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