Question

What should be the degree of the remainder when q cubic polynomial is divided by a quadratic polynomial

Answer 1

Answer:

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

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Answer 2

Answer:

Its should be 0 or 1(hopefully I am right)

Step-by-step explanation:

This is because if the degree is 2,

Then after multiplying with the quadratic polynomial, the resulting polynomial will have degree 4 which should not be possible here since we want a degree of 3.

It can be 0 if the quadratic perfectly divides the cubic (for example try dividing x³ + x² - x - 1 by x² - 1)or leaves a remainder as a constant(for example try dividing x³ - 1 by x²),

It can have 1 as well if the cubic polynomial is not perfectly divisible by the quadratic and leaves a remainder as a variable with degree 1 (for example divide x³ - x - 1 by x²)

Thus, we can infer that either the degree of the remainder is always 0 or 1 when a cubic polynomial is divided by a quadratic polynomial.

HOPE IT HELPS