Question

The polynomial 2x^3 +7x^2 + ax + b, where a and b are constants, is denoted by p(x). It is given that (x +1) is a factor of p(x), and that when p(x) is divided by (x +2) the remainder is 5. Find the values of a and b.

Answer 1

I need to know how I can solve questions like these

Answer 2

Inverse Operations

Answer 3

Can you give me some details or direct me somewhere please?

Answer 4

when it says that (x+1) is a factor of p(x) .... this means the remainder is 0 when p(x) is divided by x+1

The remainder theorem says that the remainder when dividing p(x) by (x-c) = p(c)

In other words for x+1 .... our c= -1 so remainder = p(-1)
Plug in x = -1 into polynomial and set equal to 0 since we know that remainder will be 0

Do same for x+2 ... c = -2, ----> p(-2) = 5

The result will leave with system of 2 equations of 2 variables a,b