1.

Factorise : (i) x2 – 2x2 – x + 2 (ii) x2 – 3x2 – 9x – 5 (iii) x3 + 13x2 + 32x + 20 (iv) 2y3 + y2 – 2y – 1

Answer»

(i) x3 – 2x2 – x + 2 

= x2(x – 2) – 1 (x – 2) 

= (x – 2) (x2 – 1) 

= (x – 2) (x + 1) (x- 1) 

(ii) x3 – 3x2 – 9x – 5 

= x3 – 5x2 + 2x2 – 10x + x – 5 

= x2(x – 5) + 2x(x – 5) + 1 (x – 5) 

= (x – 5) (x2 + 2x + 1) 

= (x – 5) {x2 + x + x + 1} 

= (x – 5) (x(x + 1) + 1(x + 1)} 

= (x- 5)(x + 1) (x + 1) 

(iii) x3 + 13x2 + 32x + 20 

= x3 + 10x2 + 3x2 + 30x + 2x + 26 

= x2(x + 10) + 3x(x + 10) + 2(x + 10) 

= (x + 10) (x2 + 3x + 2) 

= (x + 10) {x2 + 2x + x + 2) 

= (x + 10) {x(x + 2) + 1 (x + 2)) 

= (x + 10) (x + 2) (x + 1) 

(iv) 2y3 + y2 – 2y – 1 

= y2(2y + 1) – 1(2y + 1) 

= (2y + 1) (y2– 1)

= (2y + 1) {(y)2 – (1)2

= (2y+ 1) (y + 1) (y- 1)



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