Free Printable PARTIAL FRACTION REPEATED LINEAR FACTORS

1.

The general form of partial fraction for the algebraic fraction shown is:

a)

b)

c)

d)

2.

The type of divisor factor of the following fraction is__________.

a)

Linear Factors

b)

Linear and Repeated Linear Factors

c)

Quadratic and Linear Factors

d)

Quadratic and Repeated Linear Factors

3.

The image shows an algebraic fraction with its general form of partial fraction.

The general form of partial fraction shown is:

a)

CORRECT

b)

INCORRECT

4.

Which one should be used in the partial fraction decomposition of $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$

a)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$

b)

$\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$

c)

$\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$

d)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$

5.

What is the type of denominator factor for the following fraction?

a)

Linear Factors

b)

Repeated Linear Factors

c)

Quadratic Factors

d)

Cubic Factors

6.

Find the partial fraction decomposition for

\frac{6x}{x^2-9}

a)

$\frac{3}{x+3}+\frac{3}{x-3}$

b)

$\frac{3}{x+3}-\frac{3}{x+3}$

c)

$\frac{3}{x-3}+\frac{3}{x-3}$

d)

$-\frac{3}{x-3}-\frac{3}{x+3}$

7.

State the type of partial fraction above

a)

linear factor

b)

repeated factor

c)

quadratic factor

d)

improper fraction

8.

a)

b)

c)

9.

a)

b)

10.

Which one should be used in the partial fraction decomposition of $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$

a)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$

b)

$\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$

c)

$\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$

d)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$

11.

What would you multiply to "B" when creating the new numerator?

a)

b)

c)

d)

12.

Given $\frac{x-2}{\left(x-3\right)\left(2x+1\right)}=\frac{A}{x-3}+\frac{B}{2x+1}$ . Find A and B.

a)

$\frac{1}{7}\ and\ \frac{5}{7}$

b)

$-\frac{1}{7}\ and\ -\frac{5}{7}$

c)

$-\frac{1}{7}\ and\ \frac{5}{7}$

d)

$\frac{1}{7}\ and\ -\frac{5}{7}$

13.

Which one should be used in the partial fraction decomposition of $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$

a)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$

b)

$\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$

c)

$\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$

d)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$

14.

State the type of partial fraction for

\frac{x^2}{x\left(x-3\right)^2}

a)

Linear Factor Method

b)

Repeated Linear Factor Method

c)

Quadratic Factor Method

d)

Log Division Factor Method

15.

The type of divisor factor of the following fraction is__________.

a)

Linear Factors

b)

Linear and Repeated Linear Factors

c)

Quadratic and Linear Factors

d)

Quadratic and Repeated Linear Factors

16.

The general form of partial fraction for the algebraic fraction shown is:

a)

b)

c)

d)

17.

The image shows an algebraic fraction with its general form of partial fraction.

The general form of partial fraction shown is:

a)

CORRECT

b)

INCORRECT

18.

Set up the partial fractions for

\frac{3x}{\left(x+3\right)^2}

a)

$\frac{Ax}{\left(x+3\right)}+\frac{Bx}{\left(x+3\right)^2}$

b)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}$

c)

$\frac{Ax}{\left(x-3\right)}+\frac{Bx}{\left(x+3\right)}$

d)

$\frac{A}{\left(x-3\right)}+\frac{B}{\left(x+3\right)}$

19.

Set up the partial fractions for

\frac{5x+3}{x\left(x+4\right)^2}

a)

$\frac{Ax}{x}+\frac{Bx}{\left(x+4\right)}+\frac{Cx}{\left(x+4\right)^2}$

b)

$\frac{A}{x}+\frac{B}{\left(x+4\right)}+\frac{C}{\left(x+4\right)^2}$

c)

$\frac{Ax}{x}+\frac{Bx}{\left(x+4\right)}$

d)

$\frac{A}{x}+\frac{B}{\left(x+4\right)^2}$

20.

Which one should be used in the partial fraction decomposition of $\frac{x-11}{\left(x+3\right)^2\left(x-4\right)}?$

a)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)}+\frac{C}{\left(x-4\right)}$

b)

$\frac{A}{\left(x-4\right)}+\frac{Bx+C}{\left(x+3\right)^2}$

c)

$\frac{A}{\left(x+3\right)^2}+\frac{B}{\left(x-4\right)}$

d)

$\frac{A}{\left(x+3\right)}+\frac{B}{\left(x+3\right)^2}+\frac{C}{\left(x-4\right)}$

21.

State the type of partial fraction above

a)

linear factor

b)

repeated factor

c)

quadratic factor

d)

improper fraction

22.

a)

b)

c)

23.

a)

b)

24.

$\frac{2x+1}{\left(x+4\right)^2}$

a)

$\frac{2}{\left(x+4\right)}+\frac{7}{\left(x+4\right)^2}$

b)

$\frac{2}{x+4}-\frac{7}{\left(x+4\right)^2}$

c)

$\frac{-2}{x+4}+\frac{7}{\left(x+4\right)^2}$

25.

Resuelve la Siguiente fraccion parcial.

a)

b)

c)

26.

Resuelve la siguiente fraccion parcial.

a)

b)

c)

27.

$\frac{2x+1}{\left(x+4\right)^2}$

a)

$\frac{2}{\left(x+4\right)}+\frac{7}{\left(x+4\right)^2}$

b)

$\frac{2}{x+4}-\frac{7}{\left(x+4\right)^2}$

c)

$\frac{-2}{x+4}+\frac{7}{\left(x+4\right)^2}$

PARTIAL FRACTION REPEATED LINEAR FACTORS

Total questions: 27

Worksheet time: 16mins

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