00:01
In this problem, we're being asked to factor each binomial.
00:03
So let's start with part a.
00:05
Well, remember, at any time when we're factoring, the first thing we need to try and look for is a gcf, our greatest common factor.
00:11
Well, the greatest common factor for 5p squared, and for 20, is 5.
00:16
So i'm going to factor out a 5.
00:18
And then i need to divide both of my terms by 5.
00:21
Well, 5p squared divided by 5 is just p squared, and 20 divided by 5 is positive 4.
00:28
Now, i cannot factor any forward anymore because if you looked inside our parentheses, we have p squared plus four.
00:36
Well, that's the sum of two squares, which cannot be factored.
00:40
So our final answer for part a is five times the quantity of p squared plus four.
00:46
Now let's take a look at part b.
00:48
Again, when we're factoring, first thing we have to look for is the greatest common factor, which in this case is five.
00:55
So i'm going to divide both my terms by five.
00:58
Well, 5p squared divided by 5 is p squared, and negative 20 divided by 5 is negative 4.
01:06
Now, let's look at what we have left.
01:08
Well, inside our preemphasis, we have p squared minus 4.
01:11
Well, that's the difference of two squares, because the square root of p squared is p, and the square of the 4 is 2.
01:17
So this can be factored further.
01:19
So i simply leave my gcf on the outside.
01:22
I'm going to have my two binomials.
01:25
So remember, the first term in both binonials is the square root.
01:29
Of the first term p squared.
01:31
Well, the square root of p squared is p.
01:33
So both factors will start with p.
01:37
Our last term in both will be the square root of the last term.
01:40
Well, the square root of four is two, so they will both end with two.
01:44
And then remember, they're signs.
01:46
One is going to be positive, and one will be negative...