Question

For what value of k, will expression (3x^3-kx^2+4x+16) be divisible by (x-k/2)?
(a)4
(b)-4
(c)2
(d)0

Answer 1

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Answer 2

Answer:

Option(B)

Step-by-step explanation:

Given f(x) = 3x³ - kx² + 4x + 16.

Since (x - k/2) is a factor of polynomial. This means x = k/2 is the zero of the given polynomial.

⇒ f(k/2) = 3(k/2)³ - k(k/2)² + 4(k/2) + 16

⇒ 0 = 3(k³/8) - 2(k³/4) + 4(k/2) + 16

⇒ 0 = (3k³ - 2k³ + 16k + 128)/8

⇒ 0 = 3k³ - 2k³ + 16k + 128

⇒ 0 = k³ + 16k + 128

⇒ 0 = k³ - 4k² + 4k² + 32k - 16k + 128

⇒ 0 = k³ - 4k² + 32k + 4k² - 16k + 128

⇒ 0 = k(k² - 4k + 32) + 4(k² - 4k + 32)

⇒ 0 = (k + 4)(k² - 4k + 32)

⇒ k = -4.

Therefore, the value of k = -4.

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