SOLUTION: Solve each polynomial equation by factoring: 1. 4x^5 - 8x^3 + 4x = 0 2. x^4 - 12x^2 = -36 3. 4x^3 + 7x^2 - 5x = 6

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve each polynomial equation by factoring: 1. 4x^5 - 8x^3 + 4x = 0 2. x^4 - 12x^2 = -36 3. 4x^3 + 7x^2 - 5x = 6      Log On


   

Question 953637: Solve each polynomial equation by factoring:
1. 4x^5 - 8x^3 + 4x = 0
2. x^4 - 12x^2 = -36
3. 4x^3 + 7x^2 - 5x = 6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.
4x%5E5+-8x%5E3+%2B+4x+=+0
4x%28x%5E4+-2x%5E2+%2B+1%29+=+0
4x%28x%5E2+-+1%29%5E2+=+0
4x%28x%5E2+-+1%29%28x%5E2+-+1%29+=+0
4x%28x+-+1%29%28x%2B1%29%28x+-+1%29%28x%2B1%29+=+0
solutions:
if 4x+=+0=>x=0
if%28x+-+1%29+=+0=>x=1...double solution since we have factor x-1 twice
%28x%2B1%29+=+0=>x=-1...double solution since we have factor x%2B1 twice

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E5+-8x%5E3+%2B+4x%29+


2.
x%5E4+-12x%5E2+=+-36
x%5E4+-12x%5E2+%2B36=0.............recall the rule %28a-b%29%5E2=a%5E2-2ab%2Bb%5E2; in your case a=1 and 2ab=12=> b=6
now write it as a square of difference
%28x%5E2+-6%29%5E2=0
%28x%5E2+-6%29%28x%5E2+-6%29=0...since factors are same, you will have two pairs of double roots
if %28x%5E2+-6%29=0=>x%5E2=6=>x=sqrt%286%29 or x=-+sqrt%286%29 exact solution
=>x=2.5 or x=-+2.5 approximate
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+50%2C%28x%5E2+-6%29%28x%5E2+-6%29%29+


3.

4x%5E3+%2B+7x%5E2+-5x+=+6
4x%5E3+%2B+7x%5E2+-5x+-6=0
4x%5E3-x%5E2%2B8x%5E2-2x-3x-6=0
%284x%5E3%2B8x%5E2%29-%28x%5E2%2B2x%29-%283x%2B6%29=0
4x%5E2%28x%2B2%29-x%28x%2B2%29-3%28x%2B2%29=0
%284x%5E2-x-3%29%28x%2B2%29=0
%28%284x%5E2-4x%29%2B%283x-3%29%29%28x%2B2%29=0
%284x%28x-1%29%2B3%28x-1%29%29%28x%2B2%29=0
%284x%2B3%29%28x-1%29%28x%2B2%29=0
solutions:
if 4x%2B3=0=>4x=-3=>x=-3%2F4
if %28x-1%29=0=>x=1
%28x%2B2%29=0=>x=-2


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E3+%2B+7x%5E2+-5x+-6%29+