O-LevelAdditional MathematicsFactors of polynomials4037/12 · Oct/Nov 2020 · Q108 Marks
The polynomial p(x) = 6x³ +ax²+bx+2, where a and b are integers, has a factor of x-2.
- (a)Given that p(1)=-2p(0), find the value of a and of b.[4]
- (b)(i)Using your values of a and b, find the remainder when p(x) is divided by 2x-1,[2]
- (b)(ii)factorise p(x).[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- B1 For 2a + b + 25 = 0 or multiple
- B1 For a+b+12=0
- M1 for attempt to solve their equations in a and b leading to 2 values
- A1 for both a=-13, b=1
- M1 For attempt to find p(1/2) using their a and b
- A1 for 0
- M1 for realising that 2 factors are known and 3rd factor can be got by observation or algebraic long division, or for making use of x-2 or 2x-1 in order to obtain a quadratic factor
- A1 Must see all factors together (x-2)(2x-1)(3x+1)
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