2. Use long division to get a quotient and a remainder.

 

 

Divide the first term in the divisor into the first term in the dividend. x goes into 2x3 2x2 times. This is the first term in the quotient.

 

 

 

Multiply this term in the quotient by the divisor and subtract from the dividend.

 

 

Repeat the process with the remainder. Divide the first term in the quotient into the first term in the remainder. x goes into -3x -3 times. Put this term in the next place in the quotient

 

 

 

Multiply this term in the quotient times the divisor and subtract from the remainder.

 

 

Remember that subtract means change the sign and add.

 

 

 

At this point, the remainder has smaller degree than the divisor, so we stop and put the remainder over the divisor and add the fraction to the quotient,

 

 

 

or, more simply,

 

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problem 2