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

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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?

addition

math operation involving the sum of elements

algebra master (polynomials)

binomial theorem

algebraic expansion of powers of a binomial

long division

a standard division algorithm suitable for dividing multi-digit numerals that is simple enough to perform by hand.

multiplication

math operation involving the product of elements

polynomial

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

subtraction

math operation involving the difference of elements

Example calculations for the Algebra Master (Polynomials) Calculator

Algebra Master (Polynomials) Calculator Video

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