## Exam-Style Question on Functions## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 390. This question is similar to one that appeared on an A-Level paper. The use of a calculator is allowed.

The function \(f\) is defined as \(f(x) = 12x^3 - 5x^2 -11x + 6 \).

(a) Use the Factor Theorem to show that \( (4x-3) \) is a factor of \(f(x)\)

(b) Express \(f(x)\) as a product of linear factors.

(d) Hence solve the equation \( g(\theta ) = 0 \), giving your answers, in radians, in the interval \(0 \le \theta \le 2 \pi \).

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