Answer

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**Hint:**First we have to define the terms that we need to solve the problem.

The coefficient of the First term $ ({x^2}) $ is $ 1 $

The coefficient of the First term $ (x) $ is $ - 3 $

The last term (constant is $ - 10 $

Given equation is the quadratic equation. We need to factorize this equation by using splitting the middle term method.

**Complete step by step answer:**

We need to find the factors of\[{x^2} - 3x - 10\] $ $

Let us note down the all terms,

Thus,

The coefficient of the First term $ ({x^2}) $ is $ 1 $

The coefficient of the First term $ (x) $ is $ - 3 $

The last term (constant) is $ - 10 $

We need to find one of the factors of the equation. We will factorize this equation by splitting the middle term method.

We need to split the middle term such that the sum is

We need to split the middle term such that the sum is $ - 3 $ and multiplication is $ - 10 $

\[{x^2} - 3x - 10\]

Let us split the middle term according to above mentioned condition, we have

\[{x^2} - 3x - 10\]\[ = {x^2} - 5x + 2x - 10\]

On taking $ x $ common from the first two terms and taking $ 2 $ common from the latter two terms we get,

\[ = x(x - 5) + 2(x - 5)\]

On taking $ (x - 5) $ common from the both terms we get,

\[ = (x - 5)(x + 2)\]

So \[(x - 5){\text{ and }}(x + 2)\] are two factors of the equation \[{x^2} - 3x - 10\]

Therefore we can say that $ (x - 5) $ is one of the factors of the equation \[{x^2} - 3x - 10\]

OR

We can say that $ (x + 2) $ is one of the factors of the equation \[{x^2} - 3x - 10\].

**Note:**We can calculate roots of the quadratic equation by equating each factor to zero and calculating value of variables.

Factor is a number or expression when multiplied with another number or expression to obtain the final required expression.

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