SOLUTION: Using synthetic division, how do I determine whether the first expression is a factor of the second? If it is, how do I indicate factorization? x-2, 4x^3-3x^2-8x+4

Algebra ->  Rational-functions -> SOLUTION: Using synthetic division, how do I determine whether the first expression is a factor of the second? If it is, how do I indicate factorization? x-2, 4x^3-3x^2-8x+4      Log On


   

Question 1136876: Using synthetic division, how do I determine whether the first expression is a factor of the second? If it is, how do I indicate factorization?
x-2, 4x^3-3x^2-8x+4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

p%28x%29=+4x%5E3-3x%5E2-8x%2B4 divide by x-2
The synthetic division table is:

Step 1 : Write down the coefficients of the polynomial p%28x%29. Put the zero from x-2=0=>+x=2 at the left.

2 | 4.....-3.....-8.....4
Step 2 : Bring down the leading coefficient to the bottom row.
2 | 4.....-3.....-8.....4
_______________________________________________________
.......... 4....

Step 4 : Add down the column: -3%2B8=5
2 | 4.....-3.....-8.....4
......................8
______________________________________________________
.......... 4....5

Step 5 : Multiply by the number on the left, and carry the result into the next column: 2%2A5=10

2 | 4.....-3.....-8.....4
......................8......10
______________________________________________________
.......... 4....5

Step 6 : Add down the column: -8%2B10=2

2 | 4.....-3.....-8.....4
......................8......10
______________________________________________________
.......... 4....5.......2

Step 7 : Multiply by the number on the left, and carry the result into the next column: 2%2A2=4

2 | 4.....-3.....-8.....4
......................8......10.....4
______________________________________________________
.......... 4....5.......2

Step 8 : Add down the column: 4%2B4=8

2 | 4.....-3.....-8.....4
......................8......10.....4
______________________________________________________
.......... 4....5.......2.....8

Bottom line represents the polynomial quotient 4x%5E2%2B5x%2B2 with a remainder of 8.

So we have: %284x%5E3-3x%5E2-8x%2B4%29%2F%28x-2%29=4x%5E2%2B5x%2B2%2B8%2F%28x-2%29