SOLUTION: The polynomial 3x^3+mx^2+nx-8 is divisible by 3x-2 where m and n are constants .If the quotient is x^2-3x+4 ,find the values of m and n.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial 3x^3+mx^2+nx-8 is divisible by 3x-2 where m and n are constants .If the quotient is x^2-3x+4 ,find the values of m and n.      Log On


   

Question 1200414: The polynomial 3x^3+mx^2+nx-8 is divisible by 3x-2 where m and n are constants .If the quotient is x^2-3x+4 ,find the values of m and n.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
If the polynomial division is performed and then simplified, the result can be shown as x%5E2%2B%28%28m%2B2%29%2F3%29x%2B%282m%2B3n-28%29%2F3 as the quotient.

If that is given to be equal to x%5E2-3x%2B4, then equate the corresponding terms.

system%28%28m%2B2%29%2F3=-3%2Cand%2C%282m%2B3n-28%29%2F3=4%29.
Solve this system for m and n.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


This one is simple, because there is no remainder. So 3x%5E3%2Bmx%5E2%2Bnx-8 is the product of 3x-2 and x%5E2-3x%2B4

%283x-2%29%28x%5E2-3x%2B4%29
3x%5E3-2x%5E2-9x%5E2%2B6x%2B12x-8
3x%5E3-11x%5E2%2B18x-8

ANSWERS: m = -11; n = 18