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• Expression: Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.

• Equation: says that two things are equal. It will have an equals sign "=“

• what is on the left (7 + 2) is equal to what is on the right (10 − 1)

Polynomials:

• an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)

• Polynomials can have constants, variables and exponents, but never division by a variable

Polynomial:

• Monomial: A monomial is a variable, a real number, or a multiplication of one or more variables and a real number with whole-number exponents

• Binomial:

• Trinomial:

Binomial 2 2x + 5, x2 - x, x - 5

Trinomial 3 x2 + 5x + 6, x5 - 3x + 8

Standard form

• (Linear) Standard form: written with highest degree first (the degree is the exponent)

• y = mx + b

Polynomials are also sometimes named for their degree:

• a second-degree polynomial, such as 4x2, x2 –

9, or ax2 + bx + c, is also called a "quadratic"

• a third-degree polynomial, such as –6x3 or x3 – 27, is also called a "cubic"

• a fourth-degree polynomial, such as x4 or 2x4 – 3x2 + 9, is sometimes called a "quartic"

• a fifth-degree polynomial, such as 2x5 or x5 – 4x3 – x + 7, is sometimes called a "quintic"

Add and subtract polynomials

• To add polynomials we simply add any like terms together

• To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual

• Example #1: add the polynomials • 2x2 + 6x + 5 and 3x2 - 2x – 1 • Example#2: subtract the polynomials • (x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6)

Polynomials:

• Multiply and divide: see examples on board – We will either use F.O.I.L or box method and then there is

always distribution

• Law of exponents: see sheet (handout that I provide for you)

• You must know what a term is when multiplying polynomials. It is because the goal is to multiply each term of the polynomial on the left by each term of the polynomial on the right and then adding the whole thing!

• http://www.basic-mathematics.com/multiplying-polynomials.html

Multiplying Polynomials (mainly binomials)

• F.O.I.L

• First

• Outer

• Inner

• Last

• Box method

Example Problem #1

• The area of a fence around a quadrilateral-shaped pasture is 3a2 + 15a + 9 long. Three sides of the fence have the following lengths:

5a

10a – 2

a2 – 7

• What is the length of the fourth side of the fence?

Example Problem #2

• A small town wants to compare the number of students enrolled in public and private schools. The polynomials below show the enrollment for each

• Public -19c2 + 980c + 48,989

• Private 40c + 4046

• Write a polynomial for how many more students are enrolled in public school than private school?

Example Problem #3

• Area of a trapezoid is found using the formula A = (1/2)h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the bases.

• The height is 4

• Top of trapezoid is x – 3

• Bottom of trapezoid is x + 7

Factoring

• Greatest common factor (GCF)

• A*C (grouping)

• Criss-cross

• Slip and slide

• Quadratic formula

Review

• https://www.superteachertools.net/jeopardyx/jeopardy-review-game.php?gamefile=1393196775#.VGkpyvnF-8A

• Polynomial review game