Question

How do you find the quotient of 25a^2 – 60ab + 36b^2 ÷ 5a – 6b?

Answer 1

`(25a^2-60ab+36b^2) div (5a-6b) = (5a-6b)`

Explanation:

Best way for this case
Recognize that `25a^2-60ab+36b^2` is a square which can be factored as:
`color(white)("XXXX")(5a-6b)^2`
and
`(5a-6b)^2/(5a-6b) = (5a-6b)`

More general method: long polynomial division

#{: (,,5a,-6b,), (,,"-----","-----","-----"), (5a-6b,")",25a^2,-60ab,+36b^2), (,,25a^2,-30ab,), (,,"-----","---------",), (,,,-30ab,+36b^2), (,,,-30ab,+36b^2), (,,,"--------","--------"), (,,,,0) :}#