Bell Work: Multiply. Write the answer in descending order of the variable (4x + 2)(x – 5)

Answer: 4x - 18x

Lesson 50: Polynomial Equations, Ordered Pairs, Cartesian Coordinate System

In lesson 48, we noted that the degree of a term of a polynomial is the sum of the exponents of the variables of the term. xyz is a third-degree term

Also, we said that the degree of a polynomial is the same as the degree of its highest degree term. x + xy + m is a third degree polynomial 3

If two polynomial expressions are connected by an equals sign, we call the equation a polynomial equation.

The degree of a polynomial equation is the same as the degree of its highest degree term.

Example: What is the degree of the polynomial equation? x – 3x + 2 = 0 42

Answer: Fourth-degree polynomial equation

There is an infinite number of pairs of values of x an y that are solutions to any first-degree polynomial equation in two variables.

We will use the following equation to investigate. y = 2x + 4 If we assign a value to x, the equation will then indicate the value of y that is paired with the assigned value of x. for instance, if we assign to x a value of 2, then y = 2(2) + 4y = 8

If we give x a value of -5, then y = 2(-5) + 4 y = -6

We can replace x with any real number and use the equation to find the value of y that the equation pairs with this value of x.

The variable x, to which we assign a value, is called the independent variable. We see that in each case, the value of y depends on the value that we assigned to x. therefore, we call the variable y the dependent variable.

We found that, given the equation y = 2x + 4, if x = 2 then y = 8 as well as x = -5 and y = -6. To make this easier, we will write these as an ordered pair. It is customary to write in the form of (x, y), so (2, 8) and (- 5, -6) are two ordered pairs for the equation.

It is important to remember that in ordered pairs of x and y, the first number will always designate the value of x and the second number will always designate the value of y.

These coordinate points can be graphed on a Cartesian coordinate grid that contains an x and y axis as well as four quadrants.

The x axis is horizontal and the y axis is vertical. When graphing ordered pairs, the number written first is always the x coordinate and denotes the measure of the distance from the left or right. The number written second is always the y coordinate and denotes the measure of the distance either above or below the horizontal axis.

Example: Graph the following ordered pairs on a coordinate grid. (3, 5) (6, 0) (0, -5) (-2, -2) (-4, 1)

Answer:

HW: Lesson 50 #1-30