Question

Given f(x) = 2x² - 2x + kf(x) = 2x² - 2x + k, and the remainder when f(x) is divided by x - 2x - 2 is -3, then what is the value of k?

Answer 1

The value of k in the quadratic equation f(x) = 2x² - 2x + k, given the remainder (-3) when divided by x - 2, is -7. This was determined using the Remainder Theorem and substituting x = 2 into the polynomial.

Step-by-step explanation:

The student is asking to determine the value of k in the quadratic equation f(x) = 2x² - 2x + k given that the remainder of the division of f(x) by x - 2 is -3. To find the value of k, we can apply the Remainder Theorem which states that if a polynomial f(x) is divided by x - a, the remainder is f(a).

Using the Remainder Theorem:

• Let's substitute x = 2 into the polynomial f(x).
• So we have f(2) = 2(2)² - 2(2) + k = 8 - 4 + k = 4 + k.
• Since the remainder is -3, we set 4 + k = -3.
• Solving for k, we subtract 4 from both sides of the equation to get k = -3 - 4 = -7.

Therefore, the value of k is -7.