when a polynomial P(x) is divided by (2x-1) the quotient is x^2-2x-1 and the remainder is -4. Find P(x).

Question

rational root theorem and factoring

Answer 1

P(x) ÷ (2x-1) = quotient + (remainder)/(divisor)

 

                   = x²-2x-1 - 4/(2x-1)

 

So, P(x) = (x²-2x-1)(2x-1) - 4

 

            = 2x³ - 4x² - 2x - x² + 2x +1 - 4

 

            = 2x³ - 5x² - 3

Answer 2

According to the remainder, if we multiply the quotient by the factor, then add the remainder, we get the product.  The product is the polynomial P(x).

 

P(x) = (x² - 2x - 1)(2x - 1) - 4

 

P(x) = 2x(x² - 2x - 1) - x² + 2x + 1 - 4

 

P(x) = 2x³ - 4x² - 2x - x² + 2x + 1 - 4

 

 

Now just simplify.