Answer to Question #243134 in Algebra for enKay

Question

C)

h(X)=ax^3-x^2-5x+b, where a and b are constants. For h(X) divide by (X+2) the remainder is 40 and for h(X) divided by (x-2) the remainder is 36. Find the value of a and b.

Answer 1

$h(-2)=40\to -8a-4+10+b=40\to 8a-b=-34.$

$h(2)=36\to 8a-4-10+b=36\to 8a+b=50.$

$a=\frac{50-34}{16}=1.$

$b=50-1*8=42.$