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How do you divide #(4x^2+8x+16) / (x-2) #?

Answer 1

#(4x^2+8x+16)/(x-2) = 4x+16 " with a remainder of "48#

This can be done by polynomial long division or synthetic division.

Using synthetic division (because it is easier to format here) [Remember that when dividing by a monic binomial the multiplicative value is the negative of the constant; in this case the negative of #(-2)# is #+2#

#{: (,,x^2,x^1,x^0), (,"|",4,+8,+16), (+,"|", ,8 ,32), (xx(+2),"|",color(red)(4),color(red)(16),color(blue)(48)), (,,x^1,x^0,"Remainder") :}#

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Answer 2

Savannah Anderson

To divide (4x^2+8x+16) by (x-2), we can use long division or synthetic division. Here is the solution using long division:

     4x + 16
_______________

x - 2 | 4x^2 + 8x + 16 - (4x^2 - 8x) _____________ 16x + 16 - (16x - 32) _____________ 48

Therefore, the quotient is 4x + 16 and the remainder is 48.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.