Question

Is the binomial a factor of the polynomial nominal function?

Select Yes or No for each binomial.

I accidentally said “no” for the first two on the chart. I need everything on the chart answered. Thanks!

Answer 1

The factors for given equation f(x)=
`x^(3) +3x^(2) -25x-75`.

• (x-1) - No
• (x-3) - No
• (x+3) - Yes
• (x-5) - Yes
• (x+5) - Yes

Explanation:

The given equation is f(x)=
`x^(3) +3x^(2) -25x-75` .

Add 0 at the end of the equation.

`x^(3) +3x^(2) -25x-75` = 0.

Let us group the given equation,

`(x^(3) +3x^(2)) -(25x-75)` =0.

⇒ Group 1:
`x^(3) +3x^(2)` .

Group 2:
`- 25x +75` .

Pull out factor from each group,

⇒ Group 1:
`(x+3)(x^(2))`.

Group 2: (x+3) (-25).

Join the two group since both (x+3) is common in both groups.

`(x+3)(x^(2) -25)` =0.

One of the factor is (x+3).

Other factors are solved by the formula,
`a^(2)-b^(2) = (a+b) (a-b)` .

`(x+3)(x^(2) -25)` = (x+5) (x-5) .

The other factors are (x+5) and (x-5).