Question

How do you factor the trinomial ${x^2} + 14x + 24$?

Answer 1

Hint: In this question we will solve the equation as a quadratic equation and will simplify the equation by finding the roots.

Complete step-by-step solution:
We have the given equation as:
$ \Rightarrow {x^2} + 14x + 24$
Now since the above equation is in the quadratic format, we will find the value of $x$ as by splitting the equation, the above equation can be split up as:
$ \Rightarrow {x^2} + 12x + 2x + 24$
Now the above equation can be grouped as:
 $ \Rightarrow x(x + 12) + 2(x + 12)$
Since the term $(x + 12)$ is same in both the terms, we can take it out as common and write it as:
$ \Rightarrow (x + 12)(x + 2)$

$(x+12)$ and $(x+2)$ are the factors of the given equation.

Note: It is to be noted that in the above question we don’t have a quadratic equation, but we are factoring the trinomial using a quadratic equation.
A trinomial is an algebraic equation which has three terms in it.
A quadratic equation is a polynomial equation with a degree $2$, quadratic equations are used mostly in statistics when there is a power.
It is to be remembered that to split the middle term two terms should be such that the product is ${x^2}$ coefficient times the constant coefficient, and the sum is equal to the $x$ coefficient.
The roots of a quadratic equation can be found using the formula $({x_1},{x_2}) = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2ac}}$
Where $({x_1},{x_2})$ are the roots of the equation and $a,b,c$ are the coefficients of the terms in the quadratic equation