subtract x⁴ - 3x - 2 from the sum of 5x³ + 1 and 2x⁴ - 3x³ - 3x + 1
Answers
Answer:
(5x2 + 4x + 1) + (2x2 + 5x + 2)
In vertical form, align the like terms and add as shown below.
In horizontal form, use the Associative and Commutative Properties to regroup like terms together and combine them as shown below.
Solved Problems
Problem 1 :
Add :
3x3 + x2 - 2 and 2x2 + 5x + 5
Solution :
= 3x3 + x2 - 2 + 2x2 + 5x + 5
Group like terms together.
= 3x3 + (2x2 + x2) + 5x + (5 - 2)
Combine like terms.
= 3x3 + 3x2 + 5x + 3
Problem 2 :
Add the following polynomials :
3x - y, 2y - 2x, and x + y
Solution :
= (3x - y) + (2y - 2x) + (x + y)
= 3x - y + 2y - 2x + x + y
Group like terms together.
= (3x + x - 2x) + (2y + y - y)
Combine like terms.
= 2x + 2y
Problem 3 :
Add :
(7p3 + 4p2- 8p + 1) and (3p3- 5p2- 10p + 5)
Solution :
= (7p3 + 4p2- 8p + 1) + (3p3- 5p2- 10p + 5)
= 7p3 + 4p2- 8p + 1 + 3p3- 5p2- 10p + 5
Group like terms together.
= (7p3 + 3p3) + (4p2- 5p2) + (-8p - 10p) + (1 + 5)
Combine like terms.
= 10p3 - p2 -18p + 6
Problem 4 :
Add :
-1(x6 + x3 + 6x2 - 2) and 2(5x6 + 7x5 - 3x - 3)
Solution :
= -1(x6 + x3 + 6x2 - 2) + 2(5x6 + 7x5 - 3x - 3)
Distributive Property.
= -x6 - x3 - 6x2 + 2 + 10x6 + 14x5 - 6x - 6
Group like terms together.
= (-x6 + 10x6) + 14x5 - x3 - 6x2 - 6x + (2 - 6)
Combine like terms.
= 9x6 + 14x5 - x3 - 6x2 - 6x - 4
= 6x7 + 10x7- 2x6 + 6x6 + 4x4 - 3x3 + 2x3 + 2x2 + 2x2
= 16x7 + 4x6 + 4x4 - x3 + 4x2
Problem 5 :
The profits of two different production plants can be modeled as shown below, where x' is the number of units produced at each plant.
Eastern Plant :
-0.03x2 + 26x - 1600
Western Plant :
-0.02x2 + 20x - 1800
Use the information above to write a polynomial that represents the total profits from both plants.
Solution :
Total profits from both plants :
= Eastern plant profits + Western plant profits
= (-0.03x2 + 26x - 1600) + (-0.02x2 + 20x - 1800)
= -0.03x2 + 26x - 1600 - 0.02x2 + 20x - 1800
Group like terms together.
= (-0.03x2 - 0.02x2) + (26x + 20x) + (-1600 - 1800)
Combine like terms.
= -0.05x2 + 46x - 3400
Step-by-step explanation:
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