The polynomial:
[tex]x^2+14x+48[/tex]
has the form:
[tex]ax^2+bx+c[/tex]
with a = 1, b = 14, and c = 48.
This kind of polynomials can be factored as follows:
[tex]ax^2+bx+c=a(x-x_1)(x-x_2)[/tex]
where x₁, and x₂ are the roots of the polynomial. We can find the roots of a quadratic polynomial with the help of the quadratic formula, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-14\pm\sqrt[]{14^2-4\cdot1\cdot48}}{2\cdot1} \\ x_{1,2}=\frac{-14\pm\sqrt[]{4}}{2} \\ x_1=\frac{-14+2}{2}=-6 \\ x_2=\frac{-14-2}{2}=-8 \end{gathered}[/tex]
Using a = 1, x₁ = -6, and x₂ = -8, the factored form is:
[tex]\begin{gathered} x^2+14x+48=1(x-(-6))(x-(-8)) \\ x^2+14x+48=(x+6)(x+8) \end{gathered}[/tex]
