Question

How do you factor $2{{x}^{2}}+11x-6$?

Answer 1

Hint: To solve the given equation we will use the splitting the middle term method. In this method first we will split the middle term of the given equation such as the sum or difference of two numbers is equal to 11 and the product of two numbers is equal to 12. Then by taking the common factors out we get the desired answer.

Complete step by step solution:
We have been given an equation $2{{x}^{2}}+11x-6$.
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 $a\times c=2\times 6=12$ and their sum or difference is equal to $b=11$.
So we will use two numbers as 12 and 1.
So splitting the middle term we will get
$\Rightarrow 2{{x}^{2}}+\left( 12x-x \right)-6$
Now, simplifying the above obtained equation we will get
$\Rightarrow 2{{x}^{2}}+12x-x-6$
Now, taking the common terms out we will get
$\Rightarrow 2x\left( x+6 \right)-1\left( x+6 \right)$
Now, again taking common factors out we will get
$\Rightarrow \left( x+6 \right)\left( x-1 \right)$

Hence we get the factors of the given equation as $\left( x+6 \right)\left( x-1 \right)$.

Note: Alternatively we can use quadratic formula or completing the square method to solve the given equation. The possibility of mistake is while taking the common terms out. We have to take terms common such as we get the original equation again when we multiply the brackets.