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Algebra 2 · Chapter 3 · Lesson 3.3 · Printable PDF

Proving Polynomial Identities Worksheet with Answer Key

5 problems on proving polynomial identities: deciding if a statement is an identity, expanding both sides, using sums and differences of cubes to find numbers, building Pythagorean triples, and finding the flaw in Priya's squaring argument. 2 pages, with a worked answer key.

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Printable Proving polynomial identities worksheet with answer key - Algebra 2 (Page 1 PDF preview)
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What's on the worksheet

  1. Decide if each statement is an identity; show it, or find where it fails.
    (x - 4)(x + 1) + 3x = x^2 - 4(x + 3)^2 - x^2 = 9(x^2 - 1)^2 = x^4 - 1x(x + 1)(x + 2) - 3x^2 = x^3 + 2x(x - 1)(x + 1)(x + 2) = x^3 + 2x^2 - 2x - 4
  2. Prove each identity by expanding one or both sides.
    (x - 1)(x^2 + x + 1) + (x + 1)(x^2 - x + 1) = 2x^3(ab + 1)^2 - (a + b)^2 = (a^2 - 1)(b^2 - 1)x(x + 1)(x + 2)(x + 3) + 1 = (x^2 + 3x + 1)^2
  3. Use the difference and sum of cubes to find each number without working out cubes.
  4. Use an identity to generate Pythagorean triples, starting from 85.
  5. Find what is wrong with Priya's squaring argument for an identity.

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Proving polynomial identities: the lesson ›

More Chapter 3 worksheets: Polynomial functions