SOLUTION: Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor theorem to determine whether x+3 is a factor of f(x). f(x)=3x^6-27x^4+x^3-5 a

Algebra ->  Linear-equations -> SOLUTION: Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor theorem to determine whether x+3 is a factor of f(x). f(x)=3x^6-27x^4+x^3-5 a      Log On


   

Question 835699: Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor theorem to determine whether x+3 is a factor of f(x).
f(x)=3x^6-27x^4+x^3-5
a. what is the remainder
b. Is x+3 a factor of f(x)=3x^6-27^4+x^3-5
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use synthetic division. If a nonzero remainder, this means f%28-3%29=theNonZeroRemainder. If remainder is zero, then x+3 is a factor of f(x).


Checking -3 as possible zero.

-3____|_____3____0_____-27____1_____0_____0_____-5
______|
______|__________-9____27_____0____-3_____9_____-27
___________3____-9______0_____1____-3_____9_____highlight%28highlight%28-32%29%29


The remainder is -32, so this means, x+3 is NOT a factor of f, but that highlight%28f%28-3%29=-32%29.