How do I solve polynomials and write it in standard form? How do I find the vertical asymptote, the zeros, and the hole(in the graph)?

Question

I have a project I have to do for math and I have to solve the polynomial f(x)= (x+1)(x-0)(x+3)/(x+2)(x-0)(x+0)(x-0).  It's a fraction.. Not division. Then i have to put it in expanded form, and I'm not sure how to do it. Please help me.

Answer 1

Miquela,

 

What you need to do is reduce the expression, then multiply the numerator and denominator out.

 

f(x) = (x+1)(x)(x+3)/[(x+2)(x)(x)(x)]

 

Notice that there is a FACTOR of x in front and after the /. That means you can cancel both off. This leaves:

 

f(x) = (x+1)(x+3)/[(x+2)x²]

 

(Note that I wrote (x)(x) as x², since that is what x² means.

 

Now, you can just multiply the numerator and denominator out:

 

(x+1)(x+3) = x² + 4x + 3

 

and

 

(x+2)x² = x³ + 2x².

 

Putting this together,

 

f(x) = (x² + 4x + 3)(x³ + 2x²).

 

Since you already crossed off all of the common factors, this should be the final, simplified answer.

 

Let me know if this works out for you.