Question

x³ − 2x² − 5x + 6 > 0

simplify using m. o. i. ​

Answer 1

Let f(x)=x

3

−2x

2

−5x+6

⇒f(1)=1

3

−21

2

−5×1+6=1−2−5+6=0

Using synthetic division, we have

x

2

−x−6=0 is the other factor

(x−1)(x

2

−x−6)=0

=(x−1)(x

2

−3x+2x−6)=0

=(x−1)(x(x−3)+2(x−3))=0

=(x−1)(x+2)(x−3) are the factors of f(x)