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Master Factoring Polynomials: ax^2 + bx + c | Step-by-Step

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

<h2>What is in grade 10 math?</h2>
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Ex. 1:

Ex. 2:

Ex. 3:

Intro

- Hi, welcome to this question right here. So, here we are trying to do some factoring but this time we've got a number in the front of x square. So, this is a little bit harder, but this is a trick, okay? 
Before you may start with the bracket, bracket. We're gonna do a little bit something that's called a little bit of guessing, all right? First thing you do is, you have to think of the factor that gives you 9, the factors of 9 basically, we've got 1 and 9, 3 and 3. Now, personally I don't like the 1 and 9, I'd like to go with the 3 and 3. So, let's just go and do that, let's put the 3 and 3 just below the 9, okay? 
Now, on the other side over here, we have to look on the 2 over here. Now, the factors of 2 is just 1 and 2. So, let's say we're just gonna do randomly. Let's put 1 and 2 down. So, let's put a 1 right here, and then put a 2 right here. Now, the trick is you have to do something that is called cross multiply, all right? Why are we doing this? You will see. 3 times 1, or the cross multiplying here, 3 x 1 is 3, and 3 x 2 is a 6, okay? 
These two numbers here, you have to add them up to get you a positive 3. So, what that means is, this must be a 6 positive, and this one here must be a negative, a negative 3. So, where this negative come from? It has to come from the negative 1 at the front. Now, how does it make sense? Well, let's all go back to the very beginning. These two numbers here are the factors of 9. So what that means is 3 x 3 gives you the 9, which is true. These two numbers here are the factors of the 2, but remember this one? It was a negative, right? So 1 would had to be a negative, but we weren't sure yet so, that's why I just do the math, and then look at the answer over here, I know by adding or subtracting I need to get the 3, So, that means a negative 3 is here and that means this must be a negative 1, So, here let's just double check, 2 times negative 1 does give me negative 2. Cross multiplying 3 x negative 1 is negative 3, 3 x 2 is 6. By adding them I do get the middle number. Why is everything here and it makes sense perfectly, the final answer is just going to be bracket, bracket. But what do you put in the brackets? It's easy, take a look at the first one, that's your first bracket right there. You just have to add the x in by yourself. And this is a negative 1, so why not just put a negative 1 down there? The second one is the second bracket down here, it's a 3x again and you get yourself a positive 2. And that's it, there you go. That's the factor of that trinomial out there. Thanks for watching.

Before starting this lesson, check your understanding on how to factor \({x^2 + bx + c}\\  \) we talked about in the other lesson first. The coefficient, a, in front of \({x^2}\\  \) can make it a bit more challenging, but we will show you the tricks to make it easy!

Factoring polynomials: \(ax^2 + bx + c\)

Factorising polynomials: \(ax^2 + bx + c\)

Factoring polynomials in the form of ax^2+bx+c

Factoring polynomials: x^2 + bx + c