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Master Polynomial Components: Terms, Coefficients & Degrees

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

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Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

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Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with Polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

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Ex. 1:

Intro

- Hi, welcome to this question right here. In this chapter here we've got a couple of different things that we'll be asking you about the polynomial that we're looking at. Today we have a 2x to the power of 5, y at a power of 2, minus 3xy square minus seven, right? 
Here are the things that you might be encounter, that you have to answer the questions. So, the first one says "terms". 
What that means is what do you see, how many terms do you have. We actually have three different terms. We've got the 2x to the power of 5, we've got a 2x, 5 and y square min-- Oh, we actually don't need a minus sign and we can actually just go, a comma right there and we can go a negative 3, we have a second term right here, and finally we have the negative 7 at the very end. So, three different terms, right? 
The coefficients, it's actually just a number in front of your term, every single term. So, we've got a 2 for the first one. We also have the negative 3 for the second one, and the negative 7 for the third one, okay? 
The degree is the total number of the powers that you have on each term. This is a little bit tricky, if you look at the first one it's x power of 5 but it also has a y power of 2. So it's not just 5, you actually are gonna add up all the powers together so, 5 plus 2 gives you 7. So for the first term we have a 7 degree. The second term if we follow the concept here, it's just 1 plus the 2 so it give you a 3, right? Pretty straightforward. And the last one is a little bit tricky, there is no variables in it so, since there's no variables we just call it zero, The next one over here is called the leading term. Well, the leading term means that there is the greatest one-- there is a term here that has a highest power. So if you look at the degree here, which is a power, the first one has a 7 so that will be the leading term. You're just going to have to copy down the term with the highest power, so it's called the leading term. Now, for the leading term it has a leading coefficient which means the number of the leading term. So the number in the front of the leading term is just a 2. And sometimes they'll ask you for the degree of the entire polynomial, you have to pick the leading term. Or simply pick the highest degree in this polynomial. The degree that we have is 7, 3 and 0, so the greatest one will be 7. And that's it. Thanks for watching.

Polynomials can involve a long string of terms that are difficult to comprehend. So, before we dive into more complex polynomial concepts and calculations, we need to understand the parts of a polynomial expression and be able to identify its terms, coefficients, <a href='[[glossary.html|{"keyword":"Degree of a Polynomial","term":"Degree of a Polynomial"}]]'>degree</a>, leading term, and leading coefficient.

What are the parts of a polynomial?