Question

x(x+2)(x+3)(x+5)-72 factor

Answer 1

So, x (x+2)(x+3)(x+5)=(x-1)(x+6)(x^2+5x+12)

Answer 2

$x(x+2)(x+3)(x+5)-72$

/* Rearranging the terms, we get */

$= x(x+5)(x+2)(x+3) - 72 \\= (x^{2}+5x)(x^{2}+3x+2x+6)-72 \\= (x^{2}+5x)(x^{2}+5x+6) -72$

$Let \: a = x^{2}+5x \: --(1)$

$= a(a+6)-72 \\=a^{2}+6a-72 \\= a^{2}+12a-6a-72 \\= a(a+12)-6(a+12) \\= (a+12)(a-6)$

$= (x^{2}+5x+12)(x^{2}+5x-6 ) \:[From \:(1) ] \\= (x^{2}+5x+12)(x^{2}+6x-1x -6 )\\= (x^{2}+5x+12)[x(x+6)-1(x+6) \\= </p><p>(x^{2}+5x+12)(x+6)(x-1)$

Therefore.,

$\red{ Factors \:of \: x(x+2)(x+3)(x+5)-72}$

$\green {= (x^{2}+5x+12)(x+6)(x-1)}$

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