Q5 of 47 Page 80

Determine the value of p if (x + 3) is a factor of x3 – 3x2 – px + 24.

Let f(x) = x3 + 3x2 – px + 24.

By factor theorem,


x + 3 = 0;x = – 3


∴(x + 3) is a factor of f(x)


So, f(– 3) = 0.


f(– 3) = (– 3)3 – 3(– 3)2 – p(– 3) + 24 = 0


= >27 – 27 + 3p + 24 = 0


= > – 59 + 24 + 3p = 0


∴3p – 30 = 0


⇒ p = 30/3


⇒ p = 10


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