FACTORING POLYNOMIALS
OBJECTIVE
So let’s start with the definition of a quadratic
And that’s how we get “The Beast”
So, if there’s ever a time you can’t figure out the answer to a quadratic equation, use the quadratic formula.
Again, this is why it is important to have the elements in the quadratic equation labeled.
So, let’s see how this formula works out.
The quadratic equation works
every
single
time.
Example 1
And that’s how it’s done
Example 2
Example 3
Example 4
QUICK REVIEW OVER DIVISIBILITY RULES
So before we start factoring, it’s a really good idea to go over some divisibility rules, since we’re going to need them to factor.
So, let’s get started.
Numbers divisible by 2
A number is divisible by 2 if and only if it is even.
To be specific, a number is divisible by 2 if and only if the ones digit in the number is either a 0, 2, 4, 6 or an 8.
So a few examples of numbers that are divisible by 2:
2
14
268
3802
40246
524680
Numbers divisible by 3
Numbers divisible by 4
Numbers divisible by 5
A number is divisible by 5 if and only if its ones digit is 5 or 0.
So a few examples of numbers that are divisible by 5 are:
5
15
205
3550
40505
506060
7070705
Numbers divisible by 6
A number is divisible by 6 if and only if it is even and is divisible by 3.
Seems pretty obvious, but all you need to do is check if it is even, then add the digits together to see if it’s also divisible by 3.
So a few examples of numbers that are divisible by 6 are:
282
We know it’s even, and also 2 + 8 + 2 = 12 which is divisible by 3.
So it’s divisible by 6.
Another example:
5814
Again, an even number, so now we add the digits to see if it works:
5 + 8 + 1 + 4 = 18, which is divisible by 3.
So this number is divisible by 6.
NUMBERS DIVISIBLE BY 7
So, to be honest, finding out whether or not a number is divisible by 7 is actually harder than just dividing by 7. But for those of you who may think it’s easier to use the method, here it is:
To check if a number is divisible by 7: Take the last digit of the number, double it then subtract the result from the rest of the number. If the resulting number is evenly divisible by 7, so is the original number.
So an example of this would be:
343
3*2 = 6
So:
34 – 6 = 28
And of course, 28 is divisible by 7, so, so is 343.
Another example:
2401
1*2 = 2 and
240 – 2 = 238
8*2 = 16
23 – 16 = 7
And 7 is divisible by 7 (obviously) so 2401 is divisible by 7.
NUMBERS DIVISIBLE BY 9
Factoring a quadratic
Example 1
Factoring the quadratic
So let’s try another one
A few more examples so we can get the hang of it
Next up
One last one
That’s how you solve quadratics!
Now try some on your own