Question

Factorise : x3 – 2x2
– 5x + 6​

Answer 1

$\huge {\underbrace {\mathfrak {\pink {Factorization..}}}}$

${x}^{3} - {2x}^{2} - 5x + 6 = 0$

${x}^{3} - 2 {x}^{2} - 5x = 6$

${x}^{3} - 7 {x}^{3} = 6$

$6 {x}^{3} = 6$

${x}^{3} = \frac{6}{6}$

${x}^{3} = 1$

Answer 2

Answer:

Answer

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)