Question

tell me by solving in notebook with explanation

Answer 1

p(x) = kx³ + 9x² + 4x - 8 

p(-3) = -27k + 81 - 12 - 8 = -20 

=> -27k + 61 = -20 

=> -27k= -20-61

=> -27k= -81

=> k= -81/-27

=>k= 3


i.e. k = 3 

=> p(x) = 3x³ + 9x² + 4x - 8 

Answer 2

Given f(x) = kx^3 + 9x^2 + 4x - 10.

Given that when f(x) is divided by x + 3, it leaves a remainder 3.

By remainder theorem,

= > x + 3 = 0

= > x = -3.

Plug x = -3 in f(x), we get

= > k(-3)^3 + 9(-3)^2 + 4(-3) - 10 = -22

= > -27k + 81 - 12 - 10 = -22

= > 27k + 59 = -22

= > -27k = -22 - 59

= > -27k = -81

= > k = 3.

Therefore, the value of k = 3.

Hope this helps!