Question

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

Answer 1

k = 4

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

Answer 2

k = 4

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