Question

When a polynomial P(x) is divided by the binomial `2x^2-3` the quotient is 2x-1 and the remainder is 3x+1. How do you find the expression of P(x)?

Answer 1

When a polynomial is divided by another polynomial, its quotient can be written as `f(x) + (r(x))/(h(x))`, where `f(x)` is the quotient, `r(x)` is the remainder and `h(x)` is the divisor.

Therefore:

`P(x) = 2x - 1 + (3x+ 1)/(2x^2 - 3)`

Put on a common denominator:

`P(x) = (((2x- 1)(2x^2 - 3)) + 3x + 1)/(2x^2 - 3)`

`P(x) = (4x^3 - 2x^2 - 6x + 3 + 3x + 1)/(2x^2- 3)`

`P(x) = (4x^3 - 2x^2 - 3x + 4)/(2x^2 - 3)`

Therefore, `P(x) = 4x^3 - 2x^2 - 3x + 4`.

Hopefully this helps!