Precalculus
posted by Jayson on .
Help with these questions
help with these questions~
Thank you
1. Determine the interval(s) on which x^2 + 2x 3>0
a)x<3, x>1
b)3<x<1
c)x<3, 3<x<1, x>1
d) x>1
Answer is D, x>1

2. Determine when the function f(x)= 3x^3 + 4x^2 59x 13 is greater than 7.
a) 5<x<1/3
b) 5<x<1/3, x>4
c) x<4
d) x=5, 1/3,4
Answer is: B

3. Provde the intervals you would check to determine when 5x^2 + 37x> 15x^2 + 12x + 15.
a) x=3, x=0.5
b) x<3, 3<x<0.5, x>0.5
c) x<1, 1<x<15, x>15
d) x= 1, x=15


1. x^2 + 2x  3 > 0
(x+3)(x1) > 0
xintercepts are 3 and 1
so you are looking for the values of x when the parabola y = x^2 + 2x  3 is above the xaxis
Since it opens upwards those values are
x < 3 OR x > 1
The closest choice to that is #1, but they did not include the necessary OR. The comma is this context means AND, which would be incorrect.
2. 3x^3 + 4x^2  59x  13 > 7
3x^3 + 4x^2  59x  20 > 0
after some quick tries of ±1, ±2, ± 4, I found x=4 to be a solution, so x4 is a factor
by synthetic division,
3x^3 + 4x^2  59x  20 = (x4)(3x^2 + 16x + 5)
= (x4)(x+5)(3x+1)
so the critical values are 5, 1/3, and 4
So the curve is above the xaxis (or above 7 in the original) for
5 < x < 1/3 OR x > 4
Again, they made an error by not stating the OR condition, but it looks like they meant b) , which is what you had.
3. 5x^2 + 37x> 15x^2 + 12x + 15
10x^2 + 25x  15 > 0
2x^2 + 5x  3 > 0
(2x  1)(x + 3) > 0
critical values are 1/s and 3
so I would check
x < 3, 3 < x < 1/2, and x > 1/2
looks like b) is the correct choice. 
1. The graph is a parabola, opening upward. So, there will be a left side and a right side above the xaxis. These intervals will be outside the two roots.
A is the correct answer
2. B is correct
3. The graphs intersect at x = 3 and 0.5
So, B is the answer 
Thank you~