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Master Polynomial Components: Terms, Coefficients & Degrees

Grade 12 Math: Master Advanced Concepts & Skills

Geometric explorations

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Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Graphical representations of polynomial, logarithmic, exponential, and sinusoidal functions

Graphing exponential functions

Graphing transformations of exponential functions

Graphing logarithmic functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Regression analysis

Equation of the best fit line

Combinatorics

One to one functions

Combining transformations of functions

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Function notation (advanced)

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Operations with functions

Inequalities of combined functions

Inequalities of Combined Functions

Even and odd functions

Difference quotient: applications of functions

Odds, probability, and expected value

Applications of linear relations

What is a polynomial?

Classifying Polynomials

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Probability of independent events

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Reading and drawing Venn diagrams

Probability with Venn diagrams

Financial planning

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Binomial theorem

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

Permutation vs. Combination

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Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics 12

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade12math.png

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?

Characteristics of polynomials

Equivalent expressions of polynomials