X4 - 10x3 + 35x² – 50x + 24 > 0
Answers
x^4+10x^3+35x^2+50x+24
x
4
+10x
3
+35x
2
+50x+24=x
4
+(x
3
+9x
3
)+(9x
2
+26x
2
)+(26x+24x)+24
=(x
4
+x
3
)+(9x
3
+9x
2
)+(26x
2
+26x)+(24x+24)
=x
3
(x+1)+9x
2
(x+1)+26x(x+1)+24(x+1)
=(x+1)(x
3
+9x
2
+26x+24)
=(x+1)(x
3
+(2x
2
+7x
2
)+(14x+12x)+24)
=(x+1)((x
3
+2x
2
)+(7x
2
+14x)+(12x+24))
=(x+1)(x
2
(x+2)+7x(x+2)+12(x+2))
=(x+1)(x+2)(x
2
+7x+12)
=(x+1)(x+2)(x
2
+3x+4x+12)
=(x+1)(x+2)(x(x+3)+4(x+3))
=(x+1)(x+2)(x+3)(x+4)I h