Question

what can be the degree of the reminder at most when a fourth degree polynomial is divided by quadratic polynomial ?

Answer 1

Do you know about Euclid division lemma ? According to this concepts , a = bq + r , where 0 ≤ r < b

Here question said , any polynomial of fourth degree is divided by quadratic polynomial , then degree of remainder must be less than degree of quadratic polynomial. so, maximum degree of remainder will be possible 1 .

Let's take a example for understanding ,
A four degree polynomial : x⁴ + 2x² + x + 1 is divided by a quadratic polynomial : x² + 2
Now, x² + 2) x⁴+ 2x² + x + 1 (x²
x² + 2x²
_________
x + 1
Hence, you can see remainder : x + 1 , degree of it is less than degree of x² + 2


Hence, maximum degree of the remainder = 1

Answer 2

Hi ,

If p (x ) and g ( x ) are any two polynomials with g ( x ) ≠ 0 

then we can find polynomials q ( x ) and r ( x ) such that 

p( x ) = g( x ) × q( x ) + r( x )

Where r( x ) = 0 or degree of r( x ) < degree of g ( x )

The degree of the  remainder may be 1 or 0 .

at most degree = 1

I hope this helps you .

: )