Question

How do you factor $2{{x}^{2}}+5x=8$ ?

Answer 1

Hint: First to find the factors, let us bring all the terms to one side. For this subtract $8$ on both sides of the equation. Now again split the middle term, $5x\;$ in such a way that it gets represented into two more terms. Now group the terms together and they will be the factors of the expression. If we are not able to split the middle term, the only factor would be $1$ and the expression itself.

Complete step by step solution:
The given polynomial which must be factorized is $2{{x}^{2}}+5x=8$
We can rearrange the terms as, $2{{x}^{2}}+5x-8$
Here we rearranged the terms by subtracting $8$ on both sides of the equation.
To factorize this polynomial, we must first split the middle term.
For this, we use the product sum form.
If the polynomial’s general form is $a{{x}^{2}}+bx+c=0$
Then to split the middle term, we use the product and sum formula.
Which is,
The product of the middle terms after splitting must be $a\times c$
And the sum of the middle terms must be $b$
Here $a=2;b=5;c=-8$
The product of the terms is $2\times -8=-16$
The sum of the terms is $5$
As we can see that we are not able to split the middle term.
The only factor for this polynomial will be $1$
Now writing the factors together we get,
$\Rightarrow \left( 1 \right)\left( 2{{x}^{2}}+5x-8 \right)$

Hence the factors for the polynomial $2{{x}^{2}}+5x=8$ are $\left( 1 \right)\left( 2{{x}^{2}}+5x-8 \right)$

Note: For the polynomials in which we are not able to group the terms or split the middle terms, the factors would be $1$ and the polynomial itself. This is similar to the prime numbers. They do not have any factors other than $1$ and the number itself.