# Alegra

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solve the inequality express in interval notation
x^4 + 4x^3 - 9x^2 - 36x < 0

• Algebra -

Assistance needed.

• Alegra -

Ah yeah which is why I post the question.

• Alegra -

Alissa -- Writeacher corrected your spelling of "Algebra" so that a math expert would see your post.

Jiskha doesn't have any experts in Alegra (whatever that is).

• Alegra -

x^4 + 4x^3 - 9x^2 - 36x
= x(x^3 + 4x^2 - 9x - 36)

Cubics are hard to solve, so look for easy roots. They will be factors of 36.

A little synthetic division reveals

(x+4)(x+3)x(x-3)

Now since everything is single roots, the graph alternates between positive and negative between roots.

Since it's a quartic with a positive coefficient, it will be positive before the lowest root and after the highest root.

So,

y > 0 for x < -4
y < 0 for -4 < x < -3
y > 0 for -3 < x < 0
y < 0 for 0 < x < 3
y > 0 for x > 3

• Alegra -

Thank you I appreciate your help and the fact that you didn't make a big issue out of a typo. Again thank you.

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