Question

Please help!

Let f(x) be a polynomial. It is given that the quotient of f(x) ÷ (x-3) is 2x^(2 + 10x - 1, and f(3) = 4

find the polynomial f(x)

thanks a lot

Answer 1

Because

`(f(x))/(x-3) = 2x^(2) + 10x - 1`
therefore
f(x) = (x-3)(2x² + 10x - 1) + k, where k = constant.

Because f(3) = 4, therefore k =4.
The polynomial is
f(x) = 2x³ + 10x² - x - 6x² - 30x + 3 + 4
= 2x³ + 4x² - 31x + 7

Answer: f(x) = 2x³ + 4x² - 31x + 7