SOLUTION: 3. Use the remainder theorem to find the remainder when f(x) is divided by x-2 . Then use the factor theorem to determine whether x-2 is a factor of f(x). Please show all of y

Algebra ->  Rational-functions -> SOLUTION: 3. Use the remainder theorem to find the remainder when f(x) is divided by x-2 . Then use the factor theorem to determine whether x-2 is a factor of f(x). Please show all of y      Log On


   

Question 468490: 3. Use the remainder theorem to find the remainder when f(x) is divided by x-2 . Then use the factor theorem to determine whether x-2 is a factor of f(x). Please show all of your work.
f(x)=2x^6-4x^5+2x²+7x-6
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3. Use the remainder theorem to find the remainder when f(x) is divided by x-2 . Then use the factor theorem to determine whether x-2 is a factor of f(x). Please show all of your work.
f(x)=2x^6-4x^5+2x²+7x-6
...
using synthetic division to find remainder when f(x) is divided by x-2.
0).....2.....-4.....0.....0.....2.....7.....-6
2).....2......0......0.....0.....2....11....16
f(x)=(2x^5+2x+11)+Remainder=16
..
Using Factor Theorem:
f(2)=128-128+8+14-6=16
..
ans:
x-2 is a factor of f(x)