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answers:
say: (2x-7)(x-10)
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Latasha say: q... 2x^2 -27x +70
=> ( 2x )( x ) - ( 7 + ( 10 x 2) )( x ) + ( 7 )( 10 ) ( factorize the terms )
=> ( 2x -7 ) ( x - 10 )
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Deepak Suwalka say: Break -27x in two terms -20x-7x and rewrite
2x² - 20x - 7x + 70
Take 2x common from first two terms and -7 from last two terms
2x(x-10) -7(x-10)
(2x - 7)(x - 10)
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Mathias say: 2x^2 - 27x + 70.
2 * [x^2 - (27/2) * x + 35] <---- Complete the square at this stage.
2 * [(x - 27/4)^2 - 729/16 + 35].
2 * [(x - 27/4)^2 - 729/16 + 560/16].
2 * [(x - 27/4)^2 - 169/16].
2 * [(x - 27/4)^2 - (13/4)^2].
2 * [(x - 27/4 - 13/4) * (x - 27/4 + 13/4)].
2 * [(x - 40/4) * (x - 14/4)].
2 * [(x - 10) * (x - 7/2)].
(x - 10) * 2 * (x - 7/2).
(x - 10) * (2x - 7).
Ans.: (2x - 7) * (x - 10).
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Como say: [ 2x - 7 ] [ x - 10 ]
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la console say: = 2x² - 27x + 70
= 2.[x² - (27/2).x + 35]
= 2.[x² - (27/2).x + (27/4)² - (27/4)² + 35]
= 2.[x² - (27/2).x + (27/4)² - (729/16) + (560/16)]
= 2.[x² - (27/2).x + (27/4)² - (169/16)] → you recognize: a² - 2ab + b²
= 2.[ { x² - (27/2).x + (27/4)² } - (169/16) ] → you know that: a² - 2ab + b² = (a - b)²
= 2.[ { x - (27/4) }² - (169/16) ] → you know that: 169/16 = (13/4)²
= 2.[ { x - (27/4) }² - (13/4)² ] → recall: a² - b² = (a + b).(a - b)
= 2.[x - (27/4) + (13/4)].[x - (27/4) - (13/4)]
= 2.[x - (14/4)].[x - (40/4)] → you simplify
= 2.[x - (7/2)].[x - 10] → you put 2 into the first […]
= (2x - 7).(x - 10)
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Amy say: By factors:
2 * 70 = 140
Find a pair of factors of 140 whose sum is -27.
Answer is -7 and -20
2x^2 -27x +70 = 2x^2 -7x - 20x +70
= x(2x - 7) - 10(2x - 7)