Question

Find the value of 'k' if (x−3) is a factor of the polynomial kx^2−kx−2.

a) k=1
b) k=2
c) k=−1
d) k=−2

Answer 1

To locate the value of 'k', set x = 3 in the polynomial kx^2 - kx - 2, which should equal zero if (x - 3) is a factor. Solving the equation, we get k = 1/3, which is not among the provided multiple-choice options, suggesting a typo in the question or the options.

Step-by-step explanation:

To find the value of 'k' when (x−3) is a factor of the polynomial kx²−kx−2, we can use the fact that if (x−3) is a factor, then the value of the polynomial will be zero when x = 3.

Let's substitute x = 3 into the polynomial:

• k(3)² − k(3) − 2 = 0
• 9k − 3k − 2 = 0
• 6k − 2 = 0

Solving for k gives us:

• 6k = 2
• k = 2/6
• k = 1/3

However, the value of k = 1/3 is not present in the given options (a, b, c, and d). There seems to be a mistake in either the polynomial given or the options provided since none of the options match the found value of k. If the polynomial is correct, then none of the options are correct and there might be a typo in the provided choices. If the options given are correct, then there might be a typo in the polynomial provided.