Question

How do you factor $3{{x}^{2}}+24$ ?

Answer 1

Hint: In this question, we have to find the factors of an algebraic expression. So, we will use the basic mathematical rules and the algebraic formula to get the required solution. We start solving this problem by taking common 3 from the given algebraic expression. Then, we will apply the algebraic formula ${{a}^{2}}+{{b}^{2}}={{\left( a+b \right)}^{2}}-2ab$ in the equation. In the end, we will make the necessary calculations, to get the required solution to the problem.

Complete step by step solution:
According to the question, we have to find the factors of an algebraic expression.
So, we will apply the basic mathematical rules and the algebraic formula to get the required result.
The expression given to us is $3{{x}^{2}}+24$ ---------------- (1)
Now, we start solving our problem by taking the common 3 from the equation (1), because we know that 24 comes in the table of 3 when we multiply 3 and 8, thus we get
$\Rightarrow 3\left( {{x}^{2}}+8 \right)$
On further solving, we get
$\Rightarrow 3\left( {{x}^{2}}+{{\left( 2\sqrt{2} \right)}^{2}} \right)$
Now, we will apply the algebraic formula ${{a}^{2}}+{{b}^{2}}={{\left( a+b \right)}^{2}}-2ab$ in the above equation, that is here $a=x$ and $b=2\sqrt{2}$, thus we will put these values of a and b in the above formula, we get
 $\Rightarrow 3\left( {{\left( x+2\sqrt{2} \right)}^{2}}-2\times x\times 2\sqrt{2} \right)$
On further simplify the above equation, we get
$\Rightarrow 3\left( {{\left( x+2\sqrt{2} \right)}^{2}}-4\sqrt{2}x \right)$ which is the required solution.
Therefore, for the algebraic expression $3{{x}^{2}}+24$ , its simplified value is equal to $3\left( {{\left( x+2\sqrt{2} \right)}^{2}}-4\sqrt{2}x \right)$ .

Note: While solving this equation, make the step by step calculations to avoid confusion and mathematical errors. You can also end your solution after $3\left( {{x}^{2}}+8 \right)$ step. Also, you can use the algebraic formula ${{a}^{2}}+{{b}^{2}}={{\left( a+b \right)}^{2}}+2ab$ in this problem, to get the solution.