Polynomial Long Division 2x^3-x^2-4x 1 and x 3

Polynomial Long Division 2x^3-x^2-4x 1 and x 3 Image to Crop

Using polynomial long division, evaluate the expression below:

2x³ - x² - 4x1

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 → 2x³ ÷ x = 2x^{(3 - 1)} = 2x²
1b)  We multiply that part of the quotient by the divisor → 2x²(x3) = 2x³  →  Click here to see the Math for this Multiplication.
1c)  Subtract 2x³ from 2x³ - x² - 4x to get -x² - 4x  →  Click here to see the Math.

2x²

2x³

x²

2x³

-x²

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

2x²

2x³

x²

2x³

-x²

-4x

Step 3
3a)  Divide the first term of the dividend by the first term of the divisor → -4x ÷ x = -4x^{(1 - 1)} = -4
3b)  We multiply that part of the quotient by the divisor → -4(x3) = -4x  →  Click here to see the Math for this Multiplication.
3c)  Subtract -4x from -4x to get   →  Click here to see the Math.

2x²

2x³

x²

2x³

-x²

-4x

Since we do not have a remainder, we have our answer below:
Answer = 2x² - x - 4

Answer = 2x² - x - 4

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What is the Answer?

Answer = 2x² - x - 4

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.
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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

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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