SOLVE THE FOLLOWING
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.NO SPAM
.STEP REQUIRED
.SOLVE ATLEAST 10 QUESTION
Answers
Questions:-
Factorize the following (any 10):-
(1) x² + 8x - 20
(2) x² - 6x - 16
(3) x² - 6x + 8
(4) x² - 5x - 50
(5) x² - 2x - 63
(6) x² - 7x + 10
(7) x² + 17x + 72
(8) x² + 4x - 60
(9) x² - 18x + 80
(10) x² + 5x + 6
Solutions:-
(1) x² + 8x - 20
⟶ By splitting middle term,
= x² + 10x - 2x - 20
Taking common terms out,
= x(x + 10) - 2(x + 10)
Again taking common,
= (x + 10)(x - 2)
Ans: (x + 10)(x - 2)
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(2) x² - 6x - 16
⟶ x² - 8x + 2x - 16
= x(x - 8) + 2(x - 8)
= (x - 8)(x + 2)
Ans: (x - 8)(x + 2)
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(3) x² - 6x + 8
⟶ x² - 4x - 2x + 8
= x(x - 4) - 2(x - 4)
= (x - 4)(x - 2)
Ans: (x - 4)(x - 2)
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(4) x² - 5x - 50
⟶ x² - 10x + 5x - 50
= x(x - 10) + 5(x - 10)
= (x - 10)(x + 5)
Ans: (x - 10)(x + 5)
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(5) x² - 2x - 63
⟶ x² - 2x - 63
= x² - 9x + 7x - 63
= x(x - 9) + 7(x - 9)
= (x - 9)(x + 7)
Ans: (x - 9)(x + 7)
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(6) x² - 7x + 10
⟶ x² - 5x - 2x + 10
= x(x - 5) - 2(x - 5)
= (x - 5)(x - 2)
Ans: (x - 5)(x - 2)
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(7) x² + 17x + 72
⟶ x² + 8x + 9x + 72
= x(x + 8) + 9(x + 8)
= (x + 8)(x + 9)
Ans: (x + 8)(x + 9)
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(8) x² + 4x - 60
⟶ x² + 10x - 6x - 60
= x(x + 10) - 6(x + 10)
= (x + 10)(x - 6)
Ans: (x + 10)(x - 6)
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(9) x² - 18x + 80
⟶ x² - 10x - 8x + 80
= x(x - 10) - 8(x - 10)
= (x - 10)(x - 8)
Ans: (x - 10)(x - 8)
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(10) x² + 5x + 6
⟶ x² + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2)(x + 3)
Ans: (x + 2)(x + 3)
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Solution :
1. x² + 8x - 20
> x² + 10x - 2x - 20
> x( x + 10) - 2( x + 10)
> ( x - 2)( x + 10)
2. x² - 6x - 16
> x² - 8x + 2x - 16
> x( x - 8) + 2( x - 8)
> ( x + 2)( x - 8)
3. x² - 6x + 8
> x² - 4x - 2x + 8
> x( x - 4) + 2( x - 4)
> ( x + 2)( x - 4)
4. x² - 5x - 50
> x² - 10x + 5x - 50
> x( x - 10) + 5( x - 10)
> ( x + 5)( x - 10)
5 . x² - 2x - 63
> x² - 9x + 7x - 63
> x( x - 9) + 7( x - 9)
> ( x + 7)( x - 9)
6. x² - 7x + 10
> x² - 5x - 2x + 10
> x( x - 5) - 2( x - 5)
> ( x - 2)( x - 5)
