A-LevelMathematicsAlgebra9709/22 · May/June 2021 · Q57 Marks
Find the quotient when x⁴ – 32x + 55 is divided by (x – 2)² and show that the remainder is 7.
- (a)Find the quotient when x⁴ – 32x + 55 is divided by (x – 2)² and show that the remainder is 7.[3]
- (b)Factorise x⁴ – 32x + 48.[2]
- (c)Hence solve the equation e⁻¹²ʸ – 32e⁻³ʸ + 48 = 0, giving your answer in an exact form.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Carry out division at least as far as x² + kx or equivalent ...
- [A1] Obtain quotient x² + 4x + 12
- [A1] Confirm remainder is 7
- [M1] Include (x-2)² as a factor
- [A1] Conclude (x-2)² (x² + 4x + 12)
- [M1] Apply logarithms and use power law for e⁻³ʸ = k where k > 0
- [A1] Obtain y = -(1/3)ln 2, -(1/3)ln (1/2)
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