# Thread: Solving Polynomial Expressions

1. ## Solving Polynomial Expressions

If I can only get on a few problems I'll have an idea on how to complete the WS.... It's been driving me crazy...

Factor the expression on the left side of each equation. Then solve the equation.

4) 2x^3-250=0

Factor it (I think) to: (2x)^3 ....then what? 250 can't be squared....

Same directions...

9) x^4-5x^2+4=0

I have no idea what to do...

Two more problems:

Factor each expression.

25) x^3-125

Solve each equation:

x^4-x=0

If you could help at all, that'd be great. I tried looking for help online and in my book... and I can't find anything...

2. 4) divide across eqn by 2

then difference of cubes is given by

9) let y = x^2

solve eqn for y

then use y = x^2 to get x

25) difference of two cubes again

x^4-x = x(x^3-1)
hope this helps!

3. I'm still lost....

4. 4) 2x^3-250 = 0
x^3 -125 = 0

x^3 = 125
x = 5 ( cube root of 125)

9) let y = x^2

then eqn becomes
y^2 -5y +4 = 0

(y-4)(y-1) = 0

so y - 4 = 0 then y = 4 = x^2 so x = 2,-2
or y -1 = 0 then y = 1 = x^2 so x = 1,-1

25)

x^4 - x = x(x^3-1) = 0

so x = 0

or x^3 - 1 = 0 ie x^3 = 1 so x = 1