Bigger Splits
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 56 of 64.
When the numerator has a minus sign, the sign stays with its term when you split the fraction. So (8x^3 - 4x^2)/(2x) splits into 8x^3/(2x) - 4x^2/(2x).
Work out each piece. In the first, 8/2 = 4 and x^3/x = x^2, which gives 4x^2. In the second, 4/2 = 2 and x^2/x = x, which gives 2x. The quotient is 4x^2 - 2x.
Divide each term of the numerator by the denominator. Here both coefficients are even and each term contains a factor of x, so dividing by 2x leaves a polynomial. The original fraction is defined only for nonzero x.
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