Answer:
[tex]\left(x-\dfrac{-13+\sqrt{113}}{2}\right)\left(x-\dfrac{-13-\sqrt{113}}{2}\right).[/tex]
Step-by-step explanation:
To factor the expression [tex]x^2+13x+14[/tex] you need to know its roots.
First find the discriminant of this quadratic polynomial:
[tex]D=13^2-4\cdot 1\cdot 14=169-56=113.[/tex]
Then the roots of the expression [tex]x^2+13x+14[/tex] are
[tex]x_{1,2}=\dfrac{-13\pm \sqrt{113}}{2}.[/tex]
Now the factored form is
[tex]\left(x-\dfrac{-13+\sqrt{113}}{2}\right)\left(x-\dfrac{-13-\sqrt{113}}{2}\right).[/tex]
