Lesson 2: Subtracting Polynomials. When Subtracting Polynomials, think of the phrase: Rewrite the subtraction problem as an.
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1 Lesson 2: Subtracting Polynomials When Subtracting Polynomials, think of the phrase: Rewrite the subtraction problem as an. (3 + 2a + a 2 ) (a 2 + 4a 8) Example 1 Example 2 Example 3 The triangle has a perimeter of: 4x 2 6x + 2 Side 1 = x 2 3x + 5 Side 2 = 2x Find the measurement of side
2 Lesson 2: Subtracting Polynomials Practice Part 1: Simplify each expression by subtracting. 1. (4x 2 + 2x 2) - (4x 2 3x -8) 5. (6t 2 9t 1) - ( 2t 7t 2 + 3) 2. (7y 3 2y 2 + 9y -9) - (y 3 5y +1) 6. (b 3 2b + 8) - (8b 3 2b 2 3b -17) 3. (a 3 2a 2 +6) - (2a 3 4a 2 a -1) 7. (3x + 3x 2-6) - ( 9 2x 2x 2 ) 4. (x 4x 2 + 9) - (x 2-2x + 5) 8. (2x 3 3x + 3x 2-7) - (2x -x 3 +6x 2 +1) Part 2: Find the missing polynomial. 1. (2x 2 6x + 5) - (?) = x 2 +3x (y 3 7y +2) - (?) = 5y 3 + 4y 2-8y (3x 3 6x + 2) -(?)= 3x 2 3x (4a 2 4) - (?) = -7a (2x 2 4) - (?) = 2x 3 + 5x 2-2x (b 2 4b 3 7b + 1) -(?) = 2b 3 +3b 2-4 Part 3: Find the missing side of each shape Side 1 =x 2 3x -4 Side 2: x 2 + 2x Side 3: 5x -2 Side 4:? 4 Perimeter = 3x 2 +4x Side 1 = 5x-5 Side 2:? Side 3 = 2x 2 4x -2 Side 4 = 6x -7 Side 5 = 3x +2 Perimeter= 4x 2-2x+8 Directions: Simplify each expression. (2 points each) 1. (16y 3 4y 2 2y + 10) - (3y 2 + 2y 2) 2. (7d 2 2) - (d 3 +3d) 3. Find the missing side of the shape. 2 3 ( 3 points) 4 1 Side 1: 2x 2 + 3x - 1 Side 2: 5x-3 Side 3: x 2 +5 Perimeter: 6x 2 +10x-4
3 Lesson 2: Subtracting Polynomials Practice Answer Key Part 1: Simplify each expression by subtracting. 1. (4x 2 + 2x 2) - (4x 2 3x -8) 5. (6t 2 9t 1) - ( 2t 7t 2 + 3) (4x 2 + 2x 2) + (-4x 2 + 3x +8) 4x 2 + 2x x 2 + 3x + 8 0x 2 +5x +6 Final Answer: 5x +6 (6t 2 9t 1) + (- 2t + 7t 2-3) 6t 2 9t 1 + 7t 2-2t -3 13t 2 11t - 4 Final Answer: 13t 2 11t (7y 3 2y 2 + 9y -9) - (y 3 5y +1) 6. (b 3 2b + 8) - (8b 3 2b 2 3b -17) (7y 3 2y 2 + 9y -9) + (-y 3 + 5y -1) 7y 3 2y 2 + 9y y 3 + 0y 2 + 5y 1 6y 3 2y y - 10 Final Answer: 6y 3 2y y - 10 (b 3 2b + 8) + (-8b 3 + 2b 2 + 3b +17) b 3 + 0b 2 2b b 3 + 2b 2 + 3b +17-7b 3 + 2b 2 + b + 25 Final Answer: -7b 3 + 2b 2 + b (a 3 2a 2 +6) - (2a 3 4a 2 a -1) 7. (3x + 3x 2-6) - ( 9 2x 2x 2 ) (a 3 2a 2 +6) + (-2a 3 + 4a 2 + a +1) 1a 3 2a 2 + 0a a 3 + 4a 2 + a + 1-1a 3 +2a 2 + a + 7 Final Answer: -a 3 + 2a 2 + a + 7 (3x + 3x 2-6) + ( x + 2x 2 ) 3x 2 + 3x 6 +2x 2 + 2x - 9 5x 2 + 5x - 15 Final Answer: 5x 2 + 5x - 15
