SOLUTION: One factor of x3 + x2 + x - 3 is x - 1.What is the other factor? A. x2 + 2x - 3 B. x2 + 2x + 3 C. x3 + 2x + 3 D. x2 - 2x + 3 1. Multiply x - 1 by choices B and D in Example 1 to

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: One factor of x3 + x2 + x - 3 is x - 1.What is the other factor? A. x2 + 2x - 3 B. x2 + 2x + 3 C. x3 + 2x + 3 D. x2 - 2x + 3 1. Multiply x - 1 by choices B and D in Example 1 to       Log On


   

Question 228806: One factor of x3 + x2 + x - 3 is x - 1.What is the other factor?
A. x2 + 2x - 3 B. x2 + 2x + 3 C. x3 + 2x + 3 D. x2 - 2x + 3
1. Multiply x - 1 by choices B and D in Example 1 to find the correct answer.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If x-1 is a factor of x%5E3%2Bx%5E2%2Bx-3 then x-1 will divide into x%5E3%2Bx%5E2%2Bx-3 evenly. (Think about it.) If (x-1)*(the-other-factor) = x%5E3%2Bx%5E2%2Bx-3 then (the-other-factor) = %28x%5E3%2Bx%5E2%2Bx-3%29%2F%28x-1%29. So all we need to do to figure out the other factor is divide. Synthetic division is probably easiest:
1 |   1  1  1  -3
---      1  2   3
     ------------
      1  2  3   0

As we can see, the remainder is zero. (x-1) does actually divide into x%5E3%2Bx%5E2%2Bx-3 evenly. And the other factor is found in front of the zero: "1 2 3" or 1x%5E2+%2B+2x+%2B+3+=+x%5E2+%2B+2x+%2B+3

You can check by multiplying %28x-1%29%28x%5E2%2B2x%2B3%29 and see if you get x%5E3%2Bx%5E2%2Bx-3