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Elaborated on more cases of factorising equations (#22494)

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* Elaborated on more cases of factorising equations

-I decided to add other cases of factorising other algebraic equations that involves different values of the quadratic equation apart from 1

* Removing unnecessary <br> tags
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KevinatorTrainer5
2018-11-24 11:25:29 +11:00
committed by Randell Dawson
parent d55024c82a
commit 210a84b7e3
1 changed files with 16 additions and 7 deletions
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guide/english/mathematics/factoring-in-algebra/index.md
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@ -9,13 +9,22 @@ Factoring is how you take a quadratic in standard form and put it in factored fo
This method of factoring usually works best when a = 1. To do this when a = 1 you look at what two numbers add to equal b while also multiplying to c. Those two numbers will then be equal to d and t. This method of factoring usually works best when a = 1. To do this when a = 1 you look at what two numbers add to equal b while also multiplying to c. Those two numbers will then be equal to d and t.
#### Example 1:<br> #### Example 1:
x<sup>2</sup> + 2x + 1<br> x<sup>2</sup> + 2x + 1
Here you have to look for two numbers that multiply to 1 and add to 2. Those two numbers are 1 and 1. Then you put those numbers into the factored form like this:<br> Here you have to look for two numbers that multiply to 1 and add to 2. Those two numbers are 1 and 1. Then you put those numbers into the factored form like this:
(x + 1)(x + 1) (x + 1)(x + 1)
#### Example 2:<br> #### Example 2:
x<sup>2</sup> + 7x + 12<br> x<sup>2</sup> + 7x + 12
Here you have to look for two numbers that multiply to 12 and add to 7. Those two numbers are 3 and 4. Then you put those numbers into the factored form like this:<br> Here you have to look for two numbers that multiply to 12 and add to 7. Those two numbers are 3 and 4. Then you put those numbers into the factored form like this:
(x + 7)(x + 4). (x + 3)(x + 4).
#### Example 3:
2x<sup>2</sup> + 3x + 1
In some cases, the quadratic co-efficient, which is the value of a in ax<sup>2</sup>, can be greater than 1, where we need to consider how to create a number 3, through the combination of addition and multiplication with the factors of the quadratic co-efficient, and the co-efficient. So we consider the factors of 2 and 1 in '2' for the quadratic co-efficient, and the factors of 1 and 1 for the '1' in the co-efficient. We are required to multiply one factor of the quadratic co-efficient to another factor of the co-efficient, and consider the other case as well. So we multiply 2 from the quadratic co-efficient and 1 from the co-efficient, to receive a value of 2, while we multiply 1 from the quadratic co-efficient and 1 from the co-efficient, to receive a value of 1. Afterwards, we add the values of 2 and 1 to receive a value of 3, which corresponds to the linear co-efficient of 3x in the equation. Hence, you put these numbers into the factored form like this:
(2x+1)(x+1).
#### Example 4:
6x<sup>2</sup> + 11x + 4
In some cases, the quadratic co-efficient, which is the value of a in ax<sup>2</sup>, can be greater than 1, where we need to consider how to create a number 11, through the combination of addition and multiplication with the factors of the quadratic co-efficient, and the co-efficient. So we consider the factors of 3 and 2 in '6' for the quadratic co-efficient, and the factors of 4 and 1 for the '4' in the co-efficient. We are required to multiply one factor of the quadratic co-efficient to another factor of the co-efficient, and consider the other case as well. So we multiply 2 from the quadratic co-efficient and 4 from the co-efficient, to receive a value of 8, while we multiply 3 from the quadratic co-efficient and 1 from the co-efficient, to receive a value of 3. Afterwards, we add the values of 8 and 3 to receive a value of 3, which corresponds to the linear co-efficient of 11x in the equation. Hence, you put these numbers into the factored form like this:
(2x+1)(3x+4)