C1
What is a term?
an expression formed by the product of numbers and/or variables
What is a polynomial?
an algebraic expression consisting of one or more terms that are added or subtracted together.
What is the degree of a term?
the sum of the exponents on the variables in a term
What are like terms?
terms that have identical variables
a(x+y) = ax + ay
What is this called?
Identify the coefficient and the variable part: -de2f
coefficient: -1
variable part: de2f
State the degree of: 0.363ab3y
5
2(5a2 - 7a + 2)
10a2 - 14a + 4
What are two ways to classify a polynomial?
1. Number of terms it has
2. Degree
State the degree of: 19
0
Explain why the following simplification is incorrect.
(x2 - 3x + 1)(-5)
= x2 - 3x - 4
Not every term in polynomial is being multiplied by -5.
They have simply 'dropped' all brackets and evaluated: x2 - 3x + 1 - 5
correct: -5x2 + 15x -5
State the degree of: 3w - 6w2 + 4
2
(h + 5) - (3h - 8)
h + 5 - 3h +8
6a2 - 5a + 3 - 3a2 + 5a - 4
3a2 - 1
Consider the expression 3(x+5). Why do you need to use the distributive property? Why can you not just add the terms in the brackets first?
Answers may vary: e.g. Need to use distributive property because it allows us to expand algebraic expressions, which is what 3(x+5) is
We cannot add x and 5 because they are not like terms
3x2 - 4xy + 5y2 - 6 + 3x2 + 4xy - 2
6x2 + 5y2 -8
(x2 -2x +1) - (x2 - 2x - 5)
x2 - 2x + 1 - x2 +2x +5
= 6
Identify like terms:
2ab, 6ab2, 3ba, 2a2b, 0.67b2a
2ab, 3ba
6ab2 , 0.67b2a
Describe the process of subtracting one polynomial from another. Provide an example to support your explanation.
Add the the opposite of the polynomial that is being subtracted
(x-2) - (-x+6) = (x-2) + (x-6) = x-2+x-6 = 2x-8
-5h(3h2 - 7h - 2)
-15h3 + 35h2 +10h
A soccer team earns 4 points for a win, 2 point for a tie, and lose 1 point for each game that they lose.
Write an expression to represent the total number of points for the team.
4w + 2t - s
w= games won
t = tied games
s = lost games
An equilateral triangle has an unknown side length, x. Write a simplified expression for its perimeter.
P = x + x + x = 3x
(2/3)*(3m-2) - (3/4)*(8m-2)
(2m-4/3) - 24m/4 + 6/4
= 2m - 4/3 - 6m + 3/2
4[-3(r-5)+2r]
4[-3r+15+2r] = 4[15-r] = 60-4r
A swimming pool manufacturer installs rectangular pools whose length is thrice the width, plus 2.
Determine expressions for perimeter and area.
Perimeter = 2(3w+2+w) = 8w + 4
Area = w(3w+2) = 3w2 +2w