Question

1.Factorize the following: i) x^3 – 4x^2 + 5x – 2

Answer 1

Answer:

Here one root is x = 1 so (x - 1) is a factor. i.e

${x}^{3} - {x}^{2} - 3 {x}^{2} + 3x + 2x - 2 =$

${x}^{2} (x - 1) - 3x(x - 1) + 2(x - 1) =$

$(x - 1)( {x}^{2} - 3x + 2) =$

$(x - 1)( {x}^{2} - 2x - x + 2) =$

$(x - 1)(x(x - 2) - 1(x - 2)) =$

$(x - 1)(x - 2)(x - 1) = (x - 1) {}^{2} (x - 2)$

Answer 2

Step-by-step explanation:

Answer:

Here one root is x = 1 so (x - 1) is a factor. i.e

{x}^{3} - {x}^{2} - 3 {x}^{2} + 3x + 2x - 2 =x

3

−x

2

−3x

2

+3x+2x−2=

{x}^{2} (x - 1) - 3x(x - 1) + 2(x - 1) =x

2

(x−1)−3x(x−1)+2(x−1)=

(x - 1)( {x}^{2} - 3x + 2) =(x−1)(x

2

−3x+2)=

(x - 1)( {x}^{2} - 2x - x + 2) =(x−1)(x

2

−2x−x+2)=

(x - 1)(x(x - 2) - 1(x - 2)) =(x−1)(x(x−2)−1(x−2))=

(x - 1)(x - 2)(x - 1) = (x - 1) {}^{2} (x - 2)(x−1)(x−2)(x−1)=(x−1)

2

(x−2)