Polynomial Long Division x^2-6x+8 and x-3

Polynomial Long Division x^2-6x+8 and x-3 Image to Crop

Using polynomial long division, evaluate the expression below:

x² - 6x + 8

x - 3

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 → x² ÷ x = 1x^{(2 - 1)} = x
1b)  We multiply that part of the quotient by the divisor → x(x - 3) = x² - 3x  →  Click here to see the Math for this Multiplication.
1c)  Subtract x² - 3x from x² - 6x + 8 to get -3x + 8  →  Click here to see the Math.

			x
x	-	3	x²	-	6x	+	8
			x²	-	3x			-3x	+	8

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

			x	-	3
x	-	3	x²	-	6x	+	8
			x²	-	3x			-3x	+	8	-3x	+	9	-1

We have a remainder leftover. We take our answer piece and remainder piece below
Answer = x - 3
Remainder piece = Leftover answer divided by our denominator

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

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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