How to factorize ${x^2}\, - \,2x\, - \,80$?

Hint:For solving this equation we must have the knowledge of factorization. Thus, the factorization is a process in which the number is written as the product of smaller numbers. Generally factors of a number are the numbers that divide evenly into another number.

Step by Step answer:
With the use of factoring, we can rewrite our polynomials in its simpler form, and after applying the principles of factoring in any equations, we will obtain a lot of useful information. Factorization is used to solve quadratic equations, polynomial inequalities and simplify expressions to make them easier to work. It is helpful in solving various number related problems.

Factoring is generally considered to be harder than multiplying this is because it is not as mechanical. Many times it generally involves guesses or trial and error. It can also be tougher sometimes as things were canceled during multiplying.

Now, we will solve the equation ${x^2}\, - \,2x\, - \,80$

Since by the using the factorization method ${x^2}\, - \,2x\, - \,80$ can be written as ${x^2}\, - \,10x\, + \,\,8x\, - \,80$

Now we will solve the value of x.

Now, next step is $x\left( {x\, - \,10} \right)\, + \,8\left( {x\, - \,10} \right)$

Now, next step is $\left( {x - 10} \right)\, + \,\left( {x + 8} \right)$

Now we will put $\left( {x - 10} \right)$ equals to zero

Thus, we will get $x - 10 = 0\,\,\,\,\,\,$or $x = 10$

Thus, the value of x is 10.

Similarly, we will put $\left( {x + 8} \right)$ equals to zero

Thus, we will get $x + 8 = 0$ or $x = - 8$

Thus, the value of x is -8.

Hence, 10 and -8 are the roots of the given equation.

Note:  Generally factoring consists of writing the number as the product of several factors. These factors when generally multiplied together then we will obtain the original number.