ʕ•ᴥ•ʔ Polynomial Factoring with the Greatest Common Factor (GCF) w/ examples 2

To factor means to take out a common factor out from the expressions. In this lesson, we will try to do it by determining the greatest common factor among the terms of the expressions, and factor it out from each term.

Let's factor out this polynomial by taking out any common factors. Focus on the numbers first. Twelve, 18, and 30. What is the common factor between these three numbers? Let's find out. Twelve, 18, and 30. Since they are all even numbers, they must be divisible by 2. Twelve divided by 2, 6. Eighteen divided by 2, 9. Thirty divided by 2, you get 15. Now focus on these three numbers. Is there a common factor? Yes, they are all divisible by three. Six divided by 3 equals 2. Nine divided by 3 equals 3. Fifteen divided by 3, you get 5. Now, focus on the three numbers right here. Is there a common factor between these three numbers? No. Then we must stop right here. So the greatest common factor is 2 times 3, you get 6. So between the three numbers here, we can factor out six. Okay? Now, how about the p? Is p common for everyone here? Is p common for all three terms here? Let's see. First term we have p to a power of 7. Second term we have p to a power of 2. How about the third term? We don't have p. And guess what, then p is not common for everybody. So we cannot take out p. Because in order to take something out, everybody must have that thing. So if we ever want to take out p, than everybody, every term in the polynomial must have p. But in this case, the last term here is missing the p, and guess what, we cannot take out the p. So that's it. The only thing we can take out is the common factor is six. Then what do we have left? So now for the first term, 12, factor out 6, we have 2, right? Because 12 divided by 6 we have 2. And now, since we didn't take out any p, the p will stay. So here we have 2p to a power of 7. Now how about the second term? For the second term, Negative 18 divided by 6, we have negative 3. And once again, p will stay. Now for the third term, negative 30 divided by 6, we have negative 5. There we go, we're done. Okay? So we successfully factored this polynomial as the product of two polynomials. The first polynomial is 6, happened to be just a constant, , and the second polynomial right here 2p to a power of 7 minus 3p squared minus 5.

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Is this Canada grade 11 syllabus? Can someone tell each chapters.

[H-NMR]

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im 6 years late but infinitly grateful

[lilachu]

Would this be in foundation math 11 and principle math 11 classes? I don't know which one to take in school. All I know is I hate Geometry classes

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