SOLUTION: hi, i need help on these kind of problems solve for x, then write the equation as a polynomial. the problem is (x-3)(x-2)=0 thank you

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Question 36929: hi, i need help on these kind of problems solve for x, then write the equation as a polynomial. the problem is (x-3)(x-2)=0 thank you
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Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
From just looking at the equation, there are going to be 2 values for x.
As long as one of the quantities equals zero, you multiply the other and you also get zero; therefore, you know the answer.
X = 3 or 2
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %28x-3%29%2A%28x-2%29 simplifies to x%5E2-5%2Ax%2B6
  • Text form: (x-3)*(x-2) simplifies to x^2-5*x+6
  • Cartoon (animation) form: simplify_cartoon%28+%28x-3%29%2A%28x-2%29+%29
    For tutors: simplify_cartoon( (x-3)*(x-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28x-3%29%2A%28x-2%29+%29.
Expanded term %28x-2%29 by using associative property on %28x-3%29
It becomes highlight_green%28+%28x-2%29%2Ax+%29-highlight_green%28+%28x-2%29%2A3+%29.
Look at highlight_red%28+%28x-2%29%2Ax+%29-%28x-2%29%2A3.
Expanded term x by using associative property on %28x-2%29
It becomes highlight_green%28+x%2Ax+%29-highlight_green%28+x%2A2+%29-%28x-2%29%2A3.
Look at highlight_red%28+x+%29%2Ahighlight_red%28+x+%29-x%2A2-%28x-2%29%2A3.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes highlight_green%28+x%5E2+%29-x%2A2-%28x-2%29%2A3.
Look at x%5E2-x%2A2-highlight_red%28+%28x-2%29%2A3+%29.
Expanded term -3 by using associative property on %28x-2%29
It becomes x%5E2-x%2A2-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A2+%29.
Look at x%5E2-x%2A2-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29.
Multiplied numerator integers
It becomes x%5E2-x%2A2-3%2Ax%2Bhighlight_green%28+6+%29.
Look at x%5E2-highlight_red%28+x%2A2+%29-highlight_red%28+3%2Ax+%29%2B6.
Eliminated similar terms highlight_red%28+-x%2A2+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%28-2-3%29%2Ax+%29
It becomes x%5E2%2Bhighlight_green%28+%28-2-3%29%2Ax+%29%2B6.
Look at x%5E2%2B%28-highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ax%2B6.
Added fractions or integers together
It becomes x%5E2%2B%28highlight_green%28+-5+%29%29%2Ax%2B6.
Look at x%5E2%2B%28highlight_red%28+-5+%29%29%2Ax%2B6.
Removed extra sign in front of -5
It becomes x%5E2%2B%28-highlight_green%28+5+%29%29%2Ax%2B6.
Look at x%5E2%2Bhighlight_red%28+%28-highlight_red%28+5+%29%29%2Ax+%29%2B6.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes x%5E2-highlight_green%28+5+%29%2Ax%2B6.
Result: x%5E2-5%2Ax%2B6

Universal Simplifier and Solver


Done!

Now you have your polynomial.
x%5E2-5x%2B6=0
Hope this helps!