4 4. (x 4x 2 + 9) - (x 2-2x + 5) 8. (2x 3 3x + 3x 2-7) - (2x -x 3 +6x 2 +1) (x 4x 2 + 9) + (-x 2 +2x - 5) -4x 2 + x x 2 + 2x 5-5x 2 + 3x + 4 Final Answer: -5x 2 + 3x + 4 (2x 3 3x + 3x 2-7) + (-2x +x 3-6x 2-1) 2x 3 + 3x 2 3x 7 + x 3 6x 2 2x 1 3x 3 3x 2 5x - 8 Final Answer: 3x 3 3x 2 5x - 8 Part 2: Find the missing polynomial. This set of problems is a little tricky. Think of it as solving for the missing variable. Let s take a look at a problem that we are familiar with. Let s say we have 5 x = 10. What would you do to solve for x? You might: Subtract 5 from both sides and then multiply by -1 to make x positive. 5-5 x = x = 5 (-1)(-x) = -1(5) x= -5 Or you might: Add x to both sides and subtract 10 from both sides. This would make x positive too. 5-x+x = 10 +x 5 = 10 + x 5-10 = x -5 = x This is exactly how the next set of problems is set up. So, we can create a rule based on this simple equation: Subtract the right side from the left side of the equation in order to find our answer. (See the video for a better explanation)
5 1. (2x 2 6x + 5) - (?) = x 2 +3x (y 3 7y +2) - (?) = 5y 3 + 4y 2-8y -2 (2x 2 6x + 5) p = x 2 + 3x + 1 both sides and then subtract (x 2 + 3x + 1) from (2x 2 6x + 5) (2x 2 6x + 5) (x 2 + 3x + 1) Rewrite as an addition (2x 2 6x + 5) + (-x 2-3x 1) F 2x 2 6x x 2 3x 1 x 2-9x + 4 Final Answer (y 3 7y + 2) p = 5y 3 + 4y 2 8y - 2 both sides and then subtract (5y 3 + 4y 2 8y - 2) from (y 3 7y + 2) (y 3 7y + 2) - (5y 3 + 4y 2 8y - 2) Rewrite as an addition (y 3 7y + 2) + (-5y 3-4y 2 + 8y + 2) y 3 + 0y 2 7y y 3-4y 2 + 8y + 2-4y 3 4y 2 + y + 4 Final Answer 2. (3x 3 6x + 2) -(?)= 3x 2 3x (4a 2 4) - (?) = -7a 2-2 (3x 3 6x + 2) p = 3x 2 3x - 1 both sides and then subtract (3x 2 3x - 1) from (3x 3 6x + 2) (3x 3 6x + 2) - (3x 2 3x - 1) Rewrite as an addition (3x 3 6x + 2) + (-3x 2 + 3x + 1) (4a 2-4) p = -7a 2-2 both sides and then subtract (-7a 2-2) from (4a 2-4) (4a 2-4) - (-7a 2-2) Rewrite as an addition (4a 2-4) + (7a 2 + 2) 3x 3 + 0x 2 6x + 2-3x 2 + 3x + 1 3x 3 3x 2 3x + 3 Final Answer 4a a a 2-2 Final Answer
