Question

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.

Answer 1

We will say you are given the expression x^2+15x+56 and you are asked to find the other factor when the first factor you received is x+8 .

long division x+8 into x^2+15x+56 always use the leading coefficient of what you want to go into something such as x+8 into X^2+15x+56 how many times does x go into x^2
- x^2+8x
-------------------- since you are dividing you would subtract to get your answer x^2-x^2=0 15x-(+8x) 7x + 56
is equal to 7x how many times does x go into 7x x+7
-7x+56= -7x-56
7x+56
-7x-56
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0

or you could set it up like a fraction which is really what division really is

x^2+15x+56 if the polynomial factors here you can use this method
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x+8

x^2+15x+56 (x+8) (x+7) what multiplied comes out to 56 and added will equal 15 8,7

(x+8)(x+7)
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(x+8) the 2 x+8 's cancel and you have x+7 as your answer