3.24: Factor and remainder determine two coefficients

0606/21/O/N/25 — Question 1 · 5 marks

The polynomial pp is such that p(x)=x3+ax2+bx−2p(x) = x^{3} + ax^{2} + bx - 2, where aa and bb are constants.
It is given that:
• x+2x + 2 is a factor of p(x)p(x)
• when p(x)p(x) is divided by x−3x - 3 the remainder is 4040.
Find the values of aa and bb.
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