Question

Which of the following is equal to x²+ 7x + 6?

Answer 1

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:

`x^2+7x+6`

We can find the factors by finding the roots, and we can use the quadratic formula to find the roots of this expression:

`\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=(-7\pm5)/(2) \\ x_1=(-7-5)/(2)=(-12)/(2)=-6 \\ x_2=(-7+5)/(2)=(-2)/(2)=-1 \end{gathered}`

Then, we can use this roots to write the factorized form of the expression:

`x^2+7x+6=(x+6)(x+1)`

This expression is equivalent to option A.

Answer: the expression is equivalent to (x+1)(x+6) [Option A]