SOLUTION: The polynomial R(x) = x^4 + Ax^3 + Bx^2 + 10x - 1 has a remainder of -15 when divided by x+1 and a remainder of 39 when divided by x-2. Determine A & B.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial R(x) = x^4 + Ax^3 + Bx^2 + 10x - 1 has a remainder of -15 when divided by x+1 and a remainder of 39 when divided by x-2. Determine A & B.      Log On


   

Question 941465: The polynomial R(x) = x^4 + Ax^3 + Bx^2 + 10x - 1 has a remainder of -15 when divided by x+1 and a remainder of 39 when divided by x-2. Determine A & B.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description means that two of the points for R(x) are (-1,-15) and (2,39). Check in your textbook about the Remainder Theorem and the Factor Theorem.

Turn the form of the equations around this way, and form the system using the two points.

x%5E4%2BAx%5E3%2BBx%5E2%2B10x-1=R




system%281-A%2BB-10-1=-15%2C16%2B8A%2B4B%2B20-1=39%29

system%28A%2BB=-5%2C8A%2B4B=4%29

highlight_green%28system%28A%2BB=-5%2C2A%2BB=1%29%29

Simple system to solve.
R2-R1 gives highlight%28A=6%29, from this, highlight%28B=-11%29.