00:02
And here we have another one that looks like it is possible to factor.
00:08
The lead term is twice the degree of the middle term.
00:13
So that tells us we can factor it as we would just a normal quadratic.
00:18
With just a little bit of a twist, we're looking for two numbers that multiply to give us negative 10 that add to give us negative 3.
00:24
That's going to be negative 5 and positive 2.
00:28
So we're going to rewrite this middle term using negative 5 and positive.
00:32
Positive 2.
00:35
So x to the 6th minus 5x cubed plus 2x cubed minus 10.
00:44
And all i've done notice is i've rewritten this.
00:48
I've expanded it.
00:50
Instead of combining like terms, i'm expanding it using these two terms that i came up with here.
00:56
And i'm going to factor by grouping.
01:00
So i can factor an x cubed out of these first two, so that leaves me with x cubed times x cubed minus five.
01:08
And i can factor a two out of the second two, and that leaves me with x cubed minus five.
01:15
Then i can factor that as x cubed minus five times x cubed plus two.
01:23
So now i know that one of those has to be equal to zero, so either x cubed, cubed minus five has to be zero or x cubed minus two has to be zero so then we get x equals x cubed equals five x cubed equals two so x equals uh the cube root of five x equals the cube root of two um and we can't it can't be a negative because it can't be positive or negative because it's an odd root.
02:01
If it were a negative 5, then it would be, if x cubed equals negative 5, then x would equal a negative cube root of 5...