Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x) where a(x) b(x) q(x) and r(x) are polynomials with the degree of r(x) less than the degree of b(x).

Sample Practice Questions (3)

Look at the coefficients of the polynomial

6 x^{2} - 5 x + 2

and the divisor

3 x - 1

shown in the matrix below. Which expression represents the result of this division?

2 x - 1 + \frac{1}{3 x - 1}

2 x - 1

2 x + 1 + \frac{3}{3 x - 1}

2 x - 1 + \frac{3}{3 x - 1}

A rectangle has an area of

x^{2} + 8 x + 15

square units and a width of

x + 2

units. Express the length of the rectangle in the form

q (x) + \frac{r}{x + 2}

Rewrite the expression

\frac{2 x ^{2} + 7 x + 5}{x + 2}

in the form

q (x) + \frac{r}{x + 2}

, where

q (x)

is a polynomial and

r

is a constant.

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