A Missing Term
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 4 of 54.
Long division lines up like terms, the way number division lines up hundreds, tens and ones. In 407 the 0 holds the tens place. In x^3 - 7x + 6 there is no x^2 term, so hold its place with a zero:
x^3 + 0x^2 - 7x + 6
Now divide by x + 3. First round: x^3 over x is x^2, and x^2(x + 3) is x^3 + 3x^2. Subtract from x^3 + 0x^2: -3x^2 is left, and bring down the minus 7x. Second round: -3x(x + 3) is -3x^2 - 9x, and subtracting leaves 2x + 6. Third round: 2(x + 3) is exactly 2x + 6, so
(x^3 - 7x + 6)/(x + 3) = x^2 - 3x + 2
Without the placeholder, the 3x^2 of the first product would sit under the minus 7x, and unlike terms cannot be taken from each other.
Challenge
Divide x^3 - 8 by x - 2. The top has no x^2 or x term: think of them as 0x^2 and 0x.
Try it yourself
Divide the polynomials
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Polynomials & Rational Expressions
1Polynomial Long Division
How Long Division WorksOne Term at a TimeA Remainder Left OverA Missing TermDividing by a QuadraticRecap: Long Division7Adding and Subtracting
Same BottomDifferent BottomsSubtractingFactor the Bottoms FirstRecap: Adding Fractions2Remainders and Factors
The Remainder TheoremThe Factor TheoremFinding a Missing NumberUsing a Known FactorRecap: Remainders and Factors5Sign Charts
Between the RootsOutside the RootsA Negative Leading TermReading a Sign ChartRecap: Sign Charts