Question

Hello friends solve this question

You should answer steps by steps
So I will add you brain list answer.

Answer 1

HELLO DEAR,

★ ( 1 ) ★

√3x² + 11x + 6√3

= √3x² + 9x + 2x + 6√3

= √3x(x + 3√3) + 2(x + 3√3)

= (√3x + 2)(x + 3√3)

★ ( 2 ) ★

3√7x² + 4x - √7

= 3√7x² + 7x - 3x - √7

= √7x(3x + √7) - 1(3x + √7)

= (√7x - 1)( 3x + √7)

★ ( 3 ) ★

√7x² - 6x - 13√7

= √7x² - 13x + 7x - 13√7

= x(√7x - 13) + √7(x - 13)

= (x + √7)(√7x - 13)

★ ( 4 ) ★

3x² - 2√6x + 2

= 3x² - √6x - √6x + 2

= √3x(√3x - √2) - √2(√3x - √2)

= (√3x - √2)(√3x - √2)

★ ( 5 ) ★

√3x² - 2√2x - 2√3

= √3x² - 3√2x - √2x + 2√3

= √3x(x - √6) - √2(x - √6)

= (√3x - √2)(x - √6)

★ ( 6 ) ★

x² - 3√5x + 10

= x² - 2√5x - √5x + 10

= x(x - 2√5) - √5(x - 2√5)

= (x - √5)(x - 2√5)

★ ( 7 ) ★

x² + 3√3x - 30

= x² + 5√3x - 2√3x - 30

= x(x + 5√3) - 2√3(x + 5√3)

= (x - 2)(x + 5√3)

★ ( 8 ) ★

10x - 1/x - 3

= (10x² - 1 - 3x)/x

= (10x² - 1 - 3x)/x

= (10x² - 5x + 2x - 1)/x

= [ 5x(2x - 1) + 1(2x - 1) ] /x

= [ (5x + 1)(2x - 1) ] /x

★ ( 9 ) ★

2/x² - 5/x + 2

= (2x - 5x²)/x³ + 2

= (2x - 5x² + 2x³)/x³

= ( 2x² - 5x + 2)/x²

= [ 2x² - 4x - x + 2)/x²

= [ 2x(x - 2) - 1( x - 2)] /x²

= 1/x² [ (2x - 1)(x - 2) ]



Plz see the attachment for another question I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hey.....!!!! :)) ✌️✌️

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1.=====>>> √3x² + 11x + 6√3

=> √3x² + 9x + 2x + 6√3

=> √3x(x + 3√3) + 2(x + 3√3)

=> (√3x + 2)(x + 3√3)Ans
==========================>>>>>>>>>>>>>>>

2.=====>>>>3√7x² + 4x - √7

=> 3√7x² + 7x - 3x - √7

=> √7x(3x + √7) - 1(3x + √7)

= > (√7x - 1)( 3x + √7) Ans

======================>>>>>>>>>>>≥>>>>>

3. =====>>>>>√7x² - 6x - 13√7

=> √7x² - 13x + 7x - 13√7

=> x(√7x - 13) + √7(x - 13)

=> (x + √7)(√7x - 13) Ans

======================>>>>>>>>>>>>>>>>>
4. ======>>>>>>3x² - 2√6x + 2

=> 3x² - √6x - √6x + 2

=> √3x(√3x - √2) - √2(√3x - √2)

=> (√3x - √2)(√3x - √2) Ans
=======================>>>>>>>>>>>>>≥>>>

5. ========>>>>>>>>√3x² - 2√2x - 2√3

=> √3x² - 3√2x - √2x + 2√3

=> √3x(x - √6) - √2(x - √6)

=> (√3x - √2)(x - √6) Ans.

=============================>>>>>>>>>>

6. ==========>>>>x² + 3√3x - 30

=> x² + 5√3x - 2√3x - 30

=> x(x + 5√3) - 2√3(x + 5√3)

=> (x - 2)(x + 5√3) Ans
=========================>>>>>>≥>>>>>>>

7. ======>>>>>>>x² + 3√3x - 30

=> x² + 5√3x - 2√3x - 30

= > x(x + 5√3) - 2√3(x + 5√3)

=> (x - 2)(x + 5√3) Ans

========================>>>>>>>>>>>>>>>>

8. 10x - 1/x - 3

=> (10x² - 1 - 3x)/x

=> (10x² - 1 - 3x)/x

=> (10x² - 5x + 2x - 1)/x

=> [ 5x(2x - 1) + 1(2x - 1) ] /x

=> [ (5x + 1)(2x - 1) ] /x Ans

=============================>>>>>>>>>>>
9. ========>>>>>>2/x² - 5/x + 2

=> (2x - 5x²)/x³ + 2

= > (2x - 5x² + 2x³)/x³

=> ( 2x² - 5x + 2)/x²

=> [ 2x² - 4x - x + 2)/x²

=> [ 2x(x - 2) - 1( x - 2)] /x²

=> 1/x² [ (2x - 1)(x - 2) ]
==========================>>>>>>>>>>≥>>>>
10. =====>>>>> 5^ ( x+1) + 5 ^ ( 2+x) - 5^3-1

=> 5^x×2 + 5^2 - 5^x - 5^3-1

=> ( 5^x×5+5^2) - 126/ 5^x

=> ( 5×5^2x + 25-126×5^x) / 5x

=> ( 5×5^- 125×5^x - 5^x +25) / 5x

=> 5×5^x ( 5^x -25) - 1( 5^x-25) / 5x

=> ( 5×5 ^-1) ( 5^x - 25) / 5x Ans

===========================>>>>>>>>>>>>

11. ====>>>> 4^(x+1) + 4^ ( 1-x)-10

=> 4^x×4+4× 1/4^x -10

=> ( 4^2x ×4+4-10×4^x) / 4x

=> ( 4^2x ×4 -8×4^-2×4^x) /4x

=> (4^2x × 4-8×4^x- 2×4^x+4) / 4x

=> 4 ^2x ×4 ( 4 ^x-2) -2(4^4x-2) /4x

=> ( 4×4x-2) ( 4^x-2)/4x Ans.
==========================>>>>>>>>>>

12. ========>>>>>> 2^2x - 8×2^x × 2^x +32

=> 2^2x -12 ×2 ^x +32

=> 2^2x - 8×2^x - 4×2^x + 32

=> 2x ( 2x - 8 ) -4 ( 2^x -8)

=> ( 2^x -4 ) ( 2^x -8) Ans
===========================>>>>>>>>>>
13. ======>>>>>> 2x^2 + ax - a^2

=> 2x^2 + 2ax - ax - a^2

=> 2x ( 4+a) - a ( x +a)

=> ( 2x - a ) ( x+a) Ans.

=======================>>>>>>>>>>>>>>

14. ========>>>>>>>>>>>> a^2b^2 x ^2 + b^2x - a^2 x -1

=> b^2x ( a^2x +1) - 1 ( a^2x +1)

=> ( b^2x-1) ( a^2x+1) Ans.

===========================>>>>>>>>>>>

I hope it's help you.....!!!! :)) ✌️✌️