This week in Precalculus 11, we tackled a really cool topic: factoring trinomials. Specifically, we learned how to factor trinomials of the form ax^2 + bx + c. I chose this topic because it’s super handy and helps us solve lots of math problems.

Why I Chose This Topic:

Factoring trinomials might sound fancy, but it’s actually a pretty practical skill. It’s like learning a secret trick that helps us break down complicated math problems into simpler parts. Once we know how to do it, we can use it in all sorts of math situations, from algebra to calculus and beyond!

What I Learned:

Factoring trinomials basically means splitting them into two smaller expressions, called binomials, that we can multiply together to get the original trinomial. Let’s break down the process with an example:

We looked at product and Sum in the last blog now we can use that to factor.

Step 1: Find the factors of ‘a’ times ‘c’

Take a trinomial like x^2 + 5x + 4. First, we find the product of the first and last numbers: 2 * 3 = 6.

Step 2: Determine the binomials

Now, we need to find two numbers that multiply to 4 and add up to the middle number, which is 5 in this case.

Step 3: Factor by grouping

We group the terms and look for common factors. Let’s do it:

x^2 + 5x + (4,1)

We can split the middle term into two parts that multiply to give us 4 and add up to 5.

So, we rewrite it as:

(x^2 + 4x) + (1x + 4)

Now that we have this we can write this as

(x + 4)(x + 1)

And just like that, we’ve factored the trinomial!

 

Now we can use another method called the “Area Model”

Area model or Box method is something we can use to factor trinomial when you are not able to find the answer using the Product and Sum.

lets see how we can do that-

Seeing this problem we can see that we cannot use the Product and Sum in this example so for this we will use the Area Model.

So the box method is when you use a 2×2 box to solve the equation.

When we use the box method the x^2 is on the top left corner and the number without x is on the bottom right corner.

 

 

 

When we diagonally multiply, the product is the same.

So, in this case product is 30x^2 and sum is 17x.

 

 

once we have all the boxes filled and checked we can now find common factors horizontally and vertically both sides and write them on top and the side of the box.

 

now we have it factored with one binomial on the side and the other one on top.

 

 

NOTE- if there is a minus sign on the top right corner the common factor vertically is going to be negative, which is the same for the bottom left corner horizontally.

 

Learning how to factor trinomials might seem tricky at first, but it’s a really useful skill. It helps us simplify problems and understand math better. So, keep practicing, and soon you’ll be a factoring pro!