The equation of a polynomial is given by $p(x) = x^3 - 7x^2 + 18x - 24$. Show that $x - 4$ is a

Question

The equation of a polynomial is given by $p(x) = x^3 - 7x^2 + 18x - 24$. Show that $x - 4$ is a factor of $p(x)$.[2] Find the remainder when $p(x)$ is divided by $2x - 1$.[2] Show that $p(x) = 0$ only has one real root.[4] Using the answers from (a) and (c), solve $2^{3y} - 7(2^{2y}) + 18(2^y) = 24$.[2]

Accepted Answer

(a) $x-4$ is a factor (b) $-\dfrac{133}{8}$ (c) only real root $x=4$ (d) $y=2$

2023 CSS AM S3 EOY Q6

2023 CSS AM S3 EOY Q6

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