Problem 4 Writing and Evaluating an Expression
Sports In football, a touchdown (TD) is worth six points, an extra-point kick (EPK) one point, and a field goal (FG) three points. What algebraic expression models the total number of points that a football team scores in a game, assuming each scoring play is one of the three given types? Suppose a football team scores 3 touchdowns, 2 extra-point kicks, and 4 field goals. How many points did the team score?
| Know | Need | Plan |
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| Relate | points per TD | ⋅ |
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+ | points per EPK | ⋅ |
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+ | points per FG | ⋅ |
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| Define | Let
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| Let
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| Let
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| Write | 6 | ⋅ |
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+ | 1 | ⋅ |
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+ | 3 | ⋅ |
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Think
How many points come from touchdowns?
The number of points from touchdowns is six times the number of touchdowns.
The expression 6t + 1k + 3f models the team's total score.
The football team scores 3 touchdowns, 2 extra-point kicks, and 4 field goals, so t = 3, k = 2, and f = 4.
The team scored 32 points.
✓ Got It?
- In basketball, teams can score by making two-point shots, three-point shots, and one-point free throws. What algebraic expression models the total number of points that a basketball team scores in a game? If a team makes 10 two-point shots, 5 three-point shots, and 7 free throws, how many points does it score in all?
An expression that is a number, a variable, or the product of a number and one or more variables is a term. A coefficient is the numerical factor of a term. A constant term is a term with no variables. You can add terms to form longer expressions. The expression below has three terms.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions