Find the value of a for which (x-4) is a factor of

Question

Philoid · Accepted Answer

Let, f(x) = 2x³ – 3x² – 18x + a

Now, we have

x - 4 = 0

x = 4

Hence,

f(4) = 2(4)³ – 3(4)² – 18 × 4 + a

= 128 – 48 – 72 + a

= 128 – 120 + 8

= 8 + a

As per question,

(x - 4) is the factor of f(x)

Now, by using factor theorem we get

(x – a) will be the factor of f(x) if f(a) = 0 and hence f(4) = 0

So,

f(4) = 8 + a = 0

a = -8