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# Find the Value of K, If 2x + 1 is a Factor of (3k + 2)X3 + (K − 1) - ICSE Class 10 - Mathematics

#### Question

Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1)

#### Solution

Let f(x) = (3k + 2)x3 + (k − 1)
2x + 1 = 0 ⟹ x = (−1)/2
Since, 2x + 1 is a factor of f(x), remainder is 0.
∴ (3k + 2)((-1)/2)^3+ (k -1)= 0
⇒ (-(3k+ 2))/8 + (k-1) =0
⇒ (-3k- 2 +8k -8)/ 8 = 0
⇒ 5k- 10 = 0
⇒ k  = 2

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Solution Find the Value of K, If 2x + 1 is a Factor of (3k + 2)X3 + (K − 1) Concept: Factor Theorem.
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