Question

What can be the degree of the remainder at most when a 4th degree polynomial is divided by a quadratic polynomial?

Answer 1

please give me equation
no and yes 4 degree polynomial is divided by a quadratic polynomial

Answer 2

The degree of remainder, which can be denoted by R(x) is less than equal to 1.  

Solution:

To find the degree of the remainder when a 4th degree polynomial is divided by a F(x):

Let’s say a Dividend and a G(x) which is a Divisor.  

G(x) denotes the quadratic polynomial  = $ax^{2}+ bx + c$

The degree of dividend F(x) is equal to 4, the degree of divisor G(x) is equal to 2.

To find the degree of the quotient Q(x) we subtract the degree of the dividend and the degree of the divisor = (4 - 2) = 2.  

Degree of remainder R(x) is less than or equal to 1.