Question

What must be a factor of the polynomial function f(x) graft on the coordinate plane below

Answer 1

Answer:

The correct answer option is B. (x - 1).

Step-by-step explanation:

We are to determine the factor of the polynomial function $f(x)$ which is graphed on the given coordinate plane.

We know that if the zeros (or intercepts) of an equation are $r _ 1$ and $r _ 2$ then the factors for this equation will be $( x - r _ 1 )$ and $( x - r _ 2 )$.

From the graph, we can see that it intercepts the x axis at $1$ and $6$. So the roots will be $(x-1)$ and $(x-6)$.

Therefore, the correct answer option is B. (x - 1).

Answer 2

Answer: SECOND OPTION.

Step-by-step explanation:

We can verify each option by making eac equal to zero and solving for "x":

First option

$x-3=0\\x=0+3\\x=3$

The first option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at $x=3$.

Second option

$x-1=0\\x=0+1\\x=1$

The second option is a factor of the polynomial function, because the parabola intersects the x-axis at $x=1$.

Third option

$x+1=0\\x=0-1\\x=-1$

The third option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at $x=-1$.

Fourth option

$x+3=0\\x=0-3\\x=-3$

The fourth option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at $x=-3$.