What is the Value of k if the Remainder of p(x) Divided by x-1 is 12?

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To find the value of k in the polynomial p(x) = (x+2)(x+k) when the remainder is 12 upon division by x-1, the Remainder Theorem is applied. By substituting x=1 into the polynomial, the equation (1+2)(1+k) must equal 12. This simplifies to 3k + 3 = 12, leading to the conclusion that k = 3. The solution is confirmed through both long division and the Remainder Theorem. Thus, the value of k is 3.
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If p(x) = (x+2)(x+k) and if the remainder is 12 when p(x) is divided by x-1, then what is the value of k?
 
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I'm not sure if it is the right answer, but I think it is 3.

After using long division, we get the remainder 3k+3, which equals 12, meaning k=3.
 
Yes that is rite, found by long division or by saying that when x=1, expression =12 (remainder theorem or something like that)

(1+2)(1+k)=12

k=3
 

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