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If $x − 4$ is a factor of the polynomial $2 x 3 − 3 x 2 − 18 x + a,$ then the value of $a$ is [[1]].

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answer is -8.

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Detailed Solution

x − 4

is a factor of the polynomial

2 x 3 − 3 x 2 − 18 x + a,

then the value of

a

is -8.
The given polynomial is

2 x 3 − 3 x 2 − 18 x + a .

We know by Factor theorem that if

x − k

is a factor of the given polynomial

p (x)

, then

p k = 0.

Therefore, if

x − 4

is a factor of the polynomial

2 x 3 − 3 x 2 − 18 x + a,

then

p 4 = 0.

⇒ 2 (4) 3 − 3 (4) 2 − 18 (4) + a = 0 ⇒ 128 − 48 − 72 + a = 0 ⇒ 8 + a = 0 ⇒ a = − 8

Therefore the value of

a

is -8.

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