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Master Polynomial Components: Terms, Coefficients & Degrees

Grade 10 Math: Master Essential Skills & Concepts

Operations on powers with integral exponents

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Product rule of exponents

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Prime factorization

Evaluating and simplifying radicals

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Functions and relations: connecting data, graphs, and situations

Introduction to quadratic functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Linear functions: slope and equations of lines

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

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

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

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

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Systems of linear equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Linear programming word problems

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Multiplication of polynomial expressions

What is a polynomial?

Classifying Polynomials

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Polynomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring difference of cubes

Factoring sum of cubes

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Primary trigonometric ratios

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Use tangent ratio to calculate angles and sides (Tan = o / a)

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

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Foundations of Mathematics and Pre-Calculus 10

math

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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade10math.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