We have a quadratic expression in standard form.
We have to factorize it in order to compare it to the options given.
The expression is:
[tex]x^2+7x+6[/tex]
We can find the factors by finding the roots, and we can use the quadratic formula to find the roots of this expression:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-7\pm\sqrt[]{7^2-4\cdot1\cdot6}}{2\cdot1} \\ x=\frac{-7\pm\sqrt[]{49-24}}{2} \\ x=\frac{-7\pm\sqrt[]{25}}{2} \\ x=\frac{-7\pm5}{2} \\ x_1=\frac{-7-5}{2}=\frac{-12}{2}=-6 \\ x_2=\frac{-7+5}{2}=\frac{-2}{2}=-1 \end{gathered}[/tex]
Then, we can use this roots to write the factorized form of the expression:
[tex]x^2+7x+6=(x+6)(x+1)[/tex]
This expression is equivalent to option A.
Answer: the expression is equivalent to (x+1)(x+6) [Option A]
