SOLUTION: Studying for final exam and require assistance with the following problems: If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0. If f(x)=x(x-1)(x-

Question 69410This question is from textbook Algebra & Trigonometry with Geometry
: Studying for final exam and require assistance with the following problems:
If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0.
Find the quotient and remainder of f(x)=x^3-4x^2+5x+5 divided by p(x)=x-1.
Find the quotient and remainder of f(x)=x^4-2 divided by p(x)=x-1.
Stressing out please help... Thanks, John This question is from textbook Algebra & Trigonometry with Geometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
The product is zero when x=-3 or x=0 or x=1
Draw a number line and put those values in the proper order on the line.
You now have four intervals to look at. Find a value in each interval
as a test interval to see in what intervals the product is greater than zero.
-------
Interval (-inf,-3); pick x=-100; then f(x)= (-)(-)(-) which is <0
Interval (-3,0); pick x= -2 ; then f(x)= (-)(+)(-) which is >0
Interval (0,1) ; pick x= 1/2 ; then f(x)= (+)(+)(-) which is <0
Interval (1,inf); pick x = 100; then f(x)= (+)(+)(+) which is >0
---------
From this you see the answer is : (-3,0) or (1,inf)
================================================================
If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where
f(x)>0
-------
Same procedure as above using x=0,x=1,x=4
==========================
Find the quotient and remainder of f(x)=x^3-4x^2+5x+5 divided by p(x)=x-1.
Use synthetic division :
1)....1....-4....5....5
........1....-3...2..| 7
Quotient = x^2-3x+2
Remainder = 7
---------------------------

Find the quotient and remainder of f(x)=x^4-2 divided by p(x)=x-1
Use synthetic division:
1)....1,,,,0....0....0....-2
........1....1....1....1..|..-1
Quotient: x^3+x^2+x+1
Remainder: -1
===========================
Cheers,
Stan H.

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