Question

Find k. ..................​

Answer 1

k = -10

Step-by-step explanation:

From the remainder theorem, we know that the remainder, 210, is equal to f(2).

∵
`f(2) = 210` ,

⇒
`4(2)^3 - 3 k(2)^2+44(2) - 30 = 210`

⇒
`32 -12k + 88 - 30 = 210`

⇒
`90 - 12k = 210`

⇒
`-12k = 120`

⇒
`k = -10`

Answer 2

k = -10

Step-by-step explanation:

f(x) = 4x³ - 3kx² + 44x - 30

The divisor is:

• (x - 2)

Set divisor to zero:

• (x - 2) = 0

• x = 2

Insert this into equation.

⇒ 4(2)³ - 3k(2)² + 44(2) - 30 = 210

⇒ 32 - 12k + 88 - 30 = 210

⇒ -12k + 90 = 210

⇒ -12k = 210 - 90

⇒ -12k = 120

⇒ k = 120/-12

⇒ k = -10