Algebra Master (Polynomials) Calculator

Algebra Master (Polynomials) Calculator Using polynomial long division, evaluate the expression below:

2x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1

x2 - 1

First, we write our expression in long division format and follow the steps below.
Step 1
 1a)  Divide the first term of the dividend by the first term of the divisor → 2x7 ÷ x2 = 2x(7 - 2) = 2x5
 1b)  We multiply that part of the quotient by the divisor → 2x5(x2 - 1) = 2x7 - 2x5  →  Click here to see the Math for this Multiplication.
 1c)  Subtract 2x7 - 2x5 from 2x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1 to get 3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1  →  Click here to see the Math.

2x5

x2

-

1

2x7

+

3x6

-

6x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

2x7

-

2x5

3x6

-

4x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

Step 2
 2a)  Divide the first term of the dividend by the first term of the divisor → 3x6 ÷ x2 = 3x(6 - 2) = 3x4
 2b)  We multiply that part of the quotient by the divisor → 3x4(x2 - 1) = 3x6 - 3x4  →  Click here to see the Math for this Multiplication.
 2c)  Subtract 3x6 - 3x4 from 3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1 to get -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1  →  Click here to see the Math.

2x5

+

3x4

x2

-

1

2x7

+

3x6

-

6x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

2x7

-

2x5

3x6

-

4x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

3x6

-

3x4

-4x5

+

9x4

-

2x3

-

8x2

+

6x

-

1

Step 3
 3a)  Divide the first term of the dividend by the first term of the divisor → -4x5 ÷ x2 = -4x(5 - 2) = -4x3
 3b)  We multiply that part of the quotient by the divisor → -4x3(x2 - 1) = -4x5 + 4x3  →  Click here to see the Math for this Multiplication.
 3c)  Subtract -4x5 + 4x3 from -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1 to get 9x4 - 6x3 - 8x2 + 6x - 1  →  Click here to see the Math.

2x5

+

3x4

-

4x3

x2

-

1

2x7

+

3x6

-

6x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

2x7

-

2x5

3x6

-

4x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

3x6

-

3x4

-4x5

+

9x4

-

2x3

-

8x2

+

6x

-

1

-4x5

+

4x3

9x4

-

6x3

-

8x2

+

6x

-

1

Step 4
 4a)  Divide the first term of the dividend by the first term of the divisor → 9x4 ÷ x2 = 9x(4 - 2) = 9x2
 4b)  We multiply that part of the quotient by the divisor → 9x2(x2 - 1) = 9x4 - 9x2  →  Click here to see the Math for this Multiplication.
 4c)  Subtract 9x4 - 9x2 from 9x4 - 6x3 - 8x2 + 6x - 1 to get -6x3 + x2 + 6x - 1  →  Click here to see the Math.

2x5

+

3x4

-

4x3

+

9x2

x2

-

1

2x7

+

3x6

-

6x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

2x7

-

2x5

3x6

-

4x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

3x6

-

3x4

-4x5

+

9x4

-

2x3

-

8x2

+

6x

-

1

-4x5

+

4x3

9x4

-

6x3

-

8x2

+

6x

-

1

9x4

-

9x2

-6x3

+

x2

+

6x

-

1

Step 5
 5a)  Divide the first term of the dividend by the first term of the divisor → -6x3 ÷ x2 = -6x(3 - 2) = -6x
 5b)  We multiply that part of the quotient by the divisor → -6x(x2 - 1) = -6x3 + 6x  →  Click here to see the Math for this Multiplication.
 5c)  Subtract -6x3 + 6x from -6x3 + x2 + 6x - 1 to get x2 - 1  →  Click here to see the Math.

2x5

+

3x4

-

4x3

+

9x2

-

6x

x2

-

1

2x7

+

3x6

-

6x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

2x7

-

2x5

3x6

-

4x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

3x6

-

3x4

-4x5

+

9x4

-

2x3

-

8x2

+

6x

-

1

-4x5

+

4x3

9x4

-

6x3

-

8x2

+

6x

-

1

9x4

-

9x2

-6x3

+

x2

+

6x

-

1

-6x3

+

6x

x2

-

1

Step 6
 6a)  Divide the first term of the dividend by the first term of the divisor → x2 ÷ x2 = 1x(2 - 2) = 1
 6b)  We multiply that part of the quotient by the divisor → 1(x2 - 1) = x2 - 1  →  Click here to see the Math for this Multiplication.
 6c)  Subtract x2 - 1 from x2 - 1 to get   →  Click here to see the Math.

2x5

+

3x4

-

4x3

+

9x2

-

6x

+

1

x2

-

1

2x7

+

3x6

-

6x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

2x7

-

2x5

3x6

-

4x5

+

6x4

-

2x3

-

8x2

+

6x

-

1

3x6

-

3x4

-4x5

+

9x4

-

2x3

-

8x2

+

6x

-

1

-4x5

+

4x3

9x4

-

6x3

-

8x2

+

6x

-

1

9x4

-

9x2

-6x3

+

x2

+

6x

-

1

-6x3

+

6x

x2

-

1

x2

-

1

Since we do not have a remainder, we have our answer below:
Answer = 2x5 + 3x4 - 4x3 + 9x2 - 6x + 1

Answer = 2x5 + 3x4 - 4x3 + 9x2 - 6x + 1

You have 1 free calculations remaining

What is the Answer?

Answer = 2x5 + 3x4 - 4x3 + 9x2 - 6x + 1

How does the Algebra Master (Polynomials) Calculator work?

Free Algebra Master (Polynomials) Calculator - Given 2 polynomials this does the following:
1) Polynomial Addition
2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.
This calculator has 2 inputs.

What 3 formulas are used for the Algebra Master (Polynomials) Calculator?

Polynomials with matching variables and exponents may be added or subtracted together
ax^2 + bx^2 = (a + b)x^2
ax^2 - bx^2 = (a - b)x^2

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Algebra Master (Polynomials) Calculator?

additionmath operation involving the sum of elementsalgebra master (polynomials)binomial theoremalgebraic expansion of powers of a binomiallong divisiona standard division algorithm suitable for dividing multi-digit numerals that is simple enough to perform by hand.multiplicationmath operation involving the product of elementspolynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).subtractionmath operation involving the difference of elements

Example calculations for the Algebra Master (Polynomials) Calculator

Algebra Master (Polynomials) Calculator Video

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