Question

What is the remainder when you divide 2x3 + 4x2 - x + 3 by x + 2?

Answer 1

The quotient is 2x^2 - 1 + (5/(x + 2))

The remainder is 5.

Answer 2

Answer:  The required remainder is 5.

Step-by-step explanation:  We are given to find the remainder when we divide the following cubic polynomial by (x+2) :

$f(x)=2x^3+4x^2-x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We have the following theorem :

Remainder theorem :  If a polynomial p(x) is divided by the factor (x-a), then the remainder is p(a).

So, for the given linear factor, we have

$x+2=0\\\\\Rightarrow x=-2.$

Substituting x = -2 in equation (i), we get

$f(-2)\\\\=2(-2)^3+4(-2)^2-(-2)+3\\\\=-16+16+2+3\\\\=5.$

Thus, the required remainder is 5.