Question

If p = x (3x + 5) - 28 , then p is divisible
by which of the following expressions?
(A) 8x + 4
(B) x-4
(C) x-7
(D) 3x-7​

Answer 1

$Given \: p = x(3x+5) - 28$

$\implies p = 3x^{2} + 5x - 28$

/* Splitting the middle term, we get */

$\implies p = 3x^{2} + 12x - 7x - 28$

$\implies p = 3x( x + 4 ) - 7( x + 4 )$

$\implies p = ( x + 4 )( 3x - 7 )$

$( x + 4 ) \:and \: ( 3x - 7 ) \: are \: factors \: p$

$p \: is \: divisible \: by \: ( x + 4 ) \:and \: (3x - 7 )$

Therefore.,

$Option \: \pink { ( D ) } \: is \: correct.$

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