NECO 2023 · Paper 1 · Q24

Given that $P_1(x) = 6x^3 + 8x^2 - 4x + 4$ and $P_2(x) = 3x^2 - 5x + 1$ , find $P_1(x) - 2P_2(x)$ .

Worked solution (try it first)

Double every term of $P_2$ : $2P_2(x) = 6x^2 - 10x + 2$ .
Taking it away changes every sign: $P_1(x) - 2P_2(x) = 6x^3 + 8x^2 - 4x + 4 - 6x^2 + 10x - 2$ .
Collect like terms: $8x^2 - 6x^2 = 2x^2$ , $-4x + 10x = 6x$ and $4 - 2 = 2$ .
So $P_1(x) - 2P_2(x) = 6x^3 + 2x^2 + 6x + 2$ , option E.