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### Course: Get ready for Precalculus>Unit 2

Lesson 4: Factoring higher degree polynomials

# Factoring higher degree polynomials

Factoring a partially factored polynomial and factoring a third degree polynomial by grouping.

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• What are some common real world applications for this? •   You may need to use factoring often if you have a real world job. If you decide to become an economist, statistician, engineer, mathematician, or any kind of physical scientist. You would commonly use factoring. For example, data containing complex algebraic fractions can look extremely difficult. You would need to factor in order to simplify and make use of the data in an easier way. Basically, it will make your life more simple though it seems annoying right now. Hope this helps!
• So I have watched video after video and I also took notes. • The first example is set up like this:
(6x^2 + 9x)(x^2 - 4x +4).
What Sal did was take the GCF out of each set of parentheses. As you may have seen in previous videos in this unit, the way to find the GCF from the left set of parentheses is to find the GCF of the coefficients. In this case, the GCF of 6 and 9 is 3. The next step to find the GCF of the full terms is to look at the variables. There is an x^2 and an x on its own. Let's list out the factors:
x^2 factors are 1 and x^2, and x and x since those numbers multiply to get to x^2.
x factors are x and 1.
We can see by looking at the factors that the greatest factor is x (assuming x is greater than one, but we aren't going to worry about that because we don't have to solve for x in this problem). Since the GCF of the variables is x and the GCF of the coefficients is 3, we multiply them together to get 3x.
Now that we have our GCF for the left set of parentheses, we can divide everything in the left set by our GCF, and bring the GCF out of the parentheses. This is better illustrated in the video Taking common factor from binomial, under Taking common factors earlier in this unit, so I am going to skip explaining that part.
(6x^2 + 9x)/3x is (2x + 3). Now we bring the 3x to the outside of the parentheses to get 3x(2x + 3).
That's one half of the equation. The other we can tell just by looking that it is a perfect square, so we split it apart as shown in the first unit called Polynomial Arithmetic, with the video Polynomial special products: perfect square.
Splitting (x^2 - 4x + 4) into its square roots results in this:
(x - 2)(x - 2).
The next step is to put all of that together. This gets us
3x(2x + 3)(x - 2)(x - 2) Since you can no longer factor this equation, it is in simplest form. That means we just leave it like that.

The second example is a little different:
x^3 - 4x^2 + 6x - 24.
The easiest way to solve this is to factor by grouping. To do that, you put parentheses around the first two terms and the second two terms.
(x^3 - 4x^2) + (6x - 24). Now we take out the GCF from both equations and move it to the outside of the parentheses.
x^2(x - 4) + 6(x - 4). As you can see, the sets of numbers inside the parentheses are the same. This means that we can take the numbers outside the parentheses and put them in their own set.
(x^2 + 6)(x + 4). When you multiply that out, you get x^3 - 4x^2 + 6x + 24. That means that this is as simplified as you can get your equation. Also, it means you just did all of that math to get a circle (start in one place, end in the same).
• I'm still confused on this still after watching an hour. • At he mentions there are other videos that he assumes we've already seen. Which videos are they? • im confused on how he does it is there more then one way to factor this same problem? • Is there a way to get like a crash course on factoring polynomials? I really need to understand it, and fast. • Is anyone else confused about this concept?! As a hormonal teenager this is making me feel a little on edge and kind of frustrated. Explanation please!!😶 • at , is there an easy way to come up with two numbers whose is four and whose sum is negative four? He seems to figure it out very quickly so is there a video that I so happened to missed?   