Edexcel A-Level Mathematics AS P2.2.1 Simple Algebraic Division Questions

M1: Attempts to divide f(x) by ( x-2 ) and achieves a 3TQ quotient of the form $4 x^{2}+b x+c \quad b \neq 0, c \neq 0$ AND a remainder that is a constant. See equivalent form using synthetic division

A1: Achieves a Quotient or $Q(x)=4 x^{2}+21 x+32$. It is implied if they write (i) $4 x^{2}+21 x+32$
It cannot just be awarded from the expression within the division sum

M1: Attempts to divide f(x) by ( x-2 ) and achieves a 3TQ quotient AND a remainder that is a constant.
Alternatively attempts to find the value of f(2). Allow f(2)=72 but if it is incorrect you must see some evidence for the award such as showing an intermediate line of $4 \times 2^{3}+13 \times 2^{2}-10 \times 2+8$
or else 32+52-20+8 (or equivalent) condoning slips. See equivalent form using synthetic division
A1: States that Remainder or R=72. It is implied if they write (ii) 72
It cannot just be awarded from sight of 72 within the division sum BUT if a candidate gets the division sum completely correct and does not state $Q(x)=4 x^{2}+21 x+32$ and R=72 (o.e.) they should be awarded SC 1,1,1,0
Alt (a) via an identity BUT other acceptable methods exist such as by inspection which is a less formal version of this.
Sets up a correct identity $\mathrm{f}(x)=4 x^{3}+13 x^{2}-10 x+8 \equiv(x-2)\left(A x^{2}+B x+C\right)+R$ AND then
M1: Compares terms and achieves A=4 and values for B and C
A1: States that Quotient, (i) or $Q(x)=4 x^{2}+21 x+32$
M1: Finds R via f(2) or solving $8=R \pm 2 C$ with their value for C.
A1: States that Remainder, (ii) or R=72