Question

The polynomial function f(y) = 2y + 5y²-18y + 50, when divided by

(y+c) or (y-c)leaves the same remainder. Find all possible values of c

Answer 1

To find the value of c for which the polynomial f(y) = 2y + 5y² - 18y + 50 gives the same remainder when divided by (y+c) or (y-c), we use the Remainder Theorem and solve the equation f(c) = f(-c) to find c.

Step-by-step explanation:

The student's question is about finding the value of c such that the polynomial function f(y) = 2y + 5y² - 18y + 50 leaves the same remainder when divided by (y+c) or (y-c).

The remainder when a polynomial is divided by a binomial of the form (y + c) or (y - c) is a constant. This is based on the Remainder Theorem which states that if a polynomial f(y) is divided by (y - r), the remainder is f(r). Therefore, we are essentially looking for a value of c such that f(-c) = f(c).

By substituting c and -c into the polynomial, we can then equate the two results and solve for c.

Let's apply this to the given polynomial:

1. Substitute y = c: f(c) = 2c + 5c² - 18c + 50.
2. Substitute y = -c: f(-c) = -2c + 5c² + 18c + 50.
3. Equate f(c) and f(-c) and solve for c:

2c + 5c² - 18c + 50 = -2c + 5c² + 18c + 50

Simplifying this will give us the possible values for c.