Florida B.E.S.T. MA.912.AR.1.5

MathGrades 9–12Interpret and rewrite algebraic expressions and equations in equivalent forms.

The Standard

Divide polynomial expressions using long division, synthetic division or algebraic manipulation.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students find how many times one polynomial fits into another and determine any remainder. They select a suitable method and check the result by multiplication.
What Mastery Looks Like: Students choose long division, synthetic division, or factoring based on the divisor. They find the correct quotient and remainder, then verify that divisor times quotient plus remainder equals the dividend.
Common Misconceptions: Students often omit zero coefficients for missing terms or lose negative signs during subtraction. Some use synthetic division with non-linear divisors or forget to include the remainder in the final expression.
How to Assess It: Ask students to divide 2x³ − 3x² + 4x − 5 by x − 2, write the remainder correctly, and verify by multiplication.

Lesson moves

Use algebra tiles to model dividing x² + 3x + 2 by x + 1, then identify the quotient from the completed rectangle.
Have students compare long and synthetic division for one problem, then write when each method can be used.
Run a card sort matching dividend, divisor, quotient, and remainder cards, with students checking each set by multiplication.
Give a rectangular garden with area x² + 7x + 12 and width x + 3, then have students find its length.

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