Question

Divide the polynomial 6x³ + 8x² by the monomial 2x. What is the quotient and remainder?

Answer 1

Answer:

3 x^2 + 4 x

Step-by-step explanation:

Given Divide the polynomial 6x³ + 8x² by the monomial 2x. 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.

        2 x ) 6 x^3 + 8 x^2 ( 3 x^2 + 4 x

                 6 x^3                             by subtracting

             --------------------------------

                         - 8 x^2

                           8 x^2

            ---------------------------------

                              0

So now quotient is zero and remainder is 3 x^2 + 4 x

Answer 2

Divide the polynomial 6x³ + 8x² by the monomial 2x. What is the quotient and remainder?

numerator =

$6 {x}^{3} + 8 {x}^{2} \\ \\ = 2 {x}^{2} \times 3x + 2 {x}^{2} \times 4 \\ \\ = 2 {x}^{2} (3x + 4) \\ \\ = 2x \times x \times (3x + 4)$

Denominator = 2x

cancelling 2x from numerator and denominator

= x (3x +4)

quotient = x (3x +4)

$= 3 {x}^{2} + 4x$

remainder = 0