Factorise :
(i) x3 - 2x2 - x + 2
(iii) x + 13x2 + 32x + 20
(ii) x3 - 3x2 - 9x-5
(iv) 2y3 + y2 – 2y-1
please explain me briefly....
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1
Answer:
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)
Answered by
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