for what value of b will be polynomial p(x) = -2x^3 + bx^2 - 5x + 2 have the same remainder when it is divided by x- 2 and by x+1 ?

Divide it by x-2 and get:



Divide by x+1:



Can you finish?

Look at the remainder terms. Equate the numerators in the remainder terms and solve for b.

noo. Don't you have to sub 1 into 2 to get the other value.

No.

If you use the remainder theorem, then you apply it. It says that for a given polynomial f(x), the remainder, when f(x) is divided by (x - a), is given by f(a).

Hence;



Substituting 2;



Substituting -1;



If both remainder are equal, then:



Solve for b.