Three more polynomial questions

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• May 28th 2008, 04:56 PM
haflore
Three more polynomial questions
hello again (Hi) I need confirmation on some questions please!

"Simplify each of the following fractions. If they are already simplified say so.

1) a^2-2ab+b^2/a-b[my answer was: already simplified]

2) a^2-2ab+b^2/a+b[my answer was: already simplified]

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"Some students simplify 2x^2-32/x-4 as 2x-8.

Choose values of x to show that this is not true.Then simplify it correctly."

I answered: Any value of x proves them incorrect. my simplification was:2x+8

thanks for all your help!
• May 28th 2008, 06:52 PM
Reckoner
Quote:

Originally Posted by haflore
Simplify each of the following fractions. If they are already simplified say so.

1) a^2-2ab+b^2/a-b[my answer was: already simplified]

2) a^2-2ab+b^2/a+b[my answer was: already simplified]

Do you mean $\frac{a^2 - 2ab + b^2}{a\pm b}$? If so, please mind the standard order of operations and use parentheses where appropriate to make your notation clearer.

Number one can be simplified, but you will need to place a restriction on $a \text{ and } b$. Here's a hint: factor the numerator.

Quote:

Originally Posted by haflore
"Some students simplify 2x^2-32/x-4 as 2x-8.

Choose values of x to show that this is not true.Then simplify it correctly."

I answered: Any value of x proves them incorrect. my simplification was:2x+8

thanks for all your help!

$\frac{2x^2-32}{x-4} = \frac{2(x + 4)(x - 4)}{x - 4} = 2x + 8,\;x\neq4$

So, your answer is correct, provided that you make the restriction that $x\neq4$.
• May 28th 2008, 07:21 PM
haflore
Thanks for your help Reckoner...

Quote:

Originally Posted by Reckoner
Do you mean $\frac{a^2 - 2ab + b^2}{a\pm b}$? If so, please mind the standard order of operations and use parentheses where appropriate to make your notation clearer.

I posted that question exactly as presented in the text.

Thanks again