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 | 2s2 – t2 + st + 7t – 4
____________________________________________________________
Addition
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
6x ÷ 2x = 3
4x ÷ 2x = 2
3+2
___________________________________________________________
Reflection