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Master Dividing Polynomials by Monomials: Step-by-Step Guide

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

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

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

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

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of 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

Introduction to 3-Dimensional Objects

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

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Parent Assignments

Challenge Zone

Foundation Review

EQAO Grade 9 Principles of Math

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Intro

Dividing 6x² minus 24x by 3x using algebra and area model

Dividing a binomial with negatives by negative x using algebra and models

- Hi and welcome to this question right here. So we've got a 4x squared plus 12xy divided by 2x. Now if you're trying to divide a bunch of variables and there's two terms on top divided by something. It's probably better if you just separate them, okay? I didn't change the question. I just simply just give the 2x back to their own position. So basically we have 4x squared for the front divided by 2x and we also have the 12xy divided by 2x, okay? 
You can actually do that. What happened is it looks easier now because you can actually just do the calculations individually. We have four over two gives me two. X squared over x gives you 1x . 
Now remember what happened is during the work we are actually subtracting the exponents, okay? So two minus one is left with just 1x. Then we go back to the question for the next part. We get a plus sign right there. So just put a plus sign. What's 12 over two? We get a 6. This is one right here. This is x power one and that's x power one. If you do the subtraction because they're the same variable, one minus one will give you how much? That's a zero, right? Anything to the power of zero is simply just a one. So you just leave nothing. Then you give yourself a y at the very end. So down one, has nothing to do, so you just have to bring it down, okay? So there you go. That's your final answer right here. 2x plus 6y is your final answer. Thanks for watching.

Dividing Polynomials by Monomials: Essential Algebra Skills

What You'll Learn

Distribute division across each term when dividing polynomials by monomials

Apply exponent laws to subtract powers when dividing variables with the same base

Simplify polynomial expressions by dividing coefficients and variables separately

Recognize that division must be applied to every term in the polynomial

What You'll Practice

Dividing binomials and trinomials by monomials with numerical and variable terms

Working with expressions involving decimals and fractions in division

Solving word problems involving polynomial division with volume and dimensions

Using area models to visualize polynomial division

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

9 Video lessons

Learning resources

Skills

Polynomials

Monomials

Division

Distributive Property

Exponent Laws

Simplification

Algebra