# Factor and Remainder Theorem

Please help me with this exam style question from the IGCSE 2020 Specimen Paper. The polynomial $$p(x)=2x^3 -3x^2 +qx+56$$ has $$x-2$$ as a factor. Show that $$q=-30$$.

• Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor – GK A Nov 16 '18 at 13:46
• I think $q = \color{blue}{-}30$. Just set $p(2) = 0$. – trancelocation Nov 16 '18 at 13:49

If $$x-2$$ is a factor, then $$p(2)= 2\cdot 2^3 -3 \cdot 2^2 + q\cdot 2 + 56 = 0$$. $$\Rightarrow 2q = -60$$
You want $$P(2)=0$$
What is $$P(2)$$ when $$p(x)=2x^3 -3x^2 +qx+56$$?
Let $$x=2$$ and solve for $$q$$