70 pointsss for the correct answer When the function f(x) is divided by 4x−5, the quotient is 3x^2 −x+3 and the remainder is −2. Find the function f(x) and write the result in standard form.

f(x) = 12x³ - 19x² + 17x - 17

Step-by-step explanation:

We can the numerator by multiplying the denominator by the quotient, and then adding the remainder.

We're given a denominator of 4x - 5

a quotient of 3x² - x + 3

and a remainder of -2

so the original numerator is:

(4x - 5)(3x² - x + 3) - 2

= 12x³ - 4x² + 12x - 15x² + 5x - 15 - 2

= 12x³ - 19x² + 17x - 17

Let's test that by dividing it by 4x -5 with long division:

That matches, so we know our answer's right, and:

f(x) = 12x³ - 19x² + 17x - 17