O-LevelAdditional MathematicsFactors of polynomials4037/11 · May/June 2015 · Q68 Marks
The polynomial f(x) = ax³ – 15x² + bx – 2 has a factor of 2x – 1 and a remainder of 5 when divided by x – 1.
- (i)Show that b = 8 and find the value of a.[4]
- (ii)Using the values of a and b from part (i), express f(x) in the form (2x – 1) g(x), where g(x) is a quadratic factor to be found.[2]
- (iii)Show that the equation f(x) = 0 has only one real root.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [M1] correct use of either f(1/2) or f(1)
- [A1] paired correctly both equations correct (allow unsimplified)
- [M1,A1] M1 for solution of equations Al for both a and b. AG for b.
- [M1,A1] M1 for valid attempt to obtain g(x), by either observation or by algebraic long division.
- [M1] use of b² - 4ac
- [A1] correct conclusion; must be from a correct g(x) or 2g(x) www
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