DIVIDING POLYNOMIALS BY LONG DIVISION WORKSHEET

Divide the following polynomials using long division.

Problem 1 :

(2x³ - 6x² + 5x + 4) ÷ (x - 2)

Problem 2 :

(4x³ - 5x² + 6x - 2) ÷ (x - 1)

Problem 3 :

(x³ - 7x² - x + 6) ÷ (x + 2)

Problem 4 :

(10- 4x + 3x²) ÷ (x - 2)

1. Answer :

(2x³ - 6x² + 5x + 4)  ÷  (x - 2)

Let P(x) = 2x³ - 6x² + 5x + 4 and g(x) = x - 2

To divide the given polynomial by x - 2, we have divide the first term of the polynomial P(x) by the first term of the polynomial g(x).

If we divide 2x³ by x, we get 2x². Now we have to multiply this 2x² by x - 2. From this we get 2x³ - 4x². 

Now we have to subtract 2x³ - 4x² from the given polynomial. So we get -2x² + 5x + 4.

Now we have to subtract 2x³ - 4x² from the given polynomial. So we get -2x² + 5x + 4.

repeat this process until we get the degree of p(x) ≥ degree of g(x).

So,

Quotient  =  2x² - 2x + 1

Remainder = 6

2. Answer :

(4x³ - 5x² + 6x - 2)  ÷  (x - 1)

So,

Quotient  =  4x² - x + 5

Remainder  =  3

3. Answer :

(x³ - 7x² - x + 6)  ÷  (x + 2)

So, 

Quotient  =  x² - 9x + 17

Remainder  =  -28

4. Answer :

(10- 4x + 3x²)  ÷  (x - 2)

Let us first write the terms of each polynomial in descending order ( or ascending order).

Thus, the given problem becomes (10- 4x + 3x²) ÷ (x - 2)

f(x)  =  10- 4x + 3x²

=  3x² - 4x + 10

g(x) = x - 2  

Step 1 :

In the first step, we are going to divide the first term of the dividend by the first first term of the divisor.

After changing the signs, +3x² and -3x² will get canceled. By simplifying, we get 2x + 10.

Step 2 :

In the second step again we are going to divide the first term that is 2x by the first term of divisor that is x.

So,

Quotient  =  3x + 2

Remainder  =  14

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