Master dividing polynomial expressions by constants and monomials. Grade 9 Alberta math.
Lesson 5.6 of Polynomials in Grade 9 Math — Alberta curriculum lessons.
When we divide a polynomial by a constant, we divide each term of the polynomial by that number.This means we split the tiles evenly into groups, or divide the coefficients (numbers in front of variables) by the constant.
Understanding Division with Algebra Tiles
Algebra tiles help us visualize division as splitting a collection of tiles into equal groups. Think of it like sharing items equally among people.
How It Works:
Example 1: Dividing 4x² ÷ 2You have 4 large square tiles (each representing x²). When you divide by 2, you're asking: "How can I split these 4 tiles into 2 equal groups?" Split the 4 x² tiles into 2 groups; Each group gets 2 x² tiles; Answer: 2x² (what's in one group)
Example 2: Dividing (4x² − 6x) ÷ 2You have 4 large square tiles (x²) and 6 rectangular tiles (x) but the 6x tiles are negative (shown as white/empty tiles in the diagram).Dividing by 2 means: "Split everything into 2 equal groups" Group 1: 2 x² tiles and 3 negative x tiles → 2x² − 3x; Group 2: 2 x² tiles and 3 negative x tiles → 2x² − 3x; Each group is the same, so the answer is: 2x² − 4x
Key Insight:
When dividing a polynomial by a monomial that contains a variable, divide each term of the polynomial by that monomial.This means you'll divide both the coefficients and the variables.If the variables are the same, subtract their exponents: = xᵃ⁻ᵇ
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