The factors for given equation f(x)=[tex]x^{3} +3x^{2} -25x-75[/tex].
- (x-1) - No
- (x-3) - No
- (x+3) - Yes
- (x-5) - Yes
- (x+5) - Yes
Step-by-step explanation:
The given equation is f(x)=[tex]x^{3} +3x^{2} -25x-75[/tex] .
Add 0 at the end of the equation.
[tex]x^{3} +3x^{2} -25x-75[/tex] = 0.
Let us group the given equation,
[tex](x^{3} +3x^{2}) -(25x-75)[/tex] =0.
⇒ Group 1: [tex]x^{3} +3x^{2}[/tex] .
Group 2: [tex]- 25x +75[/tex] .
Pull out factor from each group,
⇒ Group 1: [tex](x+3)(x^{2})[/tex].
Group 2: (x+3) (-25).
Join the two group since both (x+3) is common in both groups.
[tex](x+3)(x^{2} -25)[/tex] =0.
One of the factor is (x+3).
Other factors are solved by the formula, [tex]a^{2}-b^{2} = (a+b) (a-b)[/tex] .
[tex](x+3)(x^{2} -25)[/tex] = (x+5) (x-5) .
The other factors are (x+5) and (x-5).
