Question

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

Answer 1

Answer: SECOND OPTION.

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`.

Answer 2

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

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).