Question

How do you factor $6{{x}^{2}}+8x+2$?

Answer 1

Hint: To solve the given equation we will use the split middle term method. In this method we will split the middle term of the equation $a{{x}^{2}}+bx+c=0$ such as the product of two numbers is equal to $a\times c$ and sum of two numbers is equal to $b$.

Complete step by step answer:
We have been given an equation $6{{x}^{2}}+8x+2$.
We have to find the factors of the given equation.
Now, we will use the split middle term method. We have to find two numbers such as the product of two numbers is equal to $a\times c=6\times 2=12$ and their sum is equal to $b=8$.
So we will use two numbers as 6 and 2.
So splitting the middle term we will get
$\Rightarrow 6{{x}^{2}}+6x+2x+2$
Now, taking the common terms out we will get
$\Rightarrow 6x\left( x+1 \right)+2\left( x+1 \right)$
Now, again taking common factors out we will get
$\Rightarrow \left( 6x+2 \right)\left( x+1 \right)$
Again taking common terms out we will get
$\Rightarrow 2\left( 3x+1 \right)\left( x+1 \right)$
Hence above are the required factors of the given equation.

Note: Here in this question we use the split middle term method as it is a simple question. We can also divide the whole equation by 2 to simplify the equation and then split the middle term. We can also use other methods like quadratic formula, completing the square method also to solve the equations. Also we can find the values of x by solving the equation and writing it into factor form.