Looking Ahead 2 - Adding Polynomials
Add. Use models if needed.
1. (x + 5) + (2x + 3)
SOLUTION: 2. (x2 – 4x) + (x2 – 5x)
SOLUTION: 3. (2x2 + 6) + (–x2 + 3x – 1)
SOLUTION: 4. (x2 – 7x + 2) + (–3x2 + x + 4)
SOLUTION: 5. GEOMETRY Use the figure shown.
a. Write and simplify a polynomial expression for the perimeter of the figure.
b. Find the perimeter of the figure if x = 4.
SOLUTION: a. The perimeter is the sum of all of the sides.
b. Substitute 4 for x in the equation P = 6x + 3.
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Looking Ahead 2 - Adding Polynomials
5. GEOMETRY Use the figure shown.
a. Write and simplify a polynomial expression for the perimeter of the figure.
b. Find the perimeter of the figure if x = 4.
SOLUTION: a. The perimeter is the sum of all of the sides.
b. Substitute 4 for x in the equation P = 6x + 3.
The perimeter of the figure is 27 units.
Add. Use models if needed.
6. (7x + 5) + (x + 2)
SOLUTION: 7. (–x + 3) + (–5x + 6)
SOLUTION: 8. (3x2 – 7x + 1) + (x2 – x)
SOLUTION: 9. (6x2 + 5x) + (–9x + 4)
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Looking Ahead 2 - Adding Polynomials
9. (6x2 + 5x) + (–9x + 4)
SOLUTION: 10. (–4x2 – 2x) + (–x2 + 2x + 10)
SOLUTION: 11. (–3x2 + x – 1) + (x2 + x – 4)
SOLUTION: GEOMETRY For each of the figures write and simplify a polynomial expression for the perimeter of the
figure. Then find the perimeter of each figure if x = 0.8.
12. SOLUTION: The perimeter is the sum of all of the sides.
Substitute 0.8 for x in the equation P = 20x – 5.
The perimeter of the figure is 11 centimeters.
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Looking
Aheadof 2the- figure
Adding
The perimeter
is 11Polynomials
centimeters.
13. SOLUTION: The perimeter of a rectangle is equal to twice the length plus twice the width.
2
Substitute 0.8 for x in the equation P = 8x + 6x – 4.
The perimeter of the figure is 5.92 inches.
18. OPEN ENDED Write two polynomials that have a sum of 3x2 – 8x.
SOLUTION: 2
2
Sample answer: (5x – 10x + 4) and (–2x + 2x – 4)
19. CHALLENGE What polynomial would you add to 3y 2 – 4y + 2 to have a sum of 2y 2 + 5?
SOLUTION: 2
2
In order to find what polynomial you would need to add, subtract the polynomial 3y – 4y + 2 from the sum of 2y +
5.
2
2
To check your answer, add –y + 4y + 3 to 3y – 4y + 2.
2
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Manual
- Powered is
by–y
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So, the
polynomial
+ 4y
+ 3.
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Looking Ahead 2 - Adding Polynomials
19. CHALLENGE What polynomial would you add to 3y 2 – 4y + 2 to have a sum of 2y 2 + 5?
SOLUTION: 2
2
In order to find what polynomial you would need to add, subtract the polynomial 3y – 4y + 2 from the sum of 2y +
5.
2
2
To check your answer, add –y + 4y + 3 to 3y – 4y + 2.
2
So, the polynomial is –y + 4y + 3.
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