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Adding Polynomials

Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in.


Simplify (2x + 5y) + (3x – 2y)

Adding horizontally...

= 2x + 5y + 3x – 2y

= 2x + 3x + 5y – 2y

= 5x + 3y


Adding vertically, like






Subtracting Polynomials

Simplify (x[super]3[/super] + 3x[super]2[/super] + 5x − 4) − (3x[super]3[/super] − 8x[super]2[/super] – 5x + 6)

Change minus sign to a plus, and change to opposite sign in polynomial after that plus

(x[super]3[/super] + 3x[super]2[/super] + 5x − 4) + (3x[super]3[/super] + 8x[super]2[/super] + 5x − 6)

answer: −2x[super]3[/super] + 11x[super]2[/super] + 10x – 10

Multiplying Polynomials

Simplify (5x[super]2[/super])(–2x[super]3[/super])

Apply rules of exponents, negative numbers, and variables

(5x[super]2[/super])(–2x[super]3[/super]) = -10x[super]5[/super]


Simplify (x + 3)(x + 2)





answer: x[super]2[/super] + 5x + 6


FOIL

There is also a special method, useful ONLY for a two-term polynomial times another two-term polynomial. The method is called "FOIL". The letters F-O-I-L come from the words "first", "outer", "inner", "last", and are a memory device for helping you remember how to multiply horizontally, without having to write out the distribution and without dropping any terms. Here is what FOIL stands for: