The remainder when 3x3+ kx2+ 5x - 6 is divided by (x + 1) is -7. What is the value of k?a)-14b)14c)-7d)7Correct answer is option 'D'. Can you explain this answer?

Question

Answer

To find the value of k, we need to use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by (x-a), the remainder is equal to f(a).

In this case, the polynomial we are given is 3x^3 + kx^2 + 5x - 6, and we are told that the remainder when this polynomial is divided by (x-1) is -7. So, we can set up the following equation:

f(1) = -7

Now, let's substitute x = 1 into the polynomial and solve for k.

f(1) = 3(1)^3 + k(1)^2 + 5(1) - 6

Simplifying this equation, we get:

3 + k + 5 - 6 = -7

Combining like terms, we have:

k + 2 = -7

Subtracting 2 from both sides, we get:

k = -9

Therefore, the value of k is -9. However, none of the given options match this answer, so there might be an error in the question or the answer choices. Without further information, it is not possible to determine the correct value of k from the options provided.

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