Question

What is the factorization of the Polynomial graphed below? Assume it has no constant factor. Write each factor as a polynomial in descending order. Enter exponents using the caret (^).y=

Answer 1

From the graph below, we have the equation of the curve to be:

`x=-6\text{ twice}`

Let us get the factors of the equation,

`\begin{gathered} x=-6\text{ or x=-6} \\ x+6=0\text{ or x+6=0} \\ (x+6)(x+6)=0 \end{gathered}`

Let us now expand the factors,

`y=(x+6)(x+6)`
`\begin{gathered} y=x(x+6)+6(x+6) \\ y=x^2+6x+6x+36 \end{gathered}`
`y=x^2+12x+36`

Hence, the factorization of the polynomial graphed is,

y = x^2 + 12x + 36.