Question

When the function f(x) is divided by 3x + 1, the quotient is 2x^2 + 2x - 9 and the remainder is 7. Find the function f(x) and write the result in standard

form.

Answer 1

When the function f (x) is divided by 3x – 1, the quotient is 2x² – 3x + 6 a

Explanation:

Step 1 Devisor = 3x - 1Quotient = 2x2 - 3x + 6Remainder = 7Dividend = f(

Answer 2

To find the function f(x), we need to use the Remainder Theorem. The Remainder Theorem states that if we divide a polynomial by x - a, the remainder will be equal to the value of the polynomial at x = a.

We know that f(x) divided by 3x + 1 leaves a remainder of 7, so we can set up the equation:

f(x) = (3x + 1)(2x^2 + 2x - 9) + 7

Expanding the left side of the equation, we get:

f(x) = 6x^3 + 2x^2 - 27x - 9 + 7

Simplifying, we get:

f(x) = 6x^3 + 2x^2 - 27x + 2

The function f(x) is in standard form.