Sunday

March 29, 2015

March 29, 2015

Posted by **Alex** on Sunday, August 12, 2012 at 11:38pm.

(x-1)(x+2)

I know the answer is : x<-2, x>1

please show me the steps on how to solve this math problem.

- Algebra -
**Steve**, Sunday, August 12, 2012 at 11:59pmto have the product be positive, either both factors are negative, or both are positive.

Both negative:

x-1 < 0 AND x+2 < 0

x < 1 AND x < -2

==> x < -2

Both positive:

x-1 > 0 AND x+2 > 0

x > 1 AND x > -2

==> x > 1

or, you can consider what you know about polynomials. If there are no repeated roots, then the graph crosses the x-axis at various points. In between those points, the function does not change sign. When crossing the axis, the function changes sign.

So, consider x very large negative. Both factors are negative, so the product is positive. Each time it crosses the x-axis (at one of the roots), it changes sign. So, looking at the number line, and marking + or -, we start way out on the left with +, and change sign at each root:

++++++ -2 ----- 1 +++++++

Repeated roots modify this algorithm some, as the graph may just touch the axis and not change sign.

**Answer this Question**

**Related Questions**

math ergent please please... - 10.a)Solve the inequality x^3-5x^2+2x+8<0 by i...

math ergent please... - 10.a)Solve the inequality x^3-5x^2+2x+8<0 by i) using...

Algebra - Solve the inequality and express the solution in terms of intervals ...

algebra - Given the following function, find: (a) vertex (b) axis of symmetry (c...

algebra - Show all steps solve the problem evaluate the expression for given ...

Math - Could you show me how to work through this problem? Show me steps Solve ...

math - . Given the following function, f(x)=-x^2 -8x find: (a) vertex, (b) axis...

Algebra - Find the domains of rational expressions 2b-2/2b^2-8 please show steps

algebra - How do you solve this math problem? h= -8t^2+40t then it says: when t=...

Math - 3x-4 to y+15 is constant and y=3 when x=2 then when y=12, x equals? My ...