5x-2 is factor of x3-3x2+kx+15

Answer 1

Since 5 x - 2 is a facto.

For

5 x - 2 = 0

x³ - 3 x² + k x + 15 is also equlal zero

5 x - 2 = 0

Add 2 to both sides

5 x = 2

x = 2 / 5

so

f(2/5) = 0

f(2/5) =

( 2 / 5 )³ - 3 ( 2 / 5 )² + k • 2 / 5 + 15 = 0

When you calculate this it will be:

1823 / 125 + 2 k / 5 = 0

Subtract 1823 / 125 to both suded.

2 k / 5 = - 1823 / 125

Multiply both sides by 5

2 k = - 5 • 1823 / 125

2 k = - 5 • 1823 / 5 • 25

2 k = - 1823 / 25

Divide both sides by 2

k = - 1823 / 50