so the parentheses, when factored, look like:
, so far we have:
but notice that is the difference of two cubes and this can be factored.
The difference of two cubes is factored thus:
so, in this case:
putting it all together, we have:

j) Factor as:
But again, we have the difference of two cubes:, so...
or:

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