Find k so that x+2 is a factor of x^3 - kx^2 + 2x + 7k

k =  4

Step-by-step explanation:

If (x + 2) is a factor then f(- 2) = 0

f(x) = x³ - kx² + 2x + 7k , then

f(- 2) = (- 2)³ - k(- 2)² + 2(- 2) + 7k = 0      

     ⇒   - 8 - k(4) - 4 + 7k = 0

     ⇒  - 8 - 4k - 4 + 7k = 0

     ⇒ 3k - 12 = 0 ( add 12 to both sides )

     ⇒ 3k = 12 (divide both sides by 3 )

     ⇒ k = 4

k = 4

Step-by-step explanation:

If x + 2 is a factor of x³ - kx² + 2x + 7k then

the value of x = -2

Solve for k

plug -2 as x in the expression.

expand the exponents

combine like terms

add 12 to both side

divide each side by 3

160

step-by-step explanation:

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