Polynomial Function Question

Question

When the polynomial P(x) = ax3 + bx2 + 3x − 2 is divided by x + 1, the remainder is -3. When

P(x) is divided by x − 2, the remainder is 3. What are the values of a and b?

Answer 1

a = -3/4 = -0.75

b = 5/4 = 1.25

just do long division to get for the x+1 divisor a remainder of -5+b-a =-3

which gives -a+b = 2 or -4a+4b=8

for the x-2 divisor, the remainder is 4+8a+4b = 3 or 8a+4b =-1

take those two equations and subtract

8a+4b=-1

-4a+4b=8

12a =-9

a=-9/12 =-3/4

b=2+a = 2-3/4 = 5/4