Question

Factor this polynomial completely
`{x}^(2) + 13x + 40`

Answer 1

In order to factor this polynomial, first let's calculate the zeros using the quadratic formula:

`\begin{gathered} x^2+13x+40=0\\ \\ a=1,b=13,c=40\\ \\ x=(-b\pm√(b^2-4ac))/(2a)\\ \\ x=(-13\pm√(169-160))/(2)\\ \\ x_1=(-13+3)/(2)=-5\\ \\ x_2=(-13-3)/(2)=-8 \end{gathered}`

Now, we can write the polynomial in the factored form below:

`\begin{gathered} a(x-x_1)(x-x_2)\\ \\ =(x+5)(x+8) \end{gathered}`
`\begin{gathered} a(x-x_1)(x-x_2)\\ \\ =(x+5)(x+8) \end{gathered}`