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1 Pure Mathematics

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Question 226

The cubic polynomial 6x3+kx2−19x+46x^3 + kx^2 - 19x + 46x3+kx2−19x+4 is denoted by f(x)f(x)f(x), where k k\,k is a constant.

It is given that (2x−1)(2x - 1)(2x−1) is a factor of f(x)f(x)f(x).

a.

Use the factor theorem to show that k=19k = 19k=19.

[2]
b.

Using this value of kkk, factorise f(x)f(x)f(x) completely.

[3]
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1 Pure Mathematics Questions

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