O-LevelAdditional MathematicsFactors of polynomials4037/22 · May/June 2021 · Q46 Marks
The polynomial p(x) = mx³-29x2+39x+n, where m and n are constants, has a factor 3x-1, and remainder 6 when divided by x-1. Show that x-2 is a factor of p(x).
- The polynomial p(x) = mx³-29x2+39x+n, where m and n are constants, has a factor 3x-1, and remainder 6 when divided by x-1. Show that x-2 is a factor of p(x).[6]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- B1 m/27 - 29/9 + 39/3 + n = 0 oe
- B1 m - 29 + 39 + n = 6 oe
- M1 Eliminates one unknown correctly for a pair of linear equations in m and n and solves for one unknown
- A2 A1 for either m = 6, n = -10
- A1 [p(2) =] 48 - 116 + 78 – 10 = 0 oe, nfww
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