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Find the value of k, if x – 1 is a factor of p(x) in each of the following cases: (i) p(x) =  (ii) p(x) = (iii) p(x) =  (iv) p(x) = 

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If x − 1 is a factor of polynomial p(x), then p(1) must be 0. (i) p(x) = x2 + x + k p(1) = 0 ⇒ (1)2 + 1 + k = 0 ⇒ 2 + k = 0 ⇒ k = −2 Therefore, the value of k is −2. (ii) p(1) = 0 (iii) p(1) = 0 (iv) p(x) = kx2 − 3x + k ⇒ p(1) = 0 ⇒ k(1)2 −...
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If x − 1 is a factor of polynomial p(x), then p(1) must be 0.

(i) p(x) = x2 + x + k

p(1) = 0

⇒ (1)2 + 1 + k = 0

⇒ 2 + k = 0

⇒ k = −2

Therefore, the value of k is −2.

 

(ii) 

p(1) = 0

 

(iii) 

p(1) = 0

 

(iv) p(x) = kx2 − 3x + k

⇒ p(1) = 0

⇒ k(1)2 − 3(1) + k = 0

⇒ k − 3 + k = 0

⇒ 2− 3 = 0

Therefore, the value of k is.

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