00:01
So here is problem 11 from chapter 2.
00:04
We are asked to solve the equation by factoring.
00:08
So we have on the left a binomial equal zero.
00:13
So let's start by checking to see whether there's a greatest common factor among the two terms.
00:19
So we've got a 3x squared and a 75.
00:21
So those are both divisible by 3.
00:23
So we can factor out a 3.
00:27
And then what's left inside the brackets is what we get when we're, divide each term by the gcf, the greatest common factor that we factored out, that three.
00:38
So we're left with now x squared minus 75 divided by 3 is 25.
00:46
So that is now what we look at and we go, can we factor a bracket any further? so now we see we have x squared, which is a perfect square, minus 25, which is also a perfect square.
01:01
So what we have here is what's called a difference of squares.
01:05
So that factors into two binomials where in each bracket we have the square root of the first term in the first position.
01:20
So the square root of x squared, square root of x squared is x.
01:26
So we're going to have an x in the first position in both binomials.
01:32
And then we take this.
01:34
Square root of 25, which is 5...