Question

determine the value of k such that (x+3) is a factor of the polynomil p(X)=kx3+x2-22x-21

Answer 1

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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.