Bigger Splits
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 56 of 64.
Signs ride along in a split exactly as they ride in a sum. (8x^3 - 4x^2)/(2x) splits into 8x^3/(2x) - 4x^2/(2x): the minus stays with its term.
Work the pieces: 8/2 = 4 with x^3/x = x^2, then 4/2 = 2 with x^2/x = x. The quotient is 4x^2 - 2x.
Every term of the top must be divisible for the split to come out clean: here both terms carried at least one x and even coefficients, so nothing was left over. The next lesson is about the one tempting shortcut that breaks this split.
Challenge
MediumDivide: (10x^3 - 5x^2)/(5x).
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