Question

How do you factor $2{{x}^{2}}+15x+18$?

Answer 1

Hint: The given equation is a quadratic equation. 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 $2{{x}^{2}}+15x+18$ such that the product of two numbers is equal to $a\times c$ and sum of two numbers is equal to $b$.

Complete step by step solution:
We have been given an equation $2{{x}^{2}}+15x+18$.
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 $a\times c=2\times 18=36$ and their sum is equal to $b=15$.
So we will use two numbers as 12 and 3.
Now, splitting the middle term we will get
$\Rightarrow 2{{x}^{2}}+12x+3x+18$
Now, taking the common terms out we will get
$\Rightarrow 2x\left( x+6 \right)+3\left( x+6 \right)$
Now, again taking common factors out we will get
$\Rightarrow \left( x+6 \right)\left( 2x+3 \right)$

Hence we get the factors of the given equation as $\left( x+6 \right)\left( 2x+3 \right)$.

Note: If it is difficult to find the numbers such as the product of two numbers is equal to $a\times c$ and sum of two numbers is equal to $b$, then we can use the quadratic formula to solve the given equation. The quadratic formula to solve the quadratic equation of the form $a{{x}^{2}}+bx+c=0$ is given as $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$. By comparing the general equation by the given equation we can easily get the values.