Looking Ahead 1 - Polynomials
Simplify each polynomial.
14. 5 + x + 2
SOLUTION: Group tiles with the same shape. Then write a polynomial.
x
+
7
So, 5 + x + 2 = x + 7.
15. –x2 + 4x – x2
SOLUTION: Group tiles with the same shape. Then write a polynomial.
–2x
2
2
+
2
4x
2
So, –x + 4x – x = –2x + 4x.
Simplify each polynomial. Use models if needed.
16. x2 – x + 4 + 2x – 3
SOLUTION: Group tiles with the same shape. Remove the zero pairs and combine like terms. Then write a polynomial.
2
+
2x
+
(–x)
x
2
2
So, x – x + 4 + 2x – 3 = x + x + 1.
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17. –x2 + 3x + x2 – 2x
+
4
+
(–3)
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–2x
2
+
4x
Looking2Ahead21 - Polynomials
2
So, –x + 4x – x = –2x + 4x.
Simplify each polynomial. Use models if needed.
16. x2 – x + 4 + 2x – 3
SOLUTION: Group tiles with the same shape. Remove the zero pairs and combine like terms. Then write a polynomial.
2
+
2x
+
(–x)
x
2
2
So, x – x + 4 + 2x – 3 = x + x + 1.
+
4
+
(–3)
17. –x2 + 3x + x2 – 2x
SOLUTION: Group tiles with the same shape. Remove the zero pairs and combine like terms. Then write a polynomial.
x
2
+
2
(–x )
2
+
3x
+
(–2x)
2
So, –x + 3x + x – 2x = x.
18. x2 + 7 + 3x2
SOLUTION: Combine like terms.
19. 9 – 5x – 2x + 2
SOLUTION: Combine like terms.
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20. –2x2 + x – 3x2 – 6
SOLUTION: Page 2
SOLUTION: Combine like terms.
Looking Ahead 1 - Polynomials
19. 9 – 5x – 2x + 2
SOLUTION: Combine like terms.
20. –2x2 + x – 3x2 – 6
SOLUTION: Combine like terms.
21. 7x – 8 + 2x + 4x2 + x2
SOLUTION: Combine like terms.
22. –6x + 4 + 2x + 7
SOLUTION: Combine like terms.
23. 5 – x2 + 7x + 4x2
SOLUTION: Combine like terms.
24. 4x2 + 5x + 1 – 4x2 – 6x
SOLUTION: Combine like terms.
25. 6 + 2x2 – 3x – 4x – x2
SOLUTION: Combine like terms.
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26. GEOMETRY Write and simplify a polynomial expression for the perimeter of the trapezoid.
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SOLUTION: Combine like terms.
Looking Ahead 1 - Polynomials
25. 6 + 2x2 – 3x – 4x – x2
SOLUTION: Combine like terms.
26. GEOMETRY Write and simplify a polynomial expression for the perimeter of the trapezoid.
SOLUTION: The perimeter of the parallelogram is (6k + 24) millimeters.
27. EXERCISE Taylor jogged x miles after school. Seth jogged twice the distance that Taylor jogged. Rashida jogged
4 miles. Write and simplify a polynomial expression to represent the total number of miles that the three students
jogged.
SOLUTION: The total number of miles is equal to the sum of the distances run by each of the three students. Let d = the total
distance that the three students jogged, in miles.
The total distance that the three students jogged is (3x + 4) miles.
28. PIZZA For a party, one classroom ordered 4 large pizzas, 2 medium pizzas, and 6 subs. Another classroom ordered
6 large pizzas and 8 subs. If ℓ represents the cost of a large pizza, m represents the cost of a medium pizza, and s
represents the cost of a sub, write an expression in simplest form for the total amount of money that the two
classrooms spent on food.
SOLUTION: The total amount of money spent on food is equal to the sum of the money spent by each classroom. Let t = the total
amount of money that the two classrooms spent on food.
The total amount of money that the two classrooms spent on food is 10l + 2m + 14s.
29. JOBS Michael and Olivia each earn x dollars per lawn that they mow and y dollars per hour for babysitting. The
table shows how many lawns each mowed and how many hours each babysat. Write an expression in simplest form
for the total amount of money they earned together.
Number
Number
of Lawns
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Babysitting
Michael
8
6
Looking Ahead 1 - Polynomials
The total amount of money that the two classrooms spent on food is 10l + 2m + 14s.
29. JOBS Michael and Olivia each earn x dollars per lawn that they mow and y dollars per hour for babysitting. The
table shows how many lawns each mowed and how many hours each babysat. Write an expression in simplest form
for the total amount of money they earned together.
Number
Number
of Lawns
of Hours
Babysitting
Michael
8
6
Olivia
9
4
SOLUTION: The total amount of money Michael and Olivia earned together is equal to the sum of the money earned by both
individually. Let m = the total amount of money they earned together.
The total amount of money Michael and Olivia earned together is 17x + 10y.
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