Respuesta :
Answer:
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
Answer:
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
- f ( x ) = x³ - kx² + 2x + 7k
plug -2 as x in the expression.
- f ( -2) = ( -2)³ - k ( -2)² + 2 ( -2 ) + 7 k = 0
expand the exponents
- = -8 -4k -4 + 7k = 0
combine like terms
- = -8 -4 + -4k + 7k = 0
- = -12 + 3k = 0
add 12 to both side
- -12 + 12 + 3k = 12
- 3k = 12
divide each side by 3
- 3k / 3 = 12/3
- k = 4
