Division of Polynomials

Division of two polynomial may or may not result in a polynomial. Let us study below the division of polynomials in detail. To divide polynomials, follow the given steps:

Polynomial Division Steps:

If a polynomial has more than one term, we use long division method for the same. Following are the steps for it.

1. Write the polynomial in descending order.
2. Check the highest power and divide the terms by the same.
3. Use the answer in step 2 as the division symbol.
4. Now subtract it and bring down the next term.
5. Repeat steps 2 to 4 until you have no more terms to carry down.
6. Note the final answer, including remainder, will be in the fraction form (last subtract term).

Polynomial Examples

Example:

Given two polynomial 7s³+2s²+3s+9 and 5s²+2s+1.

Solve these using mathematical operation.

Solution:

Given polynomial:

7s³+2s²+3s+9 and 5s²+2s+1

Polynomial Addition: (7s³+2s²+3s+9) + (5s²+2s+1)

= 7s³+(2s²+5s²)+(3s+2s)+(9+1)

= 7s³+7s²+5s+10

Hence, addition result in a polynomial.

Polynomial Subtraction: (7s³+2s²+3s+9) – (5s²+2s+1)

= 7s³+(2s²-5s²)+(3s-2s)+(9-1)

= 7s³-3s²+s+8

Hence addition result in a polynomial.

Polynomial Multiplication:(7s³+2s²+3s+9) × (5s²+2s+1)

= 7s³ (5s²+2s+1)+2s² (5s²+2s+1)+3s (5s²+2s+1)+9 (5s²+2s+1))

= (35s⁵+14s⁴+7s³)+ (10s⁴+4s³+2s²)+ (15s³+6s²+3s)+(45s²+18s+9)

= 35s⁵+(14s⁴+10s⁴)+(7s³+4s³+15s³)+ (2s²+6s²+45s²)+ (3s+18s)+9

= 35s⁵+24s⁴+26s³+ 53s²+ 21s +9

Polynomial Division: (7s³+2s²+3s+9) ÷ (5s²+2s+1)

(7s³+2s²+3s+9)/(5s²+2s+1)

This cannot be simplified. Therefore, division of these polynomial do not result in a Polynomial.

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