Question

Factorise:
${x}^{2} + \frac{1}{ {x}^{2} } - 7(x - \frac{1}{x} ) + 8$
Hint - Put (x-1/x)= y
​

Answer 1

Answer:

(i) x

3

−2x

2

−x+2

=x

2

(x−2)−1(x−2)

=(x−2)(x

2

−1)

=(x−2)(x+1)(x−1)

(ii) x

3

−3x

2

−9x−5

=x

3

−5x

2

+2x

2

−10x+x−5

=x

2

(x−5)+2x(x−5)+1(x−5)

=(x−5)(x

2

+2x+1)

=(x−5)(x+1)(x+1)

(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)

Video Explanation