Question

Factor 3x² + 10x + 8 using earmuff method.

Answer 1

`3x^2+10x+8`

To factor the above quadratic equation using Earmuff Method, here are the steps:

1. Multiply the numerical coefficient of the degree 2 with the constant term.

`3*8=24`

2. Find the factors of 24 that when added will result to the middle term 10.

1 and 24 = 25

2 and 12 = 14

3 and 8 = 11

6 and 4 = 10

Upon going over the factors, we will find that 6 and 4 are factors of 24 and results to 10 when added.

3. Add "x" on the factors 6 and 4. We will get 6x and 4x.

4. Replace 10x in the original equation with 6x and 4x.

`3x^2+6x+4x+8`

5. Separate the equation into two groups.

`(3x^2+6x)+(4x+8)`

6. Factor each group.

`3x(x+2)+4(x+2)_{}`

7. Since (x + 2) is a common factor, we can rewrite the equation into:

`(3x+4)(x+2)`

Hence, the factors of the quadratic equation are (3x + 4) and (x + 2).

Another way of factoring quadratic equation is what we call Slide and Divide Method. Here are the steps.

`3x^2+10x+8`

1. Slide the numerical coefficient of the degree 2 to the constant term by multiplying them. The equation becomes:

`\begin{gathered} 3*8=24 \\ x^2+10x+24 \end{gathered}`

2. Find the factors of 24 that results to 10 when added. In the previous method, we already found out that 6 and 4 are factors of 24 that results to 10 upon adding. So, we can say that the factors of the new equation we got in step 1 is:

`(x+6)(x+4)`

3. Since we slide "3" to the constant term, divide the factors 6 and 4 by 3.

`\begin{gathered} =(x+(6)/(3))(x+(4)/(3)) \\ =(x+2)(x+(4)/(3)) \end{gathered}`

4. Since we can't have a fraction as a factor, slide back the denominator 3 to the term x in the same factor.

`(x+2)(3x+4)_{}`

Similarly, we got the same factors of the given quadratic equation and these are (x + 2) and (3x + 4).