Additional Mathematics 0606: FACTOR THEOREM Topical Past Paper Questions

Two of the graphs A, B, C and D have equations of the form $ y = (x - 1)(x - p)(x - q) $ where p and q are constants such that $ q \geqslant p $ and q > 1. Find the two correct graphs, giving the values of p and q for each. [2] A B C D Graph ..... $p = \ldots\ldots\ldots\ldots$ $…

It is given that $ p(x) = ax^{3} - 7x^{2} - bx + 9 $, where a and b are constants. x - 3 is a factor of p(x). When p(x) is divided by x+2 the remainder is -35. Find the values of a and b.

The polynomial p is such that $ p(x) = 5x^{3} + ax^{2} + 39x + b $, where a and b are constants. (a) Given that $ x+3 $ is a factor of both p(x) and $ p'(x) $, find the values of a and b. [5] (b) Hence solve the equation $ p(x)=0 $. You must show your working. (c) Hence, using yo…