Question

Factorise

1. x³ - 2x² - x + 2

2. x³ - 3x² - 9x - 5

3. x³ + 13x² + 32x + 20

4. 2y³ + y² - 2y - 1

Answer 1

Answer- See the following attachments.

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Answer 2

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1.) x³-2x²-x+2→

x³-2x²-x+2

=> x²(x-2)-1(x-2)

=> (x²-1)(x-2)

(1 can be Expressed as 1²)

=> (x²-1²)(x-2)

(a²-b² = (a+b)(a-b))

=> (x+1)(x-1)(x-2)

The factors of x³-2x²-x+2 are→

(x+1)(x-1)(x-2)
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2.) x + 1 is the factor. 

x^3 + x^2 - 4x^2 - 4x - 5x - 5 

x^2 (x + 1) - 4x (x + 1) - 5 (x + 1) 

 (x + 1) (x^2 - 4x - 5) 

(x+1)(x² - 5x + x - 5)

= (x + 1) (x - 5) (x + 1). 

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3.) x³+13x²+32x+20
=(x+1)(x²+12x+20)   [∵, for x=-1, x³+13x²+32x+20=-1+13-32+20=0]
=(x+1)(x²+10x+2x+20)
=(x+1){x(x+10)+2(x+10)}
=(x+1){(x+10)(x+2)}
=(x+1)(x+2)(x+10)
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4.) 2y³ + y² - 2y -1

= 2y^3 - 2y + y^2 - 1

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

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

= (2y+1) ( y^2 - 1^2) 

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