# math

solve the following polynomial and rational inequalities

2x^2+x-6>0

i need some help with this

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1. 2x^2+x-6>0

A=2
B=1
C=-6

Multiply A and C together
A=2, C=-6, 2x(-6)=-12
Find factors of -12 that add up to give you a positive value of 1, B

We figure out that factors of -12 that add up to give us 1 are 4 and -3

We rewrite our equation as:
2x^2+(4x-3x)-6>0

We can group our first two and our second two and factor those.

(2x^2+4x)-(3x-6)
We factor out a 2x from first grouping
2x(x+2)

We factor out a -3 from second grouping
-3(x+2)

What is left in both groupings must be the same to complete problem

Combine our GCF's and what left as our factors

(2x-3)(x+2)>0 Solve for x on both factors.

x>(3/2) x>-2

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