# Everything I know about polynomials

Vocabulary of polynomials

Coefficient: Number before a variable

Base: The variable after a coefficient

Variable: An unknown number shown by a letter

Term: A number or variable/the sum of a number and variable

Like terms: Two or more terms with the same base

Polynomials: An expression made up of terms that are added or subtracted

Monomial: 1 term | 6x2

Binomial:   2 terms | 3a2 – 5

Trinomial:  3 terms | –w2 – 5w + 1

Polynomial: 4+ terms | 2s2t2 + st + 7t – 4

____________________________________________________________

Only like terms can be added

(1x + 2x2 – 3x)+(1x + 3x2 + 2x)

1x, 3x, 1x and 2x are like terms

1x + 3x +1x + 2x = 7x

2x2  and 3x2 are like terms

2x2 + 3x2  = 5x2

= 7x + 5x2

____________________________________________________________

Subtraction

Only like terms can be subtracted

(4x – 3x2)-(1x2 + 2x)

= 4x – 2x = 2x

= 3x2 – 1x2  = 2x2

= 2x – 2x2

____________________________________________________________

Multiplication

Using the distributive property, we multiply the monomial with each term in the polinomial.

(3x)(3x x 2x x 5x)

Multiply each term by the monomial

(9x2 + 6x2 + 15x)

____________________________________________________________

Division

Distributive property still applies $\frac{6x + 4x}{2x}$

6x ÷ 2x = 3

4x ÷ 2x = 2

3+2

___________________________________________________________

Reflection