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@Zukra
August 2022
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Разложить на множители выражение
А=(x+1)(x+3)(x+5)(x+7)+15
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NatashaFCSM
(x+1)(x+3)(x+5)(x+7)+15=(x²+4x+3)(x+5)(x+7)+15=
=(x³+9x²+23x+15)(x+7)+15=x⁴+16x³+86x²+176x+105+15=
=x⁴+16x³+86x²+176x+120=x⁴+2x³+14x³+28x²+58x²+116x+60x+120=
x³(x+2)+14x²(x+2)+58x(x+2)+60(x+2)=(x+2)(x³+14x²+58x+60)=
=(x+2)(x³+6x²+8x²+48x+10x+60)=(x+2)(x²(x+6)+8x(x+6)+10(x+6))=
=
(x+2)(x+6)(x²+8x+10)
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Answers & Comments
=(x³+9x²+23x+15)(x+7)+15=x⁴+16x³+86x²+176x+105+15=
=x⁴+16x³+86x²+176x+120=x⁴+2x³+14x³+28x²+58x²+116x+60x+120=
x³(x+2)+14x²(x+2)+58x(x+2)+60(x+2)=(x+2)(x³+14x²+58x+60)=
=(x+2)(x³+6x²+8x²+48x+10x+60)=(x+2)(x²(x+6)+8x(x+6)+10(x+6))=
=(x+2)(x+6)(x²+8x+10)