How do you factor trinomial ${{x}^{2}}-7x-8$ ?

Hint: In this question, a quadratic equation is given in the form of $a{{x}^{2}}+bx+c=0$. So, we need to solve the given equation in order to find the roots of the quadratic equation. There are 2 roots of any quadratic equation. To solve this equation, we split the middle term of -7x. It is the easiest approach to find the roots of the quadratic equation.

Complete step by step answer:
Now, let’s solve the question.
We should know that the equation having the highest degree of 2, and which is in the form $a{{x}^{2}}+bx+c=0$ is called a quadratic equation. ‘a’ and ‘b’ are coefficients and c is the constant term. There are basically two roots of any quadratic equation. Common method of finding roots of quadratic equations is middle term splitting. In this method, first we have to find the product of the coefficient of ${{x}^{2}}$ and the constant. After that, find the factors of the product in such a way that the sum or difference will result in the middle term.
Now, write the given expression.
$\Rightarrow {{x}^{2}}-7x-8$
Now, find the product of the coefficient of ${{x}^{2}}$ and the constant. The product will be $1\times \left( -8 \right)$ which will be -8. So the factors of 8 are 1, 2, 4, 8. But to form -7x will use 1 and 8 such that –8x + x results in -7x.
$\Rightarrow {{x}^{2}}-8x+x-8$
Now, make pairs and take out the common terms:
$\Rightarrow x(x-8)+1(x-8)$
Further take (x – 8) common:
$\Rightarrow (x+1)(x-8)$
If each factor is equated to 0, then we can easily get both the roots of the equation.
For (x + 1) = 0
$\therefore x=-1$
For (x – 8) = 0
$\therefore x=8$
The roots of the equations are: x = -1, 8

Note:
Students usually get confused when it is asked in question to factor the trinomial. Trinomial is nothing but an expression which contains three terms. There is no role of the trinomial term if it is given in question because we have to factorise the equation. In factorisation of quadratic equations, there are three terms only.