Easy -1.8 This is a straightforward application of the factor theorem requiring only substitution of x=2 into the polynomial and verification that it equals zero. It's a single-step 'show that' question with no problem-solving or algebraic manipulation needed, making it significantly easier than average A-level questions.
Function notation need not be used; zero must be seen
Therefore by the factor theorem \((x-2)\) is a factor
E1 [3]
Reason required
OR method:
Answer
Marks
Guidance
Answer
Marks
Guidance
\(f(x) = (x-2)(3x^2-2x-1)\)
M1, A1
Using algebraic division as far as \(3x^2\); correct quotient
No remainder so \((x-2)\) is a factor
E1 [3]
Reason required
## Question 1:
**EITHER method:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $f(2) = 3\times2^3 - 8\times2^2 + 3\times2 + 2 = 24-32+6+2=0$ | M1, A1 | Function notation need not be used; zero must be seen |
| Therefore by the factor theorem $(x-2)$ is a factor | E1 [3] | Reason required |
**OR method:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $f(x) = (x-2)(3x^2-2x-1)$ | M1, A1 | Using algebraic division as far as $3x^2$; correct quotient |
| No remainder so $(x-2)$ is a factor | E1 [3] | Reason required |
---