Download Looking Ahead 3 - Subtracting Polynomials

Looking Ahead 3 - Subtracting Polynomials
Subtract. Use models if needed.
1. (6x + 5) – (3x + 1)
SOLUTION: 2. (3x2 – 4x + 2) – (x2 – 2x)
SOLUTION: 3. (x2 + 9x – 4) – (x2 – 2x + 1)
SOLUTION: 4. (5x2 + 7) – (x2 + 2x + 4)
SOLUTION: 5. SHIPPING The cost of shipping an item that weighs x pounds from Charlotte to Chicago is shown in the table.
a. Write an expression to represent how much more Atlas charges than Mid-Atlantic for shipping an item.
b. If an item weighs 2 pounds, how much more does Atlas charge for shipping it?
SOLUTION: a. To determine how much more Atlas charges for shipping an item than Mid-Atlantic, find the difference of the
polynomials.
Atlas charges x + 1.55 more to ship an item than Mid-Atlantic.
b. Substitute 2 for x and solve.
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Looking Ahead 3 - Subtracting Polynomials
5. SHIPPING The cost of shipping an item that weighs x pounds from Charlotte to Chicago is shown in the table.
a. Write an expression to represent how much more Atlas charges than Mid-Atlantic for shipping an item.
b. If an item weighs 2 pounds, how much more does Atlas charge for shipping it?
SOLUTION: a. To determine how much more Atlas charges for shipping an item than Mid-Atlantic, find the difference of the
polynomials.
Atlas charges x + 1.55 more to ship an item than Mid-Atlantic.
b. Substitute 2 for x and solve.
Atlas charges $3.55 more than Mid-Atlantic for shipping an item weighing 2 pounds.
Subtract. Use models if needed.
6. (3x + 7) – (x + 5)
SOLUTION: 7. (2x2 – 4x) – (x2 – x)
SOLUTION: 8. (x2 + 8x – 9) – (3x – 1)
SOLUTION: 9. (–4x2 + x + 7) – (–2x2 + x + 2)
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Looking Ahead 3 - Subtracting Polynomials
9. (–4x2 + x + 7) – (–2x2 + x + 2)
SOLUTION: 10. (5x + 6) – (x2 + 2x)
SOLUTION: 11. (–4x2 + x + 5) – (x2 + 2x + 3)
SOLUTION: 12. EXERCISE The expression 5x + 2 represents the number of miles Celeste rode her bike, and 10x represents the
number of miles that Kimiko rode her bike in x hours.
a. Write an expression to show how many more miles Kimiko rode than Celeste.
b. If they each rode for 2 hours, how many more miles did Kimiko ride?
SOLUTION: a. To determine how many more miles Kimiko rode than Celeste, find the difference of the polynomials.
Kimiko rode 5x – 2 miles more than Celeste.
b. Substitute 2 for x and solve.
Kimiko rode 8 miles more than Celeste rode.
13. CARS A car accelerates for t seconds. The expression 2t + t2 represents the distance the car travels in meters.
2
Another car has twice the acceleration and travels (2t + 2t ) meters in t seconds. After 10 seconds, how much
farther does the second car travel?
SOLUTION: To determine how much farther the second car travels, find the difference of the polynomials.
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2
The difference in the distance traveled is t meters. Substitute 10 for t and solve.
Substitute 2 for x and solve.
Looking Ahead 3 - Subtracting Polynomials
Kimiko rode 8 miles more than Celeste rode.
13. CARS A car accelerates for t seconds. The expression 2t + t2 represents the distance the car travels in meters.
2
Another car has twice the acceleration and travels (2t + 2t ) meters in t seconds. After 10 seconds, how much
farther does the second car travel?
SOLUTION: To determine how much farther the second car travels, find the difference of the polynomials.
2
The difference in the distance traveled is t meters. Substitute 10 for t and solve.
The second car traveled 100 meters farther than the first car.
14. MEASUREMENT What is the difference in the areas of the rectangles shown?
SOLUTION: To determine the difference in the areas of the rectangles, find the difference of the polynomials.
2
The difference in the areas of the rectangles is x + 8x – 6.
15. OPEN ENDED Write two polynomials that have a difference of 4x + 1.
SOLUTION: Sample answer:
The polynomials 5x + 4 and x + 3 have a difference of 4x + 1.
16. CHALLENGE Suppose A and B represent polynomials. If A + B = 3x2 + 2x – 2 and A – B = –x2 + 4x – 8, find A
and B.
SOLUTION: Solve the first equation for A.
Substitute this expression for A in the second equation.
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Looking Ahead 3 - Subtracting Polynomials
The polynomials 5x + 4 and x + 3 have a difference of 4x + 1.
16. CHALLENGE Suppose A and B represent polynomials. If A + B = 3x2 + 2x – 2 and A – B = –x2 + 4x – 8, find A
and B.
SOLUTION: Solve the first equation for A.
Substitute this expression for A in the second equation.
Now substitute this expression for B in the first equation.
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