Exercises for Question Type 2: Applying partial fractions on linear factors on higher powers

Question 1

Skill question

Decompose $\frac{x ^{3} + 3 x ^{2} + x + 2}{( x + 1 ) ^{3}}$ into partial fractions.

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Question 2

Skill question

Decompose $\frac{x ^{2} + 4}{( x + 1 ) ^{3}}$ into partial fractions.

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Question 3

Skill question

Find the partial fraction decomposition of $\frac{5 x + 7}{( x - 2 ) ( x - 4 ) ^{2}}$ .

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Question 4

Skill question

Decompose $\frac{4 x + 1}{( x - 2 ) ^{4}}$ into partial fractions.

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Question 5

Skill question

Perform partial fraction decomposition for $\frac{2 x ^{2} + 3}{( x - 1 ) ^{2} ( x + 3 ) ^{2}}$ .

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Question 6

Skill question

Decompose $\frac{3 x ^{2} + 2 x + 1}{( x - 2 ) ( x + 2 ) ( x - 3 ) ^{2}}$ into partial fractions.

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Question 7

Skill question

Find the partial fraction decomposition of $\frac{2 x ^{4} - x ^{2} + 3}{( x - 3 ) ( x + 1 ) ^{2}}$ .

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Question 8

Skill question

Express $\frac{5 x + 4}{( x - 5 ) ^{3} ( x + 1 ) ^{2}}$ as partial fractions.

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Question 9

Skill question

Long Answer

Find the partial fractions of $\frac{x ^{3} + 2 x ^{2} - x + 5}{( x - 1 ) ( x - 2 ) ^{2}}$ .

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Question 10

Skill question

Express $\frac{x ^{2} + 2 x + 3}{x ( x + 1 ) ( x + 3 )}$ in partial fractions.

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IB Mathematics Analysis and Approaches Question Type 2: Applying Partial Fractions on Linear Factors on Higher Powers Exercises