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Master Solving Polynomials with Unknown Coefficients

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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All our lessons are taught by experienced grade 10 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics and Pre-Calculus 10

math

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Ex. 1:

Intro

- Hi, welcome to this question right here. So, we're trying to figure out the possible "k" that can go in here. We're doing the trinomial factoring. If you remember that in order to figure this out, there's a bracket, bracket to start off and you put an "x" here. Now, the number that goes here and here is basically this. You need to figure out the factors of 8 first so, two numbers, two numbers that'll give you the 8. What do we have? We've got 8 and 1, right? So, we've got 8 x 1. We also have 2 x the 4, okay? 
So, if you put 8 and 1 here, you have to give a negative 8 so one of them has to be a negative. It could be negative 8 or 8, negative 1, right? Those are two possible choices that would give you a negative 8 if you multiply them together. Now, if you add them together, you get yourself a possible of, this would be a negative 7 and this would be a 7. And that's what that "k" would represent. We're not here to figure this out, we're here trying to figure out the possible "k"s. So, for the first "k" that we have, we have plus minus 7. Now, on the other side we have 4 and 2, to try right? Or 2 and 4. Now, 4 times 2 does give me 8, right? But, one of them has to be negative. It could be a negative 2 and 4, or 2 and negative 4, okay? Now, if you add them together... Okay? It's either we've got a 4 minus 2 which is going to be a 2, or 2 minus 4 which is going to be a negative 2, right? 
Those are your possible "k"s that would go right in there, OK? So, more "k"s we have, we've got plus minus 2 and those are your four possibilities, okay? 
Thanks for watching.

In this lesson, we will be doing trinomial factoring to find all possible answers for the unknowns in the term in the middle of the polynomials. By doing so, we will need to reverse the process of FOIL so that we can convert the trinomials into two binomials.

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

How to find the unknown coefficients in polynomials?