[tex]a)\\\\x^2+3x-4=0\\\\x^2+4x-x-4=0\\\\x(x+4)-(x+4)=0\\\\(x+4)(x-1)=0\\\\x+4=0\ \ \ \ \vee\ \ \ \ x-1=0\\\\x=-4\ \ \ \ \ \ \ \ \vee\ \ \ \ x=1\\\\\\b)\\\\x^3=-5x^2\\\\x^3+5x^2=0\\\\x^2(x+5)=0\\\\x^2=0\ \ \ \ \vee\ \ \ \ x+5=0\\\\x=0\ \ \ \ \ \ \vee\ \ \ \ x=-5[/tex]
[tex]c)\\\\2x^3+x^2-8x-4=0\\\\x^2(2x+1)-4(2x+1)=0\\\\(2x+1)(x^2-4)=0\\\\(2x+1)(x-2)(x+2)=0\\\\2x+1=0\ \ \ \ \ \ \ \ \vee\ \ \ \ x-2=0\ \ \ \ \vee\ \ \ \ x+2=0\\\\2x=-1\ \ |:2\ \ \ \ \vee\ \ \ \ x=2\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-2\\\\x=-\frac{1}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=2\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-2[/tex]
[tex]d)\\\\x^2+3x-10 < 0\\\\x^2+5x-2x-10 < 0\\\\x(x+5)-2(x+5) < 0\\\\(x+5)(x-2) < 0\\\\x+5=0\ \ \ \ \vee\ \ \ \ x-2=0\\\\x=-5\ \ \ \ \ \ \vee\ \ \ \ x=2\\\\\\e)\\\\-x^2+2x+3\geq 0\ \ |\cdot(-1)\\\\x^2-2x-3\leq 0\\\\x^2+x-3x-3\leq 0\\\\x(x+1)-3(x+1)\leq 0\\\\(x+1)(x-3)\leq 0\\\\x+1=0\ \ \ \ \vee\ \ \ \ x-3=0\\\\x=-1\ \ \ \ \ \ \vee\ \ \ \ x=3[/tex]
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[tex]a)\\\\x^2+3x-4=0\\\\x^2+4x-x-4=0\\\\x(x+4)-(x+4)=0\\\\(x+4)(x-1)=0\\\\x+4=0\ \ \ \ \vee\ \ \ \ x-1=0\\\\x=-4\ \ \ \ \ \ \ \ \vee\ \ \ \ x=1\\\\\\b)\\\\x^3=-5x^2\\\\x^3+5x^2=0\\\\x^2(x+5)=0\\\\x^2=0\ \ \ \ \vee\ \ \ \ x+5=0\\\\x=0\ \ \ \ \ \ \vee\ \ \ \ x=-5[/tex]
[tex]c)\\\\2x^3+x^2-8x-4=0\\\\x^2(2x+1)-4(2x+1)=0\\\\(2x+1)(x^2-4)=0\\\\(2x+1)(x-2)(x+2)=0\\\\2x+1=0\ \ \ \ \ \ \ \ \vee\ \ \ \ x-2=0\ \ \ \ \vee\ \ \ \ x+2=0\\\\2x=-1\ \ |:2\ \ \ \ \vee\ \ \ \ x=2\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-2\\\\x=-\frac{1}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=2\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-2[/tex]
[tex]d)\\\\x^2+3x-10 < 0\\\\x^2+5x-2x-10 < 0\\\\x(x+5)-2(x+5) < 0\\\\(x+5)(x-2) < 0\\\\x+5=0\ \ \ \ \vee\ \ \ \ x-2=0\\\\x=-5\ \ \ \ \ \ \vee\ \ \ \ x=2\\\\\\e)\\\\-x^2+2x+3\geq 0\ \ |\cdot(-1)\\\\x^2-2x-3\leq 0\\\\x^2+x-3x-3\leq 0\\\\x(x+1)-3(x+1)\leq 0\\\\(x+1)(x-3)\leq 0\\\\x+1=0\ \ \ \ \vee\ \ \ \ x-3=0\\\\x=-1\ \ \ \ \ \ \vee\ \ \ \ x=3[/tex]