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!