Algebra Master (Polynomials) Calculator
Publish date: 2024-07-24
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 togetherax^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 elementsExample calculations for the Algebra Master (Polynomials) Calculator
Algebra Master (Polynomials) Calculator Video
Tags:
Add This Calculator To Your Website
ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVflrmoucCsq56qXqW1sYvDqHSpp6A%3D