SOLUTION: Let {{{ h(x)=4x^4+15x^3-10x+2 }}}. Express h(x) in the form h(x)= q(x)(x+3)+r where q(x) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the cor

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Let {{{ h(x)=4x^4+15x^3-10x+2 }}}. Express h(x) in the form h(x)= q(x)(x+3)+r where q(x) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the cor      Log On


   

Question 1155606: Let +h%28x%29=4x%5E4%2B15x%5E3-10x%2B2+. Express h(x) in the form h(x)= q(x)(x+3)+r where q(x) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the correct remainder.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The remainder upon doing the synthetic division is -49. 
-3    |    4    15    0    -10    2
      |
      |        -12   -9    27    -51
      ---------------------------------------
           4   3   -9     17    -49

The 'quotient' part is 4x%5E3%2B3x%5E2-9x%2B17.

The function in the form asked for is
h%28x%29=%284x%5E3%2B3x%5E2-9x%2B17%29%28x%2B3%29-49.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h%28x%29=4x%5E4%2B15x%5E3-10x%2B2+. Express h(x) in the form h(x)= q(x)(x+3)+r where q(x) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the correct remainder.
Using LONG DIVISION of POLYNOMIALS or SYNTHETIC DIVISION, we get: matrix%281%2C3%2C+q%28x%29%2C+%22=%22%2C+4x%5E4+%2B+3x%5E3++-++9x+%2B+17%29

We then get: .