property involved in the following examples 2(3/5+1/2)=2(3/5)+2(1/2)
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f(x) = (2x3 – 3x2 – 18x + a)
x – 4 = 0 ⇒ x = 4
∴ f(4) = 2(4)3 – 3(4)2 – 18 × 4 + a
= 128 – 48 – 72 + a
= 128 – 120 + a
= 8 + a
Given that (x – 4) is a factor of f(x).
By the Factor Theorem, (x – a) will be a factor of f(x) if f(a) = 0 and therefore f(4) = 0.
⇒ f(4) = 8 + a = 0
⇒ a = -8
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