6 3. (2x 2 4) - (?) = 2x 3 + 5x 2-2x (b 2 4b 3 7b + 1) -(?) = 2b 3 +3b 2-4 (2x 2-4) p = 2x 3 + 5x 2 2x - 1 both sides and then subtract (2x 3 + 5x 2 2x - 1) from (2x 2-4) (2x 2 4) - (2x 3 + 5x 2 2x - 1) Rewrite as an addition (2x 2 4) + (-2x 3-5x 2 + 2x + 1) 0x 3 + 2x 2 + 0x 4 +-2x 3-5x 2 + 2x + 1-2x 3 3x 2 + 2x - 3 Final Answer (-4b 3 + b 2 7b + 1) p = 2b 3 + 3b 2-4 both sides and then subtract (2b 3 + 3b 2-4) from (-4b 3 + b 2 7b + 1) (-4b 3 + b 2 7b + 1) - (2b 3 + 3b 2-4) Rewrite as an addition (-4b 3 + b 2 7b + 1) + (-2b 3-3b 2 + 4) -4b 3 + b 2 7b b 3-3b 2 + 0b + 4-6b 3 2b 2 7b + 5 Final Answer Part 3: Find the missing side of each shape Side 1 =x 2 3x -4 Side 2: x 2 + 2x Side 3: 5x -2 Side 4:? 4 Perimeter = 3x 2 +4x 4 In order to solve for the missing side, we will need to add the 3 sides that we know (Side 1 + Side 2+ Side3). Then figure out what we need to add in order to equal the perimeter. This will tell us the missing side. Step 1: Add the 3 sides that you know. Step 2: Find the missing addend. Side 1: x 2 3x 4 2x 2 +4x 9 (3 sides that we know) Side 2: x 2 + 2x 3 + 1x 2 +0x +5 (Missing Side) Side 3: 5x 2 3x 2 + 4x 4 (Equals the perimeter) 2x 2 4x -9 Side 4 is equal to: x 2 + 5
7 1 2 Side 1 = 5x-5 Side 2:? Side 3 = 2x 2 4x -2 Side 4 = 6x -7 Side 5 = 3x +2 Perimeter= 4x 2-2x+8 Step 1: Add the four sides that you know. Side 1: 0x 2 + 5x 5 Side 3: 2x x 2 Side 4: 0x 2 + 6x 7 Side 5: 0x 2 + 3x + 2 2x x -12 (The sum of the four sides that we know.) Step 2: Find the missing addend. 2x x 12 (Sum of the four sides that we know) + 2x 2-12x +20 (The missing side) 4x 2-2x + 8 (The perimeter of the object) The measurement of the missing side is: 2x 2-12x +20 Directions: Simplify each expression. (2 points each) 1. (16y 3 4y 2 2y + 10) - (3y 2 + 2y 2) 2. (7d 2 2) - (d 3 +3d) (16y 3 4y 2 2y + 10) + (-3y 2-2y + 2) 16y 3 4y 2 2y y 3 3y 2 2y y 3 7y 2 4y + 12 Final Answer: 16y 3 7y 2 4y + 12 (7d 2 2) + (-d 3-3d) 0d 3 + 7d 2 + 0d 2 + -d 3 + 0d 2 3d + 0 -d 3 + 7d 2 3d - 2 Final Answer: -d 3 + 7d 2 3d - 2
8 3. Find the missing side of the shape. 2 3 ( 3 points) 4 1 Side 1: 2x 2 + 3x - 1 Side 2: 5x-3 Side 3: x 2 +5 Perimeter: 6x 2 +10x-4 Step 1: Add the three sides that you know. Side 1: 2x 2 + 3x - 1 Side 2: 5x 3 Side 3: x 2 + 0x + 5 3x 2 + 8x +1 (The sum of the three sides that we know.) Step 2: Find the missing addend. 3x 2 + 8x +1 (Sum of the three sides that we know) + 3x 2 +2x -5 (The missing side) 6x x - 4 (The perimeter of the object) The measurement of the missing side is: 3x 2 + 2x - 5 Note: You could also subtract the perimeter the sum of the 3 sides: (6x 2 +10x -4) (3x 2 +8x +1) 6x 2 +10x 4 3x 2-8x -1 6x 2 3x 2 +10x -8x x 2 +2x 5 Write like terms together Combine like terms
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