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If the quotient of two polynomials is #4x^2-x-7+(11x+15)/(x^2+x+2)#, what are the two polynomials?

Answer 1

#(4x^4 +3x^3+0x^2+2x+1) -: (x^2+x+2)#

Given:#" "4x^2-x-7+(11x+15)/(x^2+x+2)#

The #11x+15# is the remainder so the denominator must be the divisor. Thus we need to build each term by using #x^2+x+2#

Note that I use a place holder. For example: #0x^4#

color(white)(.)

#4x^2(x^2+x+2) -> 4x^4+4x^3+8x^2# #-x(x^2+x+2)->0x^4-color(white)(4)x^3-color(white)(8)x^2-2x# #-7(x^2+x+2)->0x^4+0x^3-7x^2-7x-14# #"The remainder"->ul(color(white)(.)0x^4+0x^3+0x^2+11x+15) larr" Add" # #" "4x^4 +3x^3+0x^2+2x+1#

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Answer 2

Savannah Anderson

The two polynomials are 4x^2 - x - 7 and x^2 + x + 2.

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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.