Four lessons, two skills, and the second one is the reason the first one matters. First you learn to move expressions around that have more than one term in them without dropping any on the floor. Then you learn to put a pair of numbers on a grid and watch a whole equation turn into a line you can look at. Locke files everything under C for Careful, and this is the week where careful starts paying rent: an equation you can draw is an equation you can check.
What you have to be able to do
Name a polynomial and give its degree
Add, subtract, and multiply polynomials
Plot an ordered pair on the coordinate plane
Graph a linear equation, and tell a vertical line from a horizontal one on sight
The procedures
Adding or subtracting polynomials
If there is a minus sign in front of the second parentheses, distribute it through every term inside before you do anything else. This is where the points go.
Group like terms. Like means same variable at the same exponent, nothing looser than that.
Combine, and write the answer in descending order of exponent.
Multiplying polynomials
Every term in the first parentheses touches every term in the second.
Count your products before you simplify. Two terms times two terms gives four. If you wrote three, one got away.
Combine like terms, descending order.
Graphing a linear equation
Choose three values for x. Small ones. Zero is free.
Compute y for each and write the three ordered pairs.
Plot and draw the line. Use three points, not two: the third one is the witness that catches your arithmetic.
Worked
WORKED
Multiply (2x + 3)(x − 5). Four products: 2x·x, 2x·(−5), 3·x, 3·(−5). That gives 2x2 − 10x + 3x − 15. Combine the two x terms. ANSWER: 2x2 − 7x − 15
WORKED
Graph y = 2x − 1. x = −1 gives y = −3. x = 0 gives y = −1. x = 2 gives y = 3. ANSWER: plot (−1, −3), (0, −1), (2, 3) and draw the line through them
Terms
Term
Meaning
polynomial
a sum of terms, each one a number times a variable raised to a whole-number power
degree
the largest exponent on the variable anywhere in the polynomial
ordered pair
(x, y), across first and up second, and the order never changes
origin
the point (0, 0), where the two axes cross
Check yourself
1. Give the degree of 7x4 − 2x + 9
2. (3x2 + x) + (x2 − 5x)
3. Which one is the horizontal line, y = 5 or x = 5?
reveal answers
4 · 4x2 − 4x · y = 5
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 13, polynomials and the coordinate planealgebra 1 · oda