Dividing by a Variable Term
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 55 of 64.
Now the divisor carries an x: (6x^2 + 9x)/(3x). Split as before, and each piece is a full quotient-rule job: coefficients divide, exponents subtract. 6x^2/(3x) = 2x and 9x/(3x) = 3.
The quotient is 2x + 3. Note what happened to the second term: 9x/(3x) lost its x entirely, x/x = 1, leaving a plain 3. Terms can and do drop out of the letter business when the division exactly consumes their x.
Another road to the same place: factor the top first, 3x(2x + 3), and cancel the 3x whole. Splitting and factoring are both legal; the factoring road is about to become the main highway of the next section.
Challenge
MediumDivide: (12x^2 + 8x)/(4x).
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative