Definitions
In an expression, it is the term that has no variable attached to it.
What is a constant?
(3x2 + 2x) + (4x2 + 1)
7x2 + 2x + 1
a(4a + 3)
4a2 + 3a
(m + 4)(m + 1)
m2 + 5m + 4
(x + 1)(x2 + 2x + 4)
x3 + 3x2 + 6x + 4
3x, 4y, 6x2, 5xy are examples of this.
What is a monomial?
(5a + 9b) - (2a + 4b)
3a + 5b
b(b2 - 12b + 1)
b3 - 12b2 + b
(t + 4)2
t2 + 8t + 16
(w + 4)(w2 + 3w - 6)
w3 + 7w2 + 6w - 24
The number attached to the left of a variable.
What is a coefficient?
(x2+3x-1) + (5x2-5x-7)
6x2 - 2x - 8
3x(5x2 - x + 4)
15x3 - 3x2 + 12x
(3n - 7)(n + 3)
3n2 + 2n - 21
(2y - 11)(y2 - 3y + 2)
2y3 - 17y2 + 37y - 22
(x + 5) and (3y + 4x2) are examples of this.
What is a binomial?
(2g - 2h + 1) - (-3h + 4g)
-2g + h + 1
-3n2(-2n2 + 3n + 4)
6n4 - 9n3 - 12n2
(12t - 5)(12t + 5)
144t2 - 25
(4a + 7)(9a2 + 2a - 7)
36a3 + 71a2 - 14a - 49
Grouping together terms that are the same.
(ex: 5x + 10x = 15x)
What is combining like terms?
-3(5x2+2x+9) + x(2x-3)
-13x2 - 9x - 27
-9g(-2g+g2)+3(g3+4)
-6g3 + 18g2 + 12
(11z - 5y)(3z + 2y)
33z2 + 7yz - 10y2
(3b + 4)(2b2 - b + 4)
6b3 + 5b2 + 8b + 16