Vocabulary and
("translation") 
Example(s)/Translation 
Explanation 
algebra ("bind together) 
2x + 37y + 7 3x + 4 = 7 
The study of mathematics using letters.
The terms are the "words" of an algebraic expression or equation. 
terms 
12, 5, 4x^{0}, 15x^{0}y^{0}, 6x^{4},
5x^{3}, 4x^{2}y, x^{2}, x 
Terms include numbers (numerical coefficients)
and letters (variables). Terms are connected by addition or subtraction. 
monomial
("one term") 
12, 15x^{0}y^{0}, 6x^{4},
x^{2}, x 
one term polynomial 
= 3x 
binomial
("two terms") 
x2 + 3, 3y^{3}  2x 
two term polynomial 
= 3x  2 
trinomial
("three terms") 
5x^{3} + 2xy  4 
three term polynomial 
= 2x^{2} + x  1 
polynomial ("many
terms") 
15x^{0}y^{0} x2 + 3
5x^{3} + 2xy  4
6x^{4} + 4x3  7xy  9 
Polynomial can be used to represent any
number of terms. Polynomial is often used to represent more than three terms. 
polynomial degree 
6x^{5} +
5x^{3} + 3 3x^{2}y^{3}
+ 3 
The polynomial degree for both examples is
5. The degree is determined by the term with the greatest power. If there is
more than one variable in a term, add the exponents to get the degree. 
like terms 
2x, 3x, 6x 
Like terms have the same
variable(s) and the same degree for each variable. 
6x^{4}, 4x^{4}, 3x^{4} 
3x^{2}y^{3}, 5x^{2}y^{3}, 2x^{2}y^{3}, 
adding like terms 
2x + 3x
= (2+3)x = 5x 
x = x^{1} 1x = x
1x = x

3x^{2}
+ x^{2}
= 3x^{2} + 1x^{2} = (3+1)x^{2} =4x^{2} 
3x^{2}y^{3} + 5x^{2}y^{3} = (3+5)x^{2}y^{3 }= 8x^{2}y^{3} 
subtracting like terms 
 
 2x  6x

 = +
 = 2x + 6x
= (2+6)x = 4x 
ax  bx = (a  b)x
Watch your signs!!
Remember:
x = x^{1} 1x = x
1x = x

 
 2x^{2}  3x^{2}

 = +
 = 2x^{2} + 3x^{2}
= (2+3)x^{2} = 5x^{2} 
3x^{2}y^{3}  4x^{2}y^{3} = (34)x^{2}y^{3 }= 1x^{2}y^{3}
= x^{2}y^{3} 