Week 5 : Factoring Polynomials

This week we start to learn the new unit. That’s factoring polynomial expressions
Let’s star with the first example :
$x^2-4x-12$

If the leading coefficient is 1 like this. The process to do this exercise is so easy. The only two numbers have sum is −4 and that multiply them to give −12 are −6 and 2. So if you wanna find the number have sum = -4 from -12 you can try by this way :
-12×1
-6×2
-4×3
-3×4

So right now we will chosse one into them. Which ones will help us get -4. That’s -6 and 2 ( -6+2=4 ).

So let’s try with another example :

$x^2-10x+24$

It has a leading coefficient of 1, find two numbers with a product of 24 and a sum of −10.

Same as above exercise we will try each number multiply to get 24

24×1
12×2
8×3
4×6

Which one will help us get 10. Thats last. 4+6

Then we will get $x^2-4x-6x+24$. So we got it!!!!

Example 3 : $2x^2+9x-5$

This example diffirent with two example exercise cause the leading coefficient is not 1 ($x^2$) . We still find two numbers, and those numbers will still add up to 9.

$2x^2+10x-x-5$

RIght? Cause 10x-1=9x. Its same but i change it to be easy to a simpler equation

Then we will distribute them together then get :

2x(x+5)-1(x+5)

Between $2x^2+10x$ the same point is 2x then we will divide each number for 2x to get (x+5)

Same way with -1(x+5)

Finally we will make it simpler by the way, they have same (x+5). We will make the general figures between them.

(x+5)(2x-1)

Done!!!!!