Question

3
Determine the value of k if (x +3 ) is a factor of polynomial,
f(x) = k x3 + x2 – 22 x - 21.​

Answer 1

Answer:

You can see the answer in adjoining pic.

Hope it helps...

Answer 2

✞︎ Given :-

⚜️ Polynomial is

$k{x}^{3} + {x}^{2} - 22x - 21$

➪︎ Factor is (x + 3)

❦︎ To find :-

• Determine the value of k.......

✯︎ Solution :-

☯️ Given polynomial is

$k {x}^{3} + {x}^{2} - 22x - 21$

___________________________

☯️ Put x + 3 = 0

➪︎ x = -3

___________________________

Substituting x = (-3) , we get

➪︎ $k( { - 3)}^{3} + {( - 3)}^{2} - 22( - 3) - 21 = 0$

➪︎ $- 27k + 9 + 66 - 21 = 0$

➪︎ $- 27k + 54 = 0$

➪︎ $- 27k = - 54$

➪︎ $k = \frac{ - 54}{ - 27}$

✰︎ Therefore k = 2......✔️