Math CentralQuandaries & Queries


Question from Ruby, a student:

(x+3) is a factor of 2x^3-3x^2+px+30.
Determine the value of p

Hi Ruby,

If (x + 3) is a factor of 2x3 - 3x2 + px + 30 then there is some polynomial q(x) so that

2x3 - 3x2 + px + 30 = (x + 3) q(x).

Substitution of x = -3 into the right side yields zero and hence substitution of x = -3 into the left side must also yield zero. Substitute x = -3 into the left side, set the value to zero and solve for p.


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