One Term at a Time
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 2 of 54.
Long division can be written one quotient term at a time. Take (x^2 + 6x + 8)/(x + 4). Divide the leading terms: x^2 over x is x. Multiply x by x + 4 to get x^2 + 4x, and subtract it from the top: 2x + 8 is left, so the fraction is now
x + (2x + 8)/(x + 4)
That line still equals the original fraction, because x(x + 4) + 2x + 8 is the top again. Now do a second round on the fraction: 2x over x is 2, 2(x + 4) is 2x + 8, and subtracting leaves nothing:
(x^2 + 6x + 8)/(x + 4) = x + 2
When the remainder is zero the fraction disappears, and that tells you something: x + 4 divides the top exactly, so it is a factor, and x^2 + 6x + 8 = (x + 4)(x + 2).
Challenge
Divide x^2 + 7x + 10 by x + 2. Press Long division by x + 2 once for each term of the quotient.
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