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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