Posted by **Liz** on Tuesday, October 18, 2011 at 3:47pm.

Show all work

solve the Polynomial inequality and express the solution in set notation.

(3p-2p^2)/(4-p^2)<(3+p)/(2-p)

- College Algebra -
**Steve**, Tuesday, October 18, 2011 at 4:10pm
You want

(3p-2p^2)/(4-p^2) - (3+p)/(2-p) < 0

p(3-2p)/(2-p)(2+p) - (3+p)(2+p)/(2-p)(2+p) < 0

[p(3-2p) - (3+p)(2+p)]/(2-p)(2+p) < 0

(3p - 2p^2 - p^2 - 5p - 6)/(2-p)(2+p) < 0

(3p^2 + 2p + 6)/(2-p)(2+p) > 0

The numerator is always positive.

So, we want the region where 4-p^2 is positive.

That is, -2 < p < 2

Just to check, graph the two functions, and you'll see that this is the case.

- College Algebra -
**Lauren**, Tuesday, October 18, 2011 at 5:46pm
Factor the polynomials by pulling out the GCF

6r^2+12r-15

- College Algebra -
**Lauren**, Tuesday, October 18, 2011 at 5:54pm
Sorry, I posted in the wrong place :(

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