Question

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.

Answer 1

If the division below is carried out:

`(-5x^3-5x^2-2x-4)/(x^2+3x+5)`

If the following were obtained:

• Quotient = −5x+10

,

• Remainder = −7x−54

Then we have that:

`(-5x^3-5x^2-2x-4)/(x^2+3x+5)=(-5x+10)+(-7x-54)/(x^2+3x+5)`

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.