SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!! Solving Polynomial Eq

Question 166923This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!!
Solving Polynomial Equations
Solve. Identify all double roots.
(s-6)^3=27(s-8) This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Expand to get . Hint: Use Pascal's Triangle to expand

Distribute

Add 216 to both sides. Notice that they cancel out and go away.

Subtract 27s from both sides.

Combine like terms.

Factor out the GCF "s" from the left side

Factor to get

Now set each factor equal to zero:

, or

, or Now solve for s in each case

Since we have a repeating answer, our answers are or

================================

Answer:

So the solutions are or where is a double root (ie has a multiplicity of 2)
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