Answer:
(x - 6)(x + 4)(x - 2)
Step-by-step explanation:
since x = 6 is a root then (x - 6) is a factor
x³ - 4x² - 20x + 48 ÷ (x - 6)
= (x - 6)(x² + 2x - 8)
= (x - 6)(x + 4)(x - 2) ← factors of f(x)
Answer:
The other two factors are (x-2) and (x+4)
Step-by-step explanation:
Given one root of polynomial [tex]f(x)=x^3-4x^2-20x+48[/tex] which is x=6
we have to find the other factors of given function.
Polynomial: [tex]f(x)=x^3-4x^2-20x+48[/tex]
If x=6 is one of the root then by remainder theorem
Put x=6
[tex]f(6)=0[/tex]
Hence, by synthetic division the quotient is
[tex]x^2+2x-8[/tex]
By middle-term splitting method
[tex]x^2+4x-2x-8[/tex]
[tex]x(x+4)-2(x+4)[/tex]
[tex](x-2)(x+4)[/tex]
The other two factors are (x-2) and (x+4)
