Question

3. If (x + 3) is a factor of polynomial f(x) = kx³+ x²- 22x+ 21 then the value of k = ?​

Answer 1

Answer:

x+3=0

x= -3

p (x)=0

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

0= -27k+9+66+21

0= -27k+96

27k=96

k=96/27

k=32/9

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.