Algebra 2 unit 3.5

Factoring trinomials

• In Algebra 2, unit 3.5 is factoring trinomials.
• In factoring trinomials, you can perform one major task to find the factors of the trinomial or quadratic equation.

Factoring Trinomials

• Before we get started, you must know a critical term ...
• Quadratic Trinomial: a polynomial with 3 terms following the common formula of ax²+bx+c (Note: if an x³ is present, it is not a trinomial)

Factoring Trinomials

• To begin, factoring trinomials can be accomplished using one major and reliable method.
• Let's say we are trying to find the factors of the quadratic trinomial equation x²+5x+6.

Factoring Trinomials

• Firstly, we will find what numbers will add up to b, or 5, and multiply out to c, or 6.
• After writing down the original equation, we will write (ax²+y) and (z+c), having y and z being the factors of the equation.
• Once you have figured that the addends of 5 and the products of 6 are 2 and 3, you can now write this in parentheses.

Factoring Trinomials

• Writing them in parentheses should look like (x²+2x) and (3x+6) after using what was learned on the second point in the last slide, and the variables and numbers represented in the parentheses on that same point.
• Now, you should find what the greatest common factor, or GCF, of the values in the two groupings are.

Factoring Trinomials

• In the first grouping, (x²+2x), the GCF is x. In the second grouping, (3x+6), the GCF is 3.
• After finding the GCF's of the groups, we can divide the groups by their corresponding GCF and bring the GCF outside the parentheses.

Factoring trinomials

• After bringing the GCF's outside their grouping and dividing, the 2 groups should look like x(x+2) and 3(x+2).
• You will notice that you now have two groupings of (x+2) and a grouping outside the parentheses which can be written as (x+3).

factoring trinomials

• After finding the (x+2) and the (x+3), you can put them right next to each other to represent multiplication. Congrats, you have completed this problem!
• NOTE: If the problem has a value greater than 1 in the A spot, you will have to find the GCF of all 3 values, and write it next to the final answer.

Factoring Trinomials

• Now, here is an example I found from Math 10.
• The correct answer is at the bottom.

Untitled Slide

Review

• To review, let's complete a few more problems.

Review

• The first problem is x²+10x+16.

review

• If you got (x+2)(x+8), you are correct!
• Now solve n²-4n-48.

review

• If you got (n-12)(n+4), you are correct!
• Now solve y²-15y+56.

review

• If you got (y-8)(y-7), you are correct!
• Now solve p²+p-20.

review

• If you got (p+5)(p-4), you are correct!

Factoring TRinomials

• Congratulations! You now know how to factor trinomials.
• Now go practice your knowledge, and show off your skills.