Question

determine the value of k such that (x + 3) is a factor of the polynomial
f(x) = kx³ +x² -22x -21​

Answer 1

Step-by-step explanation:

x+3=0

x= -3

f(x)=kx^3+x^2-22x-21

f(-3)=k(-3)^3+(-3)^2-22(-3)-21

0. =(-27)k+9+66-21

27k=75-21.

27k=54

k=54/27

k=2

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

∵ x + 3 is a factor of polynomial p(x) = kx² + x² - 22x - 21

∴ By factor theorem, p(-3) = 0

Now, substituting the value of x

p(x) = kx² + x² - 22x - 21

p(-3) = k(-3)³ + (-3)² - 22(-3) - 21 = 0

⇒ -27k + 9 + 66 - 21 = 0

⇒-27 + 54 = 0

⇒ 27k = 54

⇒ k = 54 ÷ 27

⇒ k = 2 Ans.