Factorization

So the numerator is x plus 5 times x minus 1.

2x minus 3 times x plus b. b is minus 1.

So what is 20u squared v if we factor it out?

Yeah, 168.

If I distribute it in, you'd get back to this expression.

So you have x plus 9 times x minus 5 is equal to 0.

So this does simplify to that, so we have factored

The next thing to do, if we're going to decompose this into its components, we have to figure out the factors of the denominator right here, so that we can use those factors as the denominators in each of the components, and a third degree polynomial is much, much, much harder to factor than a second degree polynomial, normally.

I get 2x times x plus 3.

So there's two ways to do it.

In this case, you simply multiply each factor once to build 30.

That's what our numerator is equal to.

We have x plus 3 times x minus 3.

So here we've been able to factor it as well.

That's that term right there.

So what's the prime factorization of 28? It's 2 times 14. And 14 is 2 times 7.

This is a square of a binomial.

Or you could test for 0's.

So this right over here does simplify to i. And let's see if we can simplify the square root of 52, any.

Divided by, let's see, what two numbers?

And we're assuming that everything is an integer.

Now we have a nice quadratic equation, and we can factor this thing on the left hand side.

92 is 2 times 2 times 23.

And we're done!

So you get x squared plus 4x minus 45 is equal to 0.

This is probably the most common thing you'll see in a

Take any number say 30 and find all the prime numbers it can be divided into equally.

So let's see what we can do.

Sal Very, very interesting.

And just like that, we've grouped them and we're able to factor each of those groups, and then something interesting might pop out at you.

Which of the following shows 9t squared plus 12t plus 4 factored completely?

Both of these are 2.

Anyway, next problem.

This is a perfect square.

So we're done.

So a could be equal to 1, and b could be equal to 9.

So this could be 5 plus 10, and this could be 5 times 10.

So you get x equals six or x equals negative five.

So let's try to do that.

Or the other way we can do it is take the prime factorization of each of these numbers, and just say that the

And this is a crazy number and it's hopefully obvious you would not have been able to at least I would not have been able to get to this number just by factoring.

So let's figure out what it is.

So these are this or this these are both ways to factor this expression.

And then 15, let's do 15.