SOLUTION: How do I solve this following question: The remainders whe ax^4+bx cube - x - 7 is divided by (x-1) and (x+2) are 7 and -35 respectively. Find the values of a and b. ?

Question 389178: How do I solve this following question: The remainders whe ax^4+bx cube - x - 7 is divided by (x-1) and (x+2) are 7 and -35 respectively. Find the values of a and b. ?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
By the remainder theorem, f(1) = 7 and f(-2) = -35 are the remainders when the polynomial f(x) is divided by x-1 and x+2, respectively. From f(1) = 7 we get a + b = 15, while from f(-2) = -35 we get -8a + 4b = -30, or -4a + 2b = -15 in lowest terms.
We have the system
a + b= 15
-4a + 2b = -15
The solution to this system is a = b =15/2.
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