Algebra 2 help

[brit500freestyle]

I really need help with solving the following and showing all work.

1. 5x^3-2x^2+15x-6=0
2. x^2=6x+55
3. x^4-13x^2+36=0
4. 5x^3=-5000

 

[masters]

I really need help with solving the following and showing all work.

1. 5x^3-2x^2+15x-6=0
2. x^2=6x+55
3. x^4-13x^2+36=0
4. 5x^3=-5000

Hi brit500freestyle,

Might help if you showed a little of what you can do here.

(1) Factor by grouping.

\(\displaystyle 5x^3-2x^2+15x-6=0\)

\(\displaystyle x^2(5x-2)+3(5x-2)=0\)

Does that help? One real, two imaginary solutions.

(2) Set everything equal to zero.

\(\displaystyle x^2=6x+55\)

\(\displaystyle x^2-6x-55=0\)

\(\displaystyle (x-11)(x+5)=0\)

You should be okay from here...

(3) Just factor.

\(\displaystyle x^4-13x^2+36=0\)

\(\displaystyle (x^2-4)(x^2-9)=0\)

How's that for a start? Remember, there are 4 zeros here.

(4) \(\displaystyle 5x^3=-5000\)

First, divide both sides by 5.

\(\displaystyle x^3=-1000\)

Set everything equal to zero.

\(\displaystyle x^3+1000=0\)

The left side is the sum of two cubes. There's a factoring pattern for that. You should know it. But here it is just for you:

\(\displaystyle a^3+b^3=(a+b)(a^2-ab+b^2)\)

Have fun finishing everything up. Ciao!