Vocabulary Check
What is a polynomial?
A polynomial is an expression made up of terms that include variables raised to whole-number powers and coefficients
Simplify: (3x + 2) + (4x + 5)
7x + 7
(5x+3)−(2x+1)
3x + 2
2x + 3x
5x
A rectangle has length 3x+23x + 2 and width 2x+12x + 1. What is the perimeter?
Perimeter = 2(3x+2+2x+1)=2(5x+3)=10x+6
What is a term in a polynomial?
A term is a single part of a polynomial, like 3x2 or -5.
2x2 + x + x2 + 3x +1
3x2 + 4x +1
(4x2 + x) − (x2 + 2x)
3x2 − x
4x2 + 2x2
6x2
A student earns 4x + 5 dollars on Monday and 3x + 2 dollars on Tuesday. What is the total?
Total earnings = 4x + 5 + 3x + 2=7x + 7
What does “like terms” mean?
Like terms have the same variable(s) raised to the same power(s).
5x2 − 2x + 3 + 3x2 + x − 4
8x2 − x − 1
(6x2 − 3x + 2) − (2x2 + x − 5)
4x2 − 4x + 7
5x2 − 3x + 2x2 + x
7x2−2x
A car travels 5x2 + 3x km in the morning and 2x2 - x km in the afternoon. What is the total distance?
Total distance = 5x2 + 3x + 2x2 − x = 7x2 + 2x
What is the degree of a polynomial?
The degree of a polynomial is the highest exponent of the variable.
2a2 + 3a − 5 + 4a2 − a + 6
6a2 + 2a + 1
(3a2 + 4a − 1) − (a2 − 2a + 3)
2a2 + 6a − 4
3a2 + 2a − a2 + 4a
2a2 + 6a
A box has height x2 + 2x, and another box has height 3x2 - x. What is the difference in height?
Difference in height = x2 + 2x − (3x2 − x) = −2x2 + 3x
What is the leading coefficient in 4x3 + 2x − 7?
The leading coefficient is 4 (from the term 4x3).
x3 + 2x2 − x + 1 + 3x3 − x2 + 4x − 2
4x3 + x2 + 3x − 1
(x3 + 2x2 − x + 1) − (x3 − x2 + 3x − 4)
x2 − 4x + 5
x3 + 2x2 − x + 3x3 − x2 + 4x
4x3 + x2 + 3x
A company’s revenue is 6x2 + 4x - 3, and expenses are 2x2 + x - 5. What is the profit?
Profit = Revenue – Expenses = 6x2 + 4x − 3 − (2x2+ x − 5) = 4x2 + 3x + 2