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10.4 – Polynomial Multiplication

Key Terms

  • Column – A vertical list of numbers of other information in a table.

Review

Remember…
  • Rule: To multiply any two polynomials, multiply each term in one polynomial by each term in the other.

Notes

Polynomial Multiplication Using Tables
  • You can create a table to help you organize polynomials for multiplication
  • How to Use a Table to Multiply Two Polynomials
    • Step 1: Use the terms in one polynomial to label the columns (one term per column).
    • Step 2: Label the rows with the terms in the other polynomial (one term per row).
    • Step 3: Multiply each column label and row label to fill in all the entries.
    • Step 4: Add all the products in the entries.
    • Step 5: Simplify the sum, if possible.

Alg1B 10.4 Table


  • Example 1Alg1B 10.4 Table Ex1
  • Example 2

Alg1B 10.4 Table Ex2

 

The Distributive Property
  •  How to Use the Distributive Property to Multiply Polynomials
    • Step 1: Distribute the first polynomial over the second one.
    • Step 2: Use the distributive property again on the smaller products.
    • Step 3: Collect like terms and simplify the answer.

Alg1B 10.4 Distribution Ex1

 

Multiplying Polynomials Vertically
  • How to Multiply Two Binomials Vertically
    • Step 1: Multiply each term in the top binomial by the last term in the bottom binomial.
    • Step 2: Multiply each term in the top binomial by the first term in the bottom binomial.
    • Step 3: Add the two smaller products.
    • Step 4: Simplify your answer.

Alg1B 10.4 Vertical Mult


  • Example

Alg1B 10.4 Vertical Mult Ex 1


  • Another Example

Examples

  • Ex 1. Use a table to compute the product: (6x^{2}-3x-6)(3x+6)

Alg1B 10.4 Q01

 

  • Ex 2. Use a table to compute the product: (5x^{2}-4x-5)(4x+7)

Alg1B 10.4 Q02

  • Ex 3. Use a table to compute the product: (4x^{2}-2x-4)(7x^{2}+8x+7)

Alg1B 10.4 Q03


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