Adding, Subtracting, Multiplying, & Dividing Polynomials

Adding and Subtracting

So the adding and subtracting are just as you would expect. Like terms can be added together.

2x³+x³-7x²+4x²+10

Would become

3x³-3x² + 10 

Multiplication

So this basically times everything in one bracket by everything in the other and is known as the FOIL method which stands for First Outer, Inner Last. Example

  (3x + 5)(2x -3)
= (3x * 2x) + (3x * -3) + (5 * 2x) + (5 * -3) 
= 6x² -9x + 10x -15
= 6x² + x -15

Dividing

There are 3 ways to approach this

• Long Division (Covered later)
• Synthetic Division (Covered later)
• Factor

Factoring

For this approach, it only works cleanly when the divisor is a factor of the polynomial. Hopefully connected, the quadratic equation can be shown as

ax² + bx + c

For this approach we at the coefficients of b and c and look for two numbers which when multiplied = c and when added = b. An example

x²+7x+12 / x +3

Factor of 12 are 1,12, 2,6, 3,4. 3 and 4 add up to 7 so

x²+7x+12 = (x+4)(x+3) 
--------   ---------- = x+4
 (x+3)        (x+3)