



 
Asterdine, Since (x + 2)(x + 1) is a quadratic polynomial the remainder after dividing f(x) by (x + 2)(x + 1) must be a linear polynomial which means that there is a polynomial g(x) and numbers a and b so that
Since division of f(x) my (x + 1) leaves a remainder of 3 the remainder theorem says that
Substitute x = 1 into f(x) = g(x) (x + 2)(x + 1) + ax + b and this will give you a linear equation in the variables a and b. Use the fact that division of f(x) my (x + 2) leaves a remainder of 7 to find a second linear equation in a and b. Solve for a and b. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 