Question

x³+6x2+11x+6 using factor theurom​

Answer 1

Answer:

The factors are 1, 2, and 3

Step-by-step explanation:

According to Factor theorem, if (x - a) is a polynomial factor f(x), then f(a) = 0

let f(x)=x3-6x2+11x-6

Let us check if (x - 1) is the factor of f(x),

Then,

f(1)=13-6(12)+11(1)-6=1-6=1-6+11-6=0

Therefore (x-1) is a factor of f(x)

Let us check for the other factors

Hence,

f(x) =(x - 1) (x2 - 5x+6)

x2-5x+6=x2-2x-3x+6

=x(x - 2) -3(x - 2)

=(x - 2) (x - 3)

f(x) =(x - 1) (x - 2) (x - 3)

Therefore, 1, 2, 3 are the factors of f(x)