little confused as to what this question is asking of me

solve by factoring

5x^3 + x^2 - 45x -9 = 0

25 fg to whoever shows work and solves

Factor the first two and last two terms.

x^2 * (5x + 1) - 9 * (5x + 1) = 0

Rearrange:

(5x + 1) * (x^2 - 9) = 0

Expand:

(5x + 1) * (x - 3) * (x + 3) = 0

x = -1/5, 3, -3


I don't really know any "tricks" to do these, besides finding things that can be pulled out to simplify the equation until you have two of the same terms... in this case, (5x + 1)

Edit: Or like with almost all math at this level, you can probably find a calculator online that will walk you through step by step. "Polynomial Factoring Calculator" in google.

This post was edited by RzChaos on Feb 21 2016 09:54pm

this is a little confusing

the question is also confusing, why are they asking me to factor

I'm not sure what was confusing about what I posted, where did you get lost?

They are asking you to factor simply because the teacher wants you to practice that method so that you can identify the factors quicker in the future, and it presents the solution in a common form. -- Like when we all did "FOIL" for x^2 functions. Other methods would work fine to determine the answer.

so basically just forget the = 0 ?

like you want = 0, but then just basically erase it and just factor the other stuff?

also i get lost when you expand

I get to (x^2-9)(5x+1)

but I dont know why you go forward after that, and i dont know why x ends up being three different answers

"Factoring" is just expanding the left side of the equation, so that you can solve for what makes the equation equal zero. You don't really need to pay attention to the = 0 until the last step.


You don't really need to go foward after (x^2 - 9)(5x + 1), if you can recognize that (x^2 - 9) leads to answers of 3, -3.

If you just don't understand the math of how it expands:

(5x + 1) doesn't change in the "Expand" step.

(x ^2 - 9) = (x + 3)(x - 3), because when you multiply this out...."FOIL"....you get x^2 + 3x - 3x - 9 = (x^2 - 9)

To determine the final three answers, you just take the final equation.... (5x + 1) ( x - 3) ( x + 3) = 0, and look for what values of x will make this 0.

Take each individual ( ) and set it equal to zero:
5x + 1 = 0, x = -1/5
x - 3 = 0, x = 3
x + 3 = 0, x = -3

If x is any of these, you will get one of the ( ) = 0, so when you multiply them all out you get 0.

Just to expand on what RzChaos said:

Starting with (5x + 1) * (x - 3) * (x + 3) = 0

Let's make some substitutions:
A = 5x + 1
B = x -3
C = x + 3

gives us:

A*B*C = 0

The only way A*B*C can equal 0 is if A, B, or C is 0. So we break the problem into 3 problems:

A = 0, B = 0, C = 0; reverse the substitution and you get:

5x + 1 = 0
x -3 = 0
x + 3 = 0

Solve each of these and you will have the three answers given by RzChaos.

By factoring you turned it into a multiplication problem (A*B*C) which allowed you to make the argument about how they must = 0. Without factoring it would have remained an addition problem and we couldn't have used this argument to solve it (we'd be stuck).