Gateway Quiz Reminder!
Remember: If you haven’t yet passed the
Gateway Quiz, you need to review your
last one with a teacher or TA in the
open lab and take the Practice Gateway
again so you can this week’s Gateway
Quiz. Take this seriously – you can’t
pass this class without a 100% score
on the Gateway.
Gateway Quiz Retake Times
(One new attempt allowed per week,
beginning March 7)
• Mondays
• Wednesdays
– 1:25 pm
– 2:30 pm
– 10:10 am
– 11:15 am
• Tuesdays
• Thursdays
– 10:10 am
– 11:15 am
– 1:25 pm
– 2:30 pm
SIGN UP IN THE MATH TLC OPEN LAB!
If NONE of the above times work for you…
email Krystle Mayer, Math TLC Coordinator (JHSW 201) or Dr.
Laura Schmidt, to set up a date and time.
Any Questions
on the 5.1
Homework?
Please
CLOSE
YOUR LAPTOPS,
and turn off and put away your
cell phones,
and get out your notetaking materials.
Section 5.2
• Polynomial vocabulary
Term – a number or a product of a number and
variables raised to powers
Coefficient – numerical factor of a term
Constant – term which is only a number
• A polynomial in x is a sum of terms all
•
involving the variable x or a constant term.
All the terms in a polynomial must have
whole number exponents for the powers of x.
In the polynomial 7x5 + x2y2 – 4xy + 7
There are 4 terms:
7x5, x2y2, -4xy and 7.
The coefficient of term 7x5 is 7,
The coefficient of term x2y2 is 1,
The coefficient of term –4xy is –4 and
The coefficient of term 7 is 7.
7 is a constant term. (no variable part, like x or y)
• A Monomial is a polynomial with 1 term.
•
•
for example: 7x2
A Binomial is a polynomial with 2 terms.
for example: 10xy+15
A Trinomial is a polynomial with 3 terms.
for example: x2+2x-3
Degree of a term
• To find the degree, take the sum of the
exponents on the variables contained in the
term.
• Degree of the term 7x4 is 4
• Degree of a constant (like 9) is 0.
(Why? because you could write it as 9x0, since x0 = 1)
• Degree of the term 5a4b3c is 8 (add all of the
exponents of all of the variables, 4+3+1=8,
remembering that c can be written as c1).
Degree of a polynomial
• To find the degree, take the largest degree of
any term of the polynomial.
• Degree of 9x3 – 4x2 + 7 is 3.
More examples:
1. Consider the polynomial 7x5 + x3y3 – 4xy
• Is it a monomial, binomial or trinomial? Trinomial
• What is the degree of the polynomial?
CAREFUL! It is 6, not 5.
2. How about the type and degree of these
polynomials?
• 5x4 + 10 Binomial, Degree 4
• 3x + 5 Binomial, Degree 1
 5 x 3 y 7  2 xy  10
Trinomial, Degree 10
3
 y2 + 6y – 8 Trinomial, Degree 2
 7x4y3z7 Monomial, Degree 14
Example from today’s homework:
Like terms
Terms that contain exactly the same variables raised
to exactly the same powers.
Warning!
Only like terms can be combined through addition
and subtraction.
Example
Combine like terms to simplify.
x2y + xy – y + 10x2y – 2y + xy =
(like terms are grouped together)
2
2
(x y + 10x y)+ (xy + xy) – (y – 2y) =
(1 + 10)x2y + (1 + 1)xy + (-1 – 2)y = 11x2y + 2xy – 3y
3
ANSWER:
x 5  8 x  40
4
• Adding polynomials
• Combine all the like terms.
• Subtracting polynomials
• Change the signs of the terms of the polynomial
being subtracted, and then combine all the like
terms.
Example
Add or subtract each of the following, as indicated.
1) (3x – 8) + (4x2 – 3x +3) = 3x – 8 + 4x2 – 3x + 3
= 4x2 + 3x – 3x – 8 + 3
= 4x2 – 5
2) 4 – (-y – 4) = 4 + y + 4 = y + 4 + 4 = y + 8
3) (-a2 + 1) – (a2 – 3) + (5a2 – 6a + 7) =
-a2 + 1 – a2 + 3 + 5a2 – 6a + 7 =
-a2 – a2 + 5a2 – 6a + 1 + 3 + 7 =
3a2 – 6a + 11
ANSWER: 2x2 + 8
• In the previous examples, after discarding
the parentheses, we would rearrange the
terms so that like terms were next to each
other in the expression.
• You can also use a vertical format in
arranging your problem, so that like terms
are aligned with each other vertically.
An example of “vertical” subtraction
12 z 2

  7z2
5z 2
 5z  9
 3z  7
 8 z  16
Back in Chapter 1 we saw problems like this:
“Subtract − 4 from 10.”
In these problems we would find 10 −(-4)=10+4=14.
We can do the same with polynomials:
Subtract (24x2+11) from (61x2+6).
This would mean we need to take:
61x2+6−(24x2+11)=
61x2+6 − 24x2-11=
37x2 − 5
Evaluating a polynomial for a particular value
involves replacing the value for the
variable(s) involved.
Example
Find the value of 2x3 – 3x + 4 when x = -2.
2x3 – 3x + 4 = 2(-2)3 – 3(-2) + 4
= 2(-8) + 6 + 4
=−6
Another example from today’s homework.
All we need to realize here is that we are given the time, t, and
need to substitute it into our given polynomial.
So -16t2+1180= -16(1)2+1180=-16+1180=
Remember perimeter is just the sum of all the
lengths of the sides.
-3x2 + 14x - 3
Reminder:
This homework on Section 5.2 is
due before the start of the next
class period.
You may now
OPEN
your LAPTOPS
and begin working on the
homework assignment.