Given that $(x - 1)$ is a factor of $f(x)$, find the value of the constant $a$ - Edexcel - A-Level Maths Pure - Question 3 - 2021 - Paper 1
Question 3
Given that $(x - 1)$ is a factor of $f(x)$, find the value of the constant $a$. You must make your method clear.
Worked Solution & Example Answer:Given that $(x - 1)$ is a factor of $f(x)$, find the value of the constant $a$ - Edexcel - A-Level Maths Pure - Question 3 - 2021 - Paper 1
Step 1
Set up the equation using the factor
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Since (x−1) is a factor of f(x), it implies that f(1)=0. We start by substituting x=1 into the function:
f(1)=a(1)3+10(1)2−3a(1)−4
Simplifying, we get:
f(1)=a+10−3a−4
This simplifies to:
f(1)=−2a+6
Step 2
Solve the equation for constant a
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Since we know that f(1)=0, we can set up the equation:
