Given that $(x + 3)$ is a factor of $f(x)$, find the value of the constant $a$ - Edexcel - A-Level Maths Pure - Question 3 - 2019 - Paper 2
Question 3
Given that $(x + 3)$ is a factor of $f(x)$, find the value of the constant $a$.
$f(x)=3x^3+2ax^2-4x+5a$
Worked Solution & Example Answer:Given that $(x + 3)$ is a factor of $f(x)$, find the value of the constant $a$ - Edexcel - A-Level Maths Pure - Question 3 - 2019 - Paper 2
Step 1
Step 1: Evaluate f(-3)
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Answer
Since (x+3) is a factor of f(x), f(−3) must equal 0.
Calculate:
f(−3)=3(−3)3+2a(−3)2−4(−3)+5a
Substituting the values:
f(−3)=3(−27)+2a(9)+12+5a
This simplifies to:
−81+18a+12+5a=0
Thus,
−69+23a=0
Step 2
Step 2: Solve for a
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Answer
Rearranging the equation from Step 1:
23a=69
Dividing both sides by 23:
a=3
