Q. 5

# Determine the value of p if (x + 3) is a factor of x^{3} – 3x^{2} – px + 24.

Answer :

Let f(x) = x^{3} + 3x^{2} – 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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