Math, asked by kaurjesmeen4, 5 hours ago

Solve: x(x + 2)(x + 3)(x + 5) = 72.

Answers

Answered by Nishanth0376
0

Answer:

x(x+2)(x+3)(x+5)−72

/* Rearranging the terms, we get */

\begin{gathered} = 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\end{gathered}

=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)Leta=x

2

+5x−−(1)

\begin{gathered} = a(a+6)-72 \\=a^{2}+6a-72 \\= a^{2}+12a-6a-72 \\= a(a+12)-6(a+12) \\= (a+12)(a-6) \end{gathered}

=a(a+6)−72

=a

2

+6a−72

=a

2

+12a−6a−72

=a(a+12)−6(a+12)

=(a+12)(a−6)

\begin{gathered} = (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) \end{gathered}

=(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}Factorsofx(x+2)(x+3)(x+5)−72

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

2

+5x+12)(x+6)(x−1)

Step-by-step explanation:

I think it will help you

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