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# Factoring perfect squares: shared factors

Sal finds the binomial factor shared by 4x^2+12x+9 and 4x^2-9.

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• At , why did he just ignore 2*2*3x and not include it in his factoring?
• He hasn't actually ignored the 2*2*3x. Remember, factoring a quadratic expression is basically reversing FOIL (First, Outer, Inner, Last). He factored each term in 4x^2 + 12x+9, noticing that the first and last terms are perfect squares. The first term = 2x times 2x. the last term = 3 times 3. If this expression = the perfect square of one binomial, then the middle term will equal 2 times the first term times the last term. This is the Outer and Inner parts of FOIL. In symbols, 12x = 2(2x times 3). It does.
This tells him that 4x^2 + 12x + 9 = (2x+3)^2
Test the result by applying FOIL to (2x+3)(2x+3). I found that doing this while really thinking about what is happening helped me to understand factoring quadratic equations.
• The energy points just show how many videos you have watched and questions you have answered. It is a way of "gamifying" and encouraging users to keep learning more.
• in he said that it was -3^2. -3^2=-3*-3=9≠-9. -9 was up there, where as 9 wasn't. Why is that, and why did he do that?
• Sal has a negative 9. To have a negative 9, the factors must be one negative and one positive.

Also, (-3)^2 = -3(-3) = +9
When you have -3^2, the exponent applies only to the 3, not -3. Thus: -3^2 = -(3*3) = -9

Hope this helps.
• I am more comfortable with factoring quadratics by grouping. Is that okay? Is there any type of special circumstance that you have to factor using the perfect squares?
• Yes, factoring by grouping would work. However, it can take longer that using / recognizing that you have a perfect square trinomial and using the pattern to do the factoring.

There are also later topics / concept that require that you understand the relationship between perfect square trinomials and their factors. There is a process called "completing the square" that leverages this relationship. It is used to solve quadratic equations and to form / understand the equation of a circle.
• What is the FOIL method?
• This is a way to remember how to multiply two binomials.
Have a look in the Algebra 1 material
under Introduction to Polynomials
in the 4th video in the section Multiplying Binomials.
• What about (a+b)^3 and (a+b)^4,(a+b+c)^2,(a+b-c)^2,(a-b-c)^2,a^3+b^3,a^4+a^4 and a^3-a^3?
Where are explanations video?
(1 vote)
• Right now, you should only really worry about quadratics and the squares of binomials.

(a+b)^2 = a^2+b^2+2ab.

When the time comes, you'll learn about polynomials to the third degree and whatnot.
(1 vote)
• Can any positive number have negative factors? And x= 16^1/2 gives +4/-4 or both
(1 vote)
• Wait is the answer to the problem 2x + 3 or (2x + 3) or does it matter?
(1 vote)
• It doesn't matter. The parentheses only matter when the binomial is part of a larger expression.
(1 vote)
• Is there a video for factoring perfect squares that have a negative sign in it, like 3x^2 -24x +48? If not would someone be able to show me how to do that? Thank you.
(1 vote)
• What is the definition of the term Binomial factor?
(1 vote)
• It is a factor of a polynomial that has 2 terms.
If you have the trinomial: x^2-5x+6, it factors into the binomials: (x-2)(x-3). Each is a binomial factor.