SOLUTION: If f(x)=ax^4 +bx^3 -x^2 +2x +3 has a remainder 11 when divided by x-2and has a remainder 2 when divided by ( x+1 ).Find the values of a and b.

Algebra ->  Equations -> SOLUTION: If f(x)=ax^4 +bx^3 -x^2 +2x +3 has a remainder 11 when divided by x-2and has a remainder 2 when divided by ( x+1 ).Find the values of a and b.      Log On


   

Question 1058071: If f(x)=ax^4 +bx^3 -x^2 +2x +3 has a remainder 11 when divided by x-2and has a remainder 2 when divided by ( x+1 ).Find the values of a and b.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Perform the synthetic division for each binomial factor (or divisor) separately, that work not shown here, and obtain the remainders for each of them, and then equate each to the described values.

x-2 will give you 8a%2B4b-2=11
and
x+1 will give you -a%2Bb%2B4=2.

Be sure you handle the synthetic division and can find the left-side expressions of each of those; and see that I showed them equated to their given values.

Simplify each of those equations to form the system
system%288a%2B4b=13%2C-a%2Bb=-2%29;
and now just solve this system for a and b.

You could use regular polynomial division but it will be a little messy. Synthetic division will be much neater. Final answer system%28a=21%2F12=7%2F4%2Cb=-1%2F4%29.