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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 $q=-30$.

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  • $\begingroup$ 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 $\endgroup$ – GK A Nov 16 '18 at 13:46
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    $\begingroup$ I think $q = \color{blue}{-}30$. Just set $p(2) = 0$. $\endgroup$ – trancelocation Nov 16 '18 at 13:49
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If $x-2$ is a factor, then $p(2)= 2\cdot 2^3 -3 \cdot 2^2 + q\cdot 2 + 56 = 0$. $$\Rightarrow 2q = -60$$

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You want $P(2)=0$

What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?

Let $x=2$ and solve for $q$

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