Question

What is the remainder when x3 - 1 is divided
by (x + 2)?

Answer 1

Given:

The polynomial $x^3-1$ is divided by (x+2).

To find:

The remainder.

Solution:

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

Consider the polynomial:

$p(x)=x^3-1$

It is divided by (x+2). So, by the remainder theorem the remainder is p(-2).

Substituting x=-2 in the above polynomial, we get

$p(-2)=(-2)^3-1$

$p(-2)=-8-1$

$p(-2)=-9$

Therefore, the remainder is -9.

Answer 2

The remainder when x³ - 1 is divided  by (x + 2) is -9

Polynomial is an expression consisting of only the operations of addition, subtraction, multiplication of variables.

The remainder theorem states that when a polynomial f(x), is divided by a linear polynomial x - a, the remainder of that division will be equivalent to f(a).

Given the polynomial f(x) = x³ - 1.

The linear equation is x + 2, hence; x = -2

f(-2) = (-2)³ - 1 = -8 - 1 = -9

The remainder when x³ - 1 is divided  by (x + 2) is -9

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