13. (a) (i) Show that $(x + 2)$ is a factor of $f(x) = x^3 - 2x^2 - 20x - 24$ - Scottish Highers Maths - Question 13 - 2022
Question 13
13.
(a) (i) Show that $(x + 2)$ is a factor of $f(x) = x^3 - 2x^2 - 20x - 24$.
(ii) Hence, or otherwise, solve $f(x) = 0$.
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Worked Solution & Example Answer:13. (a) (i) Show that $(x + 2)$ is a factor of $f(x) = x^3 - 2x^2 - 20x - 24$ - Scottish Highers Maths - Question 13 - 2022
Step 1
(i) Show that $(x + 2)$ is a factor of $f(x) = x^3 - 2x^2 - 20x - 24$.
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Step 2
(ii) Hence, or otherwise, solve $f(x) = 0$.
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Step 3
State the value of $k$.
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Answer
Since the graph of y=f(x−k) has a stationary point at (1,0), we will find k. Given that f(1)=0, we need to find k such that:
1−k=−2
This leads to:
k=3.
Thus, the value of k is 3.
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