00:01
So whenever solving a polynomial inequality, the first thing i'm going to do is set the polynomial equal to zero.
00:06
So i know that the product, x minus 4 times x plus 1 equals 0.
00:11
And by the zero product property, i know that x minus 4 equals 0 and x plus 1 equals 0, i can subtract, add 4 to both sides.
00:19
So i have positive 4 is when my value is 0 and when i subtract 1, negative 1.
00:25
Now from this, i can compose a table of values, right? everything approaching negative infinity to negative 1.
00:32
Do i hit negative 1? well, x equals negative 1 makes the product 0, and in my inequality i'm equal to 0, so i do hit negative 1.
00:40
And then all the values between negative 1 and 4, and then 4 to infinity.
00:44
So from my 2 zeros, i have 3 intervals.
00:49
And on each interval, i'm going to pick a test point...