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How do you find the quotient of #(x^2+3x-28)div(x+7)#?

Answer 1

Eva Adamson

See the entire solution process below:

First, rewrite the problem as:

#(x^2 + 3x - 28)/(x + 7)#

Next, factor the numerator:

#((x + 7)(x - 4))/(x + 7)#

Then, cancel the common terms in the numerator and denominator:

#(color(red)(cancel(color(black)((x + 7))))(x - 4))/(color(red)(cancel(color(black)((x + 7))))#

#x - 4#

However, because you cannot divide by #0# we must qualify this answer:

#(x^2 + 3x - 28) -: (x + 7) = (x - 4)# where #x != -7#

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Answer 2

Genesis Allen

To find the quotient of (x^2+3x-28) divided by (x+7), you can use long division or synthetic division.

Using long division:

Divide x^2 by x, which gives x.
Multiply (x+7) by x, which gives x^2+7x.
Subtract (x^2+7x) from (x^2+3x-28), which gives -4x-28.
Bring down the -4x term.
Divide -4x by x, which gives -4.
Multiply (x+7) by -4, which gives -4x-28.
Subtract (-4x-28) from (-4x-28), which gives 0.

Therefore, the quotient is x-4.

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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.