Factor by Grouping
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 12 of 54.
Four terms with no factor common to all of them can still factor. Take x^3 + 2x^2 + 5x + 10. Split it into two pairs and factor each pair on its own: x^3 + 2x^2 is x^2(x + 2), and 5x + 10 is 5(x + 2).
Both pairs left the same bracket. Now x + 2 is a common factor of the two parts, just as y is in 3y + 5y, so take it out:
x^2(x + 2) + 5(x + 2) = (x + 2)(x^2 + 5)
Grouping works only when the two brackets match; here they do because 1 and 2 are in the same ratio as 5 and 10. And x^2 + 5 has no real factors: for real x it is never zero.
Challenge
Factor x^3 - 3x^2 + 4x - 12 by grouping.
Try it yourself
Factor the expression
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 Charts3Factoring Higher Degree
Factor by GroupingGrouping All the WayDifference of CubesSum of CubesA Quadratic in DisguiseRecap: Factoring6Rational Expressions
Cancelling FactorsExcluded ValuesMultiplyingDividingRecap: Rational Expressions