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

NY.A-APR.C.5+

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

auto-gen

Binomial theorem

Determining the equation of a polynomial function

NY.A-APR.D.7+

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Negative exponent rule

NY.F-BF.B.5+

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

NY.F-TF.A.3+

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Find the exact value of trigonometric ratios

NY.F-TF.C.8+

Pythagorean identities

NY.F-TF.C.9+

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

NY.G-SRT.D.10+

Law of sines

Ambiguous case: SSA triangles

Law of cosines

NY.G-SRT.D.11+

Applications of the sine law and cosine law

NY.G-SRT.D.9+

Area of triangles: 1/2 a*b sin(C)

NY.N-CN.A.3+

Complex conjugates

Complex Conjugates

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

NY.N-CN.B.4+

Polar form of complex numbers

NY.N-CN.B.5+

Operations on complex numbers in polar form

NY.N-CN.B.6+

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>

NY.N-CN.C.8+

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

Solving polynomials with unknown coefficients

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

NY.N-CN.C.9+

Word problems of polynomials

Fundamental theorem of algebra

NY.N-VM.A.1+

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

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

NY.N-VM.A.2+

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

Scalar multiplication of vectors

Equivalent vectors

NY.N-VM.A.3+

Word problems on vectors

Word problems relating guy wire in trigonometry

NY.N-VM.B.4+

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>

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

NY.N-VM.B.5+

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Unit vector

NY.N-VM.C.10+

Zero matrix

Identity matrix

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The Inverse of a 2 x 2 matrix

NY.N-VM.C.11+

Transforming vectors with matrices

Transforming shapes with matrices

NY.N-VM.C.12+

Finding the transformation matrix

NY.N-VM.C.6+

Notation of matrices

Adding and subtracting matrices

NY.N-VM.C.7+

Scalar multiplication of matrices

NY.N-VM.C.8+

Matrix multiplication

The three types of matrix row operations

NY.N-VM.C.9+

Properties of matrix multiplication

Plus (+) Standards

math

Ex. 1:

Ex. 2:

Ex. 3:

Intro

Intro to factoring trinomials when a is not 1

- 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.

Factoring 9x² + 3x - 2 using the cross multiplication method

Factoring 21x² - 41x + 10 using cross-multiplication

Factoring 15x² - 16x - 15 using cross multiplication

Factoring 8x² + x − 9 using cross multiplication

Factoring -36x² - 96xy - 64y² by extracting GCF and trinomial method

Factoring a complex trinomial with a common binomial factor

Factoring a trinomial with variable exponents and a negative leading term

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!