Create a unique example of dividing a polynomial by a monomial and provide the simplified form. Explain, in complete sentences, the two ways used to simplify this expression and how you would check your quotient for accuracy.

Question

anonymous · Answer

(3x^3 – 6x^2 + x) / 3x^2
 3x^3/3x^2 – 6x^2 / 3x^2 + x/ 3x^2
 x^1 – 2x^0 + 1/x^1
 x – 2 +1/3x
 
You divide the first term 3x^3 by 3x^2 and 3 divided by 3 gives you 1 and dividing exponents you subtract so 3 – 2 gives you the x^1 which is actually just x
 
The second term is -6x^2 divided by 3x^2 and -6 divided by 3 is -2 and x^2 – x^2 is 0 and x^0 will give you one so -2 times 1 will be -2
 
The third term is x divided by 3x^2
 so 1 – 2 is -1 so the x is on the bottom (denominator) with the 3 and you need a 1 on the top (numerator) 1/3x
 
so if I take x-2 + 1/3x and I multiply by 3x^2 I get 3x^3 – 2x^2 + 3x^2/ 3x which simplifies to x
 which is what we started out with.
 
Hope this helped

anonymous · Answer

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