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# How do you factor ${x^2} + 3x - 10$ by using any mathematical method and elaborate the method with an example(take any general algebraic equation)?

Last updated date: 22nd Feb 2024
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Hint: By using the factorization method to obtain the factors of the given equation ${x^2} + yx + z$ . Here we can use the mid term splitting method to factorise this equation in which we are going to split the middle term and can have required two factors.
For equation ${x^2} + yx + z$
Here we have to split “y” in such a way that the split number say “a” and “b” have the relationship $a \times b = z(1)$ and $a + b = y$ for the above equation.

The given equation is ${x^2} + 3x - 10$
$\Rightarrow {x^2} + 3x - 10 \\ \Rightarrow {x^2} + (5 - 2)x - 10 \\ \Rightarrow {x^2} + 5x - 2x - 10 \\ \Rightarrow x(x + 5) - 2(x + 5) \\ \Rightarrow (x + 5)(x - 2) \;$
So the factors for the above equation is $(x + 5),(x - 2)$
So, the correct answer is “ $(x + 5),(x - 2)$ ”.
For equation ${x^2} + yx + z$
Here we have to split “y” in such a way that the split number say “a” and “b” have the relationship $a \times b = z(1)$ and $a + b = y$ for the above equation.