Question

factories(x+1)(x+2)(2x-3)(2x-5)+12

Answer 1

(x+1)(x+2)(2x−3)(2x−5)+12

4x⁴−4x³−25x²+13x+42

=(x−2)(2x+3)(2x²−x−7)

Hope this will helps

Answer 2

Answer:

( 2 x + 3 )( x - 2 )( 2 x² - x - 7 )

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Step-by-step explanation:

( x + 1 )( x + 2 )( 2 x - 3 )( 2 x - 5 ) + 12

[ Using formula : ( x + a )( x + b ) = x² + a x + bx + ab  ]

==> ( x² + x + 2 x + 2 )( 2 x - 3 )( 2 x - 5 ) + 12 ]

==> ( x² + 3 x + 2 )( 2 x - 3 )( 2 x - 5 ) + 12

[ Using formula : ( x - a )( x - b ) = x² - a x - b x + ab ]

==> ( x² + 3 x + 2 )( 4 x² - 6 x - 10 x + 15 ) + 12 ]

==> ( x² + 3 x + 2 )( 4 x² - 16 x + 15 ) + 12

==> x²( 4 x² - 16 x + 15 ) + 3 x ( 4 x² - 16 x + 15 ) + 2 ( 4 x² - 16 x + 15 ) + 12

==> 4 x⁴ - 16 x³ + 15 x² + 12 x³ - 48 x² + 45 x + 8 x² - 32 x + 30 + 12

==> 4 x⁴ - 4 x³ - 25 x² + 13 x + 42

==> ( 2 x² )² - 2 x³ - 2 x³ - 12 x² - 14 x² + x² + 13 x + 42

==> ( 2 x²)² - 2 x³ - 12 x² - 2 x³ - 14 x² + x² + 13 x + 42

==> ( 2 x² )² - 2 x ( x + 6 ) - 2 x ( x + 7 ) + x² + 13 x + 42

==> ( 2 x² )² - 2 x( x + 6 ) - 2 x ( x + 7 ) + x² + 6 x +7 x + 42

==> ( 2 x² )² - 2 x( x + 6 ) - 2 x ( x + 7 ) + x( x + 6 )+7 (x + 6 )

==> ( 2 x² )² - 2 x( x + 6 ) - 2 x ( x + 7 ) + ( x + 6 )( x + 7 )

[ Using the formula: x² - a x - bx +ab = ( x - a )( x - b )

==> ( 2 x² - ( x + 6 ) )( 2 x² - ( x + 7 )) ]

==> ( 2 x² -  x - 6 )( 2 x² - x - 7 )

==> ( 2 x² - 4 x + 3 x - 6 )( 2 x² - x - 7 )

==> ( 2 x ( x - 2 ) + 3 ( x - 2 ) ) ( 2 x² - x - 7 )

==> ( 2 x + 3 )( x - 2 )( 2 x² - x - 7 )

Hope it helps you ^_^

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