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Unit 12: Polynomials

A polynomial is a sum of terms built from whole-number powers of x -- adding, subtracting, and multiplying them all follow rules you already know.

5 topics · 17 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

What a Polynomial Is

  1. How it worksHow do you identify a polynomial's degree and its leading coefficient just by looking at its terms?
  2. Worked exampleFind the degree and leading coefficient of 4x3 - 2x5 + 7x - 1.
  3. Common mistakeWhy isn't the term with the biggest number in front of it automatically the polynomial's leading term?
Your turn1 of 2
Find the leading coefficient of the polynomial 8x1 - 3x4 + 8x - 3, where 4 is greater than 1.

Adding and Subtracting Polynomials

  1. Worked exampleFind the sum of the quantities 3x2 - 5x + 2 and x2 + 4x - 7.
  2. Worked exampleFind the result of subtracting the quantity 2x2 + 3x - 1 from the quantity 5x2 - x + 4.
  3. Common mistakeWhy does subtracting a polynomial mean flipping the sign of every one of its terms, not just the first?
Your turn1 of 2
Find the sum of the quantities 7x2 - 6x + 8 and 3x2 + 2x - 3.

Multiplying a Monomial by a Polynomial

  1. How it worksHow does the distributive property extend from two terms to multiplying across an entire polynomial?
  2. Worked exampleFind the product of 3x2 and the quantity 2x3 - 5x + 4.
  3. Common mistakeWhy doesn't multiplying 3x2 by x3 give you 3x6 instead of 3x5?
Your turn1 of 2
Find the product of 5x2 and the quantity 5x3 - 8x + 3.

Multiplying Two Binomials

  1. How it worksHow does the FOIL pattern make sure you multiply every term in the first binomial by every term in the second?
  2. Worked exampleFind the product of the quantity x plus 3 and the quantity x minus 5.
  3. Worked exampleFind the product of the quantity 2x minus 1 and the quantity 3x plus 4.
  4. Common mistakeWhy doesn't multiplying the quantity x plus 3 by the quantity x minus 5 just multiply the first terms and the last terms?
Your turn1 of 2
Find the product of the quantity x plus 7 and the quantity x minus 6.

Special Products

  1. How it worksHow does a difference of squares pattern like the quantity x plus 4 times x minus 4 make the middle terms cancel out?
  2. Common mistakeWhy isn't the quantity x plus 3, squared, the same as x2 + 9?
  3. Worked exampleFind the product of the quantity x plus 6 and the quantity x minus 6 using the difference of squares pattern.
  4. Worked exampleFind the expanded form of the quantity 2x minus 3, squared, using the perfect square trinomial pattern.
Your turn1 of 2
Find the product of the quantity x plus 7 and the quantity x minus 7.