f(x) = 2x^3 - 5x^2 + ax + a
Given that (x + 2) is a factor of f(x), find the value of the constant a. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 2
Question 3
f(x) = 2x^3 - 5x^2 + ax + a
Given that (x + 2) is a factor of f(x), find the value of the constant a.
Worked Solution & Example Answer:f(x) = 2x^3 - 5x^2 + ax + a
Given that (x + 2) is a factor of f(x), find the value of the constant a. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 2
Step 1
Set f(-2) = 0
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Answer
Since (x + 2) is a factor of f(x), substituting x = -2 into f(x) should yield zero:
f(−2)=2(−2)3−5(−2)2+a(−2)+a=0
Calculating each term gives us:
2(−2)3=2(−8)=−16
−5(−2)2=−5(4)=−20
a(−2)=−2a
a
Putting it all together:
−16−20−2a+a=0
This simplifies to:
−36−a=0
Step 2
Solve the linear equation
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Answer
Rearranging the equation, we have:
−a=36⇒a=−36
Step 3
Final answer
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