What is the factorization of the polynomial graphed below? assume it has no constant factor.

a. (x+5)(x+5)
b. (x-5)(x-5)
c. x-5
d. x+5

Remember that the solutions, or zeroes, or roots of a function are the points where the function outputs zero. In other words, if , then is a solution/zero/root of . If this is the case, then the function can be factored as the multiplication of parenthesis like .

As a graphical consequences, the zeroes of a function correspond to the points , and all points like are on the x-axis.

So, the graph of a function touches the x axis at if and only if is a solution for the function.

Now, your graph represents a parabola. A parabola can either have:

- No solutions, meaning that it never touches the x axis

- Two coincident solutions, meaning that it touches the x axis "twice", in the same point

- Two different solutions, meaning that it crosses the x axis in two different points.

You parabola has two coincident solutions, because it only touches the x axis twice at .

This means that is twice a solution of the parabola, and as such, it implies the factorization

step-by-step explanation:

where is the questions