Math 10, Uncategorized

Week 7 – Math 10

March 14, 2020

Factoring

Factoring is the opposite of expanding like how division is the opposite of multiplication. There’s a three step method to find the answer when factoring with variables. This technique (taught by Mrs. Burton) is called Factoring 1,2,3.

Factoring:

  1. Find if anything is in common (GCF)
  2. If there are two terms and they’re both perfect squares use the conjugate technique
  3. If there are three terms and a simple trinomial ({x^2} + x + #) the use the simple trinomial technique
    • Double check step two before continuing.

Factoring With The GCF

For this technique you can start with a polynomial that looks like (27x+3) or ({4x^2} + 16x + 32)

Step 1. Find the GCF
Example: ({4x^2} + 16x + 32)
In this equation we can ask what factor do they all have in common?
For this equation the answer is 4.

Step 2: Divide the numbers in the equation by the GCF
Example: (\frac{4x^2}{4} + \frac{16x}{4} + \frac{32}{4}
*Note if we divide 4 from the numbers on the inside we need to multiply 4 on the outside.*

Step 3: Write out the answer and check for step 2 and 3 of factoring 1,2,3
Example: 4({x^2} + 4x + 8)

Factoring With Conjugates

To factor with this technique the all the numbers in the equation must be perfect squares and the last term must be negative/subtraction.
Example 1: {25x^2} – 49 -> (5x-7)(5x+7)
We know that this number is a conjugate because it has no middle term. In this equation because the 25 and 49 are perfect squares we know that both terms are the same in both Binomials, and because the second term is negative we know that the second term in one of the Binomial must be negative and the other is positive. A negative times a positive is negative.

Factoring Simple Trinomials

In a simple trinomial the first term is always x times x, the second term is the result of two terms added together, and the third term is the product of two terms.
Example: ({x^2} + 10x + 24) -> (x+6)(x+4)
The first term in the simple Binomials and simple trinomial will always be the same. To find the second number in the simple Binomial we first must find all the numbers that multiply to 24 then the two numbers that multiply to 24 must also add to 10.

Factoring 1,2,3 Example

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