Expert: Richard J. Raridon - 8/29/2007

Question
QUESTION: a2x3 + (5a2b + ab)x2 + (ab3 + 5ab2)x + b4 divided by ax + b

(note:  all numbers (2s,3s, & 4s) following variables are superscripts.

ANSWER: You can write it
a^2x^3 +(5a^2b+ab)x^2 +(ab^3+5ab^2)x +b^4
If you divide that by ax+b, just like long division, you get ax^2 +5abx +b^3

---------- FOLLOW-UP ----------

QUESTION: Can you show your work so I can understand how you got the answer?

Answer
Do you understand how to divide 25 into 12625?   You look at ax+b and the first term is a^2x^3 so the first term of the answer is ax^2.  Multiply that by ax+b to get
a^2x^3 +abx^2.  Subtract that from the original and you have left 5a^2bx^2 +(ab^3+5ab^2)x +b^4.  Now compare ax+b with 5a^2bx^2 and the second term of the answer is 5abx.  Multiply that by ax+b to get 5a^2bx^2 +5ab^2x.  Subtract again and all you have left is ab^3x +b^4 and the final part of your answer is b^3