Given that x + 1 is a factor of 3x3 - 14x2 – 7x + d, show that d = 10.

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

1. [B1] 3(-1)³-14(-1)²-7(-1)+ d = 0 with completion to d = 10 at least -3-14 + 7 + d = 0, d = 10; N.B. = 0 must be seen or implied by ... = d or ... = −d, may be seen in following step. or convincingly showing 3(-1)³-14(-1)²-7(-1)+10 = 0 ; at least -3-14+7+10=0 or correct synthetic division at least as far as -1 | 3 -14 -7 10 | -3 17 -10 | 3 -17 10 0
2. [B2, 1, 0] 3x²-17x+10 isw or a = 3, b = −17, c = 10 isw -1 each error; must be seen or referenced in (ii) even if found in (i) or (iii)
3. [M1] for factorising quadratic ft correct; condone omission of (x+1) or for ft correct use of formula or ft correct completing the square
4. [A1] -1, 5, 2/3 If M0 then SC1 for all three roots stated without working or verified/found by trials