Question

Find the value of k, if x – 3 is a factor of p (x) = x^2 + x – k

Answer 1

Answer:

x=3

k=12

Step-by-step explanation:

Answer 2

Given :

p(x) = x² + x - k

x - 3 is a factor of p(x)

To Find :

Value of k

Solution :

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Remainder Theorem :

If a polynomial f(x) is divided by a linear expansion ( x - A ) , then remainder is equals to f(A) .

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x - 3 is a factor of p(x)

⇒ x - 3 = 0

⇒ x = 3

So ,

p(3) = 0

⇒ (3)² + (3) - k = 0

⇒ 9 + 3 - k = 0

⇒ 12 - k = 0

⇒ 12 = k

⇒ k = 12  $\purple{\bigstar}$