Question

When f(x)=3x³+mx²+nx+2 is divided by (x−3) the remainder is 32 . A factor of f(x) is (x+1). Determine the values of m and n.

Answer 1

To find the values of m and n, use the Remainder Theorem and set up equations with f(3) and f(-1). Solve the system of equations to find the values.

Step-by-step explanation:

To find the values of m and n, we can use the Remainder Theorem and the fact that (x+1) is a factor of f(x).

Since the remainder when dividing f(x) by (x-3) is 32, we can set up the equation f(3) = 32. Plugging in the value of x into the equation and simplifying, we get 81m + 9n + 3m + n + 2 = 32.

Substituting the factor (x+1) into the equation gives us another equation which we can use to solve for m and n. Plugging in x = -1 into f(x) gives us 27 - m + n + 2 = 0.

Now, we have a system of two equations with two variables that can be solved simultaneously to find the values of m and n.