Video: Factorizing Polynomials

List all factors of π‘Β²π‘ž.

01:05

Video Transcript

List all factors of 𝑝 squared π‘ž.

These factors will be expressions that divide evenly into 𝑝 squared π‘ž. And then when multiplied together, they would give us back 𝑝 squared π‘ž. Now I’m not multiplying all the factors altogether at once together. However, there could be a combination of some that would give us back 𝑝 squared π‘ž.

So let’s begin with things that would go into 𝑝 squared π‘ž evenly: one, 𝑝, 𝑝 squared, and then two would be the highest exponent that we could go for 𝑝. So now let’s begin with π‘ž. π‘ž and then that’s it for π‘ž. There is no π‘ž squared. There aren’t enough π‘žs for π‘ž squared to go into that evenly.

So now we could put one 𝑝 and one π‘ž together into 𝑝 squared π‘ž. And then to make that a little larger, we can have 𝑝 squared and π‘ž go into there evenly. And this will be it. This will be all of the expressions that would go evenly into 𝑝 squared π‘ž. So these would be all of our factors.

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