Answer:
One Factor: x-9
Step-by-step explanation:
The polynomial function, P(x)=x³-8x²-29x+180
To verify: P(9)=0
Put x=9 into polynomial
[tex]P(9)=9^3-8\cdot 9^2-29\cdot 9+180[/tex]
[tex]P(9)=0[/tex]
At x=9, P(9)=0
Therefore, x-9 must be factor of P(x).
when divide x³-8x²-29x+180 by x-9 get remainder 0
[tex](x^3-8x^2-29x+180)\div (x-9)[/tex]
[tex]\Rightarrow x^2+x-20[/tex]
Factor quadratic equation
[tex]\Rightarrow (x+5)(x-4)[/tex]
Three factors are (x+5), (x-4) and (x-9)
