SOLUTION: when the expression x^4+ax^3+5x^2+bx+6 is divided by(x-2), the remainder is 16. when it is divided by (x+1) the remainder is 10. what is the value of the constant a, i tried eli

Question 1066989: when the expression x^4+ax^3+5x^2+bx+6 is divided by(x-2), the remainder is 16. when it is divided by (x+1) the remainder is 10. what is the value of the constant a,
i tried elimination but still cant solve it anyway how to solve it? thanks
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
Use synthetic division to "check" the roots : 2, and -1.
You will have remainders which are expressions containing a and b.

Long careful process because of those variables, but then you equate one result to 16 and the other result to 10, and then solve for a and b.

This uses the Remainder Theorem.
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