7. x² + 17x + 72
> x² + 14x + 3x + 72
> x( x + 14) + 3( x + 14)
> ( x + 3)( x + 14)
8. x² + 4x - 60
> x² + 10x - 6x - 60
> x( x + 10) - 6( x + 10)
> ( x - 6)( x + 20)
9. x² + 18x + 80
> x² + 10x + 8x + 80
> x( x + 10) + 8( x + 10)
> ( x + 8)( x + 10)
10. x² + 5x + 6
> x² + 2x + 3x + 6
>x( x + 2) + 3( x + 2)
> ( x + 2)( x + 3)
11. 10x³ - 19x² - 61x - 8
> 10x³ - 35x² + 16x² - 5x - 56x - 8
> 5x ( 2x² - 7x - 1) + 8( 2x² - 7x + 1)
> ( 5x + 8)( 2x² - 7x - 1)
12. 20x³ - 15x² + 28x - 21 [ Correction ; If its +15 x², can't be solved ]
> 20x³ + 28x - 15x² - 21
> 4x ( 5x² + 7) - 3( 5x² + 7)
> ( 4x - 3)( 5x² + 7)
13 . 36x³ - 5x² - 46x - 5
> 36x³ - 9x² - 45x + 4x² - x - 5
> 9x ( 4x² - x - 5) + ( 4x² - x - 5)
> ( 9x + 1)( 4x² - x - 5)
> ( 9x + 1)( 4x² + 4x - 5x - 5)
> ( 9x + 1)[ 4x( x + 1) - 5( x + 1) ]
> ( 9x + 1)( 4x - 5)( x + 1)
14. 10ab + 4a + 5b + 2
> 2a( 5b + 2) + ( 5b + 2)
> ( 2a + 2)( 5b + 2)
15. 2x² - 32
> 2( x² - 16)
> 2( x + 5)( x - 4)
16. x² - 7x + 12
> x² - 3x - 4x + 12
>x( x - 3) - 4( x - 3)
> (x - 3)( x - 4)
17. 2x² + 7x + 6
> 2x² + 3x + 4x + 6
> x( 2x + 3) + 2( 2x + 3)
> ( x + 2)( 2x + 3)
18. x² - 6x - 40
> x² - 10x + 4x - 40
> x( x - 10) + 4( x - 10)
> ( x + 4)( x - 10)
19. 2x² - 15x + 22
> 2x² - 4x - 11x + 22
> 2x( x - 2) - 11( x - 2)
> (x - 2)( 2x - 11)
20. 8x² - 21x + 10
> 8 x² - 16x - 5x + 10
> 8x( x - 2) - 5( x - 2)
> ( x - 2)( 8x - 5)
21. 25 x² - 20 xy + 4y²
> [ 5x ]² - 2[ 5x ][ 2y] + [ 2y ]²
> [ 5x - 2y ]²
22. 4x² + 4xy + y²
> [ 2x ]² + 2[ 2x ][ y ] + y².
> [ 2x + y ]².
23. 6x² - 11xy - 10y²
> 6x² - 15xy + 4xy - 10y²
> 3x ( 2x - 5y) + 2y( 2x - 5y)
> ( 3x + 2y)( 2x - 5y)
24. 4x² + 17x + 15
>4x² + 12x + 5x + 15
> 4x ( x + 3) + 5( x + 3)
> (x + 3)( 4x + 5)
25. 8x² - 22x + 15
> 8x² - 10x - 12x + 15
> 2x( 4x - 5) - 3( 4x - 5)
> (2x - 3)( 4x - 5)
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Additional information -
(a + b)² = a² + 2ab + b²
(a + b)² = (a - b)² + 4ab
(a - b)² = a² - 2ab + b²
(a - b)² = (a + b)² - 4ab
a² + b² = (a + b)² - 2ab
a² + b² = (a - b)² + 2ab
2 (a² + b²) = (a + b)² + (a - b)²
4ab = (a + b)² - (a - b)²
ab = {(a + b)/2}² - {(a-b)/2}²
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
(a + b)³ = a³ + 3a²b + 3ab² b³
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - 3a²b + 3ab² - b³
a³ + b³ = (a + b)( a² - ab + b² )
a³ + b³ = (a + b)³ - 3ab( a + b)
a³ - b³ = (a - b)( a² + ab + b²)
a³ - b³ = (a - b)³ + 3ab ( a - b )
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