Question

find all zeros of the poynolminal function or solve the given polynomial equation, use the rational zero theorem descartes rule of sign and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root


\[x^3-4x^2-7x+10\]

Answer 1

\[x^3-4x^2-7x+10=0\]

Answer 2

changing sign is 2 so it has 2 positive root or zero positive root

Answer 3

\[f(-x)=-x^3-4x^2+7x+10\]
so it has 1 negative root

Answer 4

factor of 10 is \[\pm1,2,5,10\]

Answer 5

factor of 1 is\[\pm1\]

Answer 6

roots might be \[\pm1,2,5,10\]

Answer 7

f(1)=0 so 1 is root of f(x)

Answer 8

\[\frac{x^3-4x^2-7x+10}{x-1}\]

Answer 9

\[\frac{x^3-4x^2-7x+10}{x-1}=x^2-3x-10\]

Answer 10

\[x^3-4x^2-7x+10=(x-1)(x^2-3x-10)\]
=(x-1)(x-5)(x+2)=0

Answer 11

\[x _1=1, x_2=5, x_3=-2\]