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Solving Polynomial Questions with Base Numbers

Learn how to solve polynomial expressions using base numbers like quarters, nickels, and pennies to make specific amounts of money. Explore different bases such as 10 and 20, and apply them to real-world scenarios like the Gettysburg Address. Understand how to find the value of expressions for different x values.

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Solving Polynomial Questions with Base Numbers

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  1. Unit 3 Adding and Subtracting Polynomials

  2. Exercise 1 • How many quarters, nickels, and pennies are needed to make $1.13?

  3. Exercise 1 • How many quarters, nickels, and pennies are needed to make $1.13? Answer: 4 quarters, 2 nickels, and 3 pennies.

  4. Exercise 2 (Base 10) • Fill in the blanks. • 8,943 = ___ x 1000 + ___ x 100 + ___ x 10 + 3 x 1 or ___ x + ___ x + ___ x 10 + 3 x 1

  5. Exercise 2 (Base 10) • Fill in the blanks. • 8,943 = _8__ x 1000 + _9__ x 100 + _4__ x 10 + 3 x 1 or _8__ x + __9_ x + __4_ x 10 + 3 x 1

  6. Exercise 3 (Base 20) • Fill in the blanks. • 8,943 = ___ x + ___ x + ___ x 20 + 3 x 1

  7. Exercise 3 (Base 20) • Fill in the blanks. • 8,943 = _1__ x + _2__ x + _7__ x 20 + 3 x 1

  8. Who else uses Base 20? • Mayan, Aztec and Celtic • Gettysburg Address • The word score (which means 20) originated from Celtic language. • Four score and seven years ago… 4 x 20 + 7 = 87 years

  9. Polynomials written in standard form are base x “numbers” • 1 x + 2 x + 7 x + 3 x 1 or equivalently: + 2 + 7 + 3 • A. What is the value of this expression if x = 10? • B. What is the value of this expression if x = 20

  10. Polynomials written in standard form are base x “numbers” • 1 x + 2 x + 7 x + 3 x 1 or equivalently: + 2 + 7 + 3 • A. What is the value of this expression if x = 10? 1,273 • B. What is the value of this expression if x = 20 8,943* * Notice 8,943 is the same answer we get from exercise #3, when we were looking at base 20. This is just a generalized form of the answer in exercise 3. However, as we change x , we get a different number each time.

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