Question

Kayla was asked to rewrite the polynomial expression x2 +6x +9. How couldshe rewrite the polynomial?A. (x + 9)(x + 1)B. (x+3)(x + 3)C. (x - 3)(x+3)D. (x-3)(x-3)

Answer 1

In order to rewrite the given polynomial, first let's find the zeros using the quadratic formula:

`\begin{gathered} x^2+6x+9=0 \\ a=1,b=6,c=9 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_1=\frac{-6+\sqrt[]{36-36}}{2}=(-6+0)/(2)=-3 \\ x_2=(-6-0)/(2)=-3 \end{gathered}`

Now, let's rewrite the polynomial in the factored form:

`\begin{gathered} y=a(x-x_1)(x-x_2) \\ y=1(x-(-3))(x-(-3)) \\ y=(x+3)(x+3) \end{gathered}`

Therefore the correct option is B.