Year 10: Long division of polynomials

This cheat-sheet provides a quick guide to performing long division of polynomials. It’s similar to long division with numbers, but with terms containing variables (like 'x').

Steps

1. Set up the problem: Write the dividend (the expression being divided) under the divisor (the expression dividing it).
2. Divide the first terms: Divide the first term of the dividend by the first term of the divisor. Write this quotient above the divisor.
3. Multiply: Multiply the divisor by the quotient you just found.
4. Subtract: Subtract the result from the corresponding term in the dividend.
5. Bring down: Bring down the next term from the dividend.
6. Repeat: Repeat steps $2-5$ until all terms of the dividend have been divided.

Example

Let's divide $(2x^2+5x-3)$ by $(x+3)$:

        $2x-1$        
$x+3$ | $2x^2+5x-3$
     - $(2x^2+6x)----------------------------x-3$
            $-(-x-3)----------------------------0$

Result: Quotient = $2x-1$, Remainder = 0

Key points

• Remember to include all terms in the dividend and divisor.
• The degree (highest power of x) of the quotient is always one less than the degree of the divisor.
• The remainder can be zero if the divisor divides evenly into the dividend.