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Master Polynomial Components: Terms, Coefficients & Degrees

NL.SO.1201AN1

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Understanding the number systems

Prime factorization

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

NL.SO.1201AN2

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Converting radicals to mixed radicals

Converting radicals to entire radicals

NL.SO.1201AN3

Product rule of 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

NL.SO.1201AN4

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

NL.SO.1201AN5

Solving polynomials with the unknown 

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

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

Using algebra tiles to factor polynomials

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

NL.SO.1201M1

Upper and lower bound

Upper and Lower Bound

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

NL.SO.1201M2

Direct variation

Identifying direct variations

NL.SO.1201M3

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

NL.SO.1201M4

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

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

NL.SO.1201RF1

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

NL.SO.1201RF2

Identifying functions

Function notation

Function notation (advanced)

NL.SO.1201RF3

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>

NL.SO.1201RF4

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)

Rate of change

NL.SO.1201RF5

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

NL.SO.1201RF6

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NL.SO.1201RF7

Parallel and perpendicular lines in linear functions

Applications of linear relations

Applications of linear equations

Academic Mathematics 1201

Algebra and Number

Measurement

Relations and Functions

math

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