Hi, I'm working through an exam pretest and I came across this problem. Looking through my notes, I can't find examples that show me how to do it. I'm not totally sure what it's asking.
a) Use the Remainder Theorem to find the remainder when x^3-2x^2+8x-16 is divided by x-2.
For this I did P(2) = (2)^3 -2(2)^2+8(2)-16
I got P(2) = 0 but was I supposed to plug in -2?
This is the part I'm stuck on:
b) Use your answer in part a to factor x^3-2x^2+8x-16 into linear factors allowing complex numbers. Clearly explain your reasoning.
Thanks in advance for any help I can get on this.
No, the remainder when a polynomial, p(x), is divided by x- a is p(a) so 2 is correct.
And, in fact, if you checked "the hard way" by actually dividing, you would see that x- 2 divides into exactly " " times, leaving a remainder of 8x- 16= 8(x- 2) and x- 2 obviously divides evenly into that. I don't know why you are questioning you answer.
You know that x- 2 is one factor. What is the quotient when you divide x^3- 2x^2+ 8x- 16 by x- 2? (Of course, I have given you the answer above.)This is the part I'm stuck on:
b) Use your answer in part a to factor x^3-2x^2+8x-16 into linear factors allowing complex numbers. Clearly explain your reasoning.
The quotient will be quadratic which you can factor once you know the zeros, if necessary by using the quadratic formula.
Thanks in advance for any help I can get on this.