Unit 1Topic 1.11Question BankHL

Mathematics: Analysis and Approaches · Unit 1: Number and Algebra

Partial fractions

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10

Questions

72

Total marks

Question 1 of 105 marks

Partial fractions

[Maximum mark: 5]Consider the rational expression $F(x)=\dfrac{2x^3-x+1}{(x^2+2)^2}$ .(a) State whether this expression is proper or improper, giving a reason.[1](b) Explain why $x^2+2$ is irreducible over the real numbers.[1](c) Write the general partial-fraction form for $F(x)$ , using unknown real constants. Explain your choice of numerators and denominators. You do not need to find the constants.[3]