Question

5. Determine the value of k such
that (x+3) is a factor of
P(x) = kx^2 -22x - 21
​

Answer 1

Answer:

Step-by-step explanation:

Given p(x)=kx²-22x-21

x+3=0

   x=0-3

   x=-3

p(-3)=k(-3)²-22(-3)-21=0

                 k(9)+66-21=0

                        9k+45=0

                               9k=0-45

                               9k=-45

                                 k=-45/9

                                 k=-5

∴The value of k is -5

∴Please mark it as brainlist answer

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.