When the function f(x) is divided by -3x−4, the quotient is 3x^2 +x+5 and the remainder is −9. Find the function f(x) and write the result in standard form.

Answer 1

To find the function f(x), we can set up the division in long division form:

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-3x - 4 | f(x)

Since the quotient is 3x^2 + x + 5 and the remainder is -9, we have:

f(x) = (-3x - 4)(3x^2 + x + 5) - 9

Simplify:

f(x) = -9x^2 - 3x - 20x^2 - 4x - 20 - 9

f(x) = -29x^2 - 7x - 29

Therefore, the function f(x) is -29x^2 - 7x - 29. Written in standard form, this becomes:

f(x) = -29x^2 - 7x - 29