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Algebraic Methods

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Question 30

The cubic polynomial 6x3+kx2+25x−126x^3 + kx^2 + 25x - 126x3+kx2+25x−12 is denoted by f(x)f(x)f(x). It is given that (2x+3)(2x + 3)(2x+3) is a factor of f(x)f(x)f(x).

a.

Use the factor theorem to show that k=31k = 31k=31.

[2]
b.

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

[3]

Algebraic Methods Questions

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