Question

Example 5. Factorise
(1) x - 2x - x + 2
(ii) x - 3x2 - 9x - 5
(iii) 7 + 73x + 32x + 20
(iv) 2y2 + y2 - 2y - 1.


please explain the process of finding it ​

Answer 1

Step-by-step explanation:

(iii) x

3

+13x

2

+32+20

Let us put x=1,2,−1,−2 and check if they satisfy the equation.

x=−2 satisfies the equation.

Dividing the equation by (x+2), we get

⇒ x

3

+13x

2

+32+20

=(x+2)(x

2

+11x+10)

=(x+2)(x

2

+x+10x+10)

=(x+2)[x(x+1)+10(x+1)]

=(x+2)(x+1)(x+10)

(iv) 2y

3

+y

2

−2y−1

=2y

3

+2y

2

−y

2

−y−y−1

=2y

2

(y+1)−y(y+1)−1(y+1)

=(y+1){2y

2

−y−1}

=(y+1){2y

2

−2y+y−1}

=(y+1){2y(y−1)+1(y−1)}

=(y−1)(y+1)(2y+1)