Question

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

A. x(x+2)
B. (x-2)(x-2)
C. x(x-2)
D. (x+2)(x+2)

Answer 1

It is B because the only point intercepting the x axis is 2. For it to be A or C, the graph would have to intercept point (0,0)

Answer 2

Option: B is correct.

The factorization of the polynomial graphed below is:

f(x)=(x-2)(x-2)

Step-by-step solution:

Clearly from the graph we could see that the graph of the function touches x=2.

that means that x=2 is a root of the function

Also when the graph touches the point of x-axis and does not pass that point than that zero is the repeated zero of the function.

That means that x=2 is a repeated zero of the function f(x).

Hence,

The factorization of the polynomial graphed below is:

f(x)=(x-2)(x-2)

Hence, option B is correct.

( Also in first option:

A) x(x+2)

x=0 must also be an zero but in the graph we could see that x=0 is not a solution.

Hence option A is false.

C)

x(x-2)

again as in option: A x=0 must be a solution.

Hence, option C is false.

D)

(x+2)(x+2)

x=-2 must be a solution but the graph does not touches x=-2.

Hence, option D is incorrect )