Question

$5 \sqrt{5x {}^{2} } + 30x + 8 \sqrt{5}$
Who can Do It.

Answer 1

Hi there !

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Given :

$\mathsf{5 \sqrt{5} x {}^{2} + 30x + 5 \sqrt{5} }$

$\huge {\bold {Solution :}}$

On splitting the middle term, we get ;

$\mathsf{5 \sqrt{5}x {}^{2} + 30x + 8 \sqrt{5} } \\ \\ \mathsf{5 \sqrt{5}x {}^{2} + 20x + 10x + 8 \sqrt{5} } \\ \\ \mathsf{(5x \times \sqrt{5} x) + (5 \times 4)x +( 2 \sqrt{5} \times \sqrt{5} )x + (2 \sqrt{5} \times 4) } \\ \\ \mathsf{5x( \sqrt{5 }x + 4) + 2 \sqrt{5}( \sqrt{5}x + 4) } \\ \\ \bold{taking \: ( \sqrt{5}x + 4) \: as \: common.. } \\ \\ \mathsf{( \sqrt{5}x + 4)(5x + 2 \sqrt{5} )}$

Hence, the answer is ( √5 x + 4 ) ( 5x + 2√5 ).

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Thanks for the question !

☺️☺️☺️

Answer 2

$<b>Heya mate. (^_-). Solution below.$
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♠ Factorization of Quadratic Trinomials ♠


Polynomials of form ax² + bx + c,


Here, we find two integers p and q such that p + q = b and pq = ac





♣ Coming back to question,


★ Given expression is 5√5x² + 30x + 8√5.

Here, 5√5 × 8√5 = (5 × 8 × √5 × √5) = 200.




♦ By midterm split method, we split 30 into two parts whose sum would be 30 and product 200.



♦ After calculating, we find 20 + 10 = 30 and 20 × 10 = 200




•°• 5√5x² + 30x + 8√5

= 5√5x² + 20x + 10x + 8√5

= 5x (√5x + 4) + 2√5 (√5x + 4)

= (5x + 2√5) (√5x + 4)



♥ Hence, 5√5x² + 30x + 8√5 = (5x + 2√5)(√5x + 4)
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Thank you.. ^_^