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1 Unit 1: Pure Mathematics A

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Question 53

Let p(x)=12x3−8x2−3x+2p(x) = 12x^3 - 8x^2 - 3x + 2p(x)=12x3−8x2−3x+2.

a.

Prove that (2x−1)(2x - 1)(2x−1) is a factor of p(x)p(x)p(x).

[2]
b.

Factorise p(x)p(x)p(x) completely.

[3]
c.

Prove that there are no real solutions to the equation

12sec⁡2θ+2cos⁡θ3=83sec⁡θ+1 \frac{12 \sec^2 \theta + 2 \cos \theta}{3} = \frac{8}{3} \sec \theta + 1 312sec2θ+2cosθ​=38​secθ+1
[4]
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1 Unit 1: Pure Mathematics A Questions

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