A-LevelMathematicsAlgebra9709/32 · May/June 2022 · Q35 Marks
The polynomial ax³ + x² + bx + 3 is denoted by p(x). It is given that p(x) is divisible by (2x – 1) and that when p(x) is divided by (x + 2) the remainder is 5. Find the values of a and b.
- (a)The polynomial ax³ + x² + bx + 3 is denoted by p(x). It is given that p(x) is divisible by (2x – 1) and that when p(x) is divided by (x + 2) the remainder is 5. Find the values of a and b.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- M1 Substitute x = ½, equate result to zero Or divide by 2x-1 and equate constant remainder to zero.
- A1 Obtain a correct simplified equation e.g. (1/8)a + (1/4) + (1/2)b + 3 = 0 or a + 4b = -26
- M1 Substitute x = -2, equate result to 5 Or divide by x+2 and equate constant remainder to 5.
- A1 Obtain a correct simplified equation e.g. -8a+4-2b+3=5 or 8a + 2b = 2
- A1 Obtain a = 2 and b = -7 WWW
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