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Suppose a classmate performs the division, (−5x^3−5x^2−2x−4)÷(x^2+3x+5), and gives the following results:Quotient = −5x+10Remainder = −7x−54Explain how you could verify that the answer is correct, without performing the division yourself.

Respuesta :

If the division below is carried out:

[tex]\frac{-5x^3-5x^2-2x-4}{x^2+3x+5}[/tex]

If the following were obtained:

• Quotient = −5x+10

,

• Remainder = −7x−54

Then we have that:

[tex]\frac{-5x^3-5x^2-2x-4}{x^2+3x+5}=(-5x+10)+\frac{-7x-54}{x^2+3x+5}[/tex]

To verify if the result is correct, we simplify the fraction on the right-hand side above and see if the numerator is obtained.

This is done below.

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