Question

(5x⁴ - 3x³ + 4x² + 2x - 6) ÷ x². What is the quotient and remainder?

Answer 1

Answer:

Step-by-step explanation:

Given (5x⁴ - 3x³ + 4x² + 2x - 6) ÷ x². What is the quotient and remainder?

So we need to divide a polynomial (more than one term) by a monomial which has one term.  

So let us divide.

    x^2) 5x⁴ - 3x³ + 4x² + 2x - 6 (5 x^2 - 3 x + 4

            5x⁴ - 3x³ + 4x²

        ------------------------------- By subtracting we get

                           2 x - 6

After dividing, the quotient will be 5 x^2 - 3 x + 4 and remainder is 2 x - 6

Answer 2

(5x⁴ - 3x³ + 4x² + 2x - 6) ÷ x². What is the quotient and remainder?

Numerator = 5x⁴ - 3x³ + 4x² + 2x - 6

taking x² common from the terms where it can be taken

= x² (5x² -3x +4) + 2x + 6

Denominator = x²

cancelling x² from numerator terms and denominator we will get quotient and remaining part as remainder .

quotient = 5x² -3x +4

remainder = 2x + 6