Question

Divide using polynomial long division. (Show your work)

Hint: don’t forget the 0x
(x^3-2x^2+4) ÷ (x+3)

Answer 1

x^3−2x2+4x+3=x2−5x+15+−41x+3

Explanation:

1.Divide the leading term of the dividend by the leading term of the divisor: x3x=x2.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: x2(x+3)=x3+3x2.

Subtract the dividend from the obtained result: (x3−2x2+4)−(x3+3x2)=−5x2+4.

2.Divide the leading term of the obtained remainder by the leading term of the divisor: −5x2x=−5x.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: −5x(x+3)=−5x2−15x.

Subtract the remainder from the obtained result: (−5x2+4)−(−5x2−15x)=15x

3.Divide the leading term of the obtained remainder by the leading term of the divisor: 15xx=15.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: 15(x+3)=15x+45.

Subtract the remainder from the obtained result: (15x+4)−(15x+45)=−41.