Question

If p(x) = (x + 2) (x + k) and if the remainder is 12 when p(x) is divided by (x - l),then k = ___.

Answer 1

To find the value of k, use the Remainder Theorem and set p(l) equal to 12. Solve the resulting quadratic equation to determine k.

Step-by-step explanation:

To find the value of k, we need to use the Remainder Theorem. According to the Remainder Theorem, if p(x) is divided by (x - l) and the remainder is 12, then p(l) = 12.

Substituting (x - l) into p(x), we get p(l) = (l + 2)(l + k) = 12.

Expanding the equation and setting it equal to 12, we can solve for k.

(l + 2)(l + k) = 12
l^2 + (2 + k)l + 2k = 12
l^2 + (2 + k)l + (2k - 12) = 0

This quadratic equation can be solved using various methods like factoring or the quadratic formula. Once you solve it, you will find the value of k.