Hello, to find the sign of the product we use the following rules.
- by + is -
"The enemy of my friend is an enemy."
+ by - is -
"The friend of my enemy is an enemy."
- by - is +
"The enemy of my enemy is a friend."
+ by + is +
"The friend of my friend is a friend."
We can build the following array.
[tex]f(x)=(x+1)(x-3)(x-7)(x+6)[/tex]
[tex]\begin{array}{|c|ccccccccc}x &-\infty & -6 & & -1 & & 3 & & 7 & +\infty\\---&---&---&---&---&---&---&---&---&---\\(x+1)&-&-5&-&0&+&4&+&8&+\\(x-3)&-&-9&-&-4&-&0&+&5&+\\(x-7)&-&-13&-&-8&-&-4&-&0&+\\(x+6)&-&0&+&5&+&9&+&13&+\\---&---&---&---&---&---&---&---&---&---\\f(x)&+&0&-&0&+&0&-&0&+\\\end{array}[/tex]
So f(x) > 0 <=> x < -6 or -1 < x < 3 or x > 7
Thank you
