ACTIVITY 1 PROBLEM SOLVING ON POLYNOMIALS Solve each problem: (with solutions) (5 points each number) 1. The cost of a ballpen is 2x + 1 pesos, a notebook is 4x + 3 pesos and a pencil cost 5x - 2 pesos. Find the total cost of the 3 items. 2. A carpenter has a wood that is (3x + 2) feet long. Find the length of the wood after cutting (2x - 5) feet? 3. Find the area of a rectangle whose length is (2x + 4)cm and the width is (5x + 2)cm, if Area = LxW. 8=xS 01-v2- 3 4. If 9b + 6b* + 12b³ is divided by3b², what is the quotient?
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1. To find the total cost of the three items, we add the costs of the ballpen, notebook, and pencil:
Cost of ballpen = 2x + 1 pesos
Cost of notebook = 4x + 3 pesos
Cost of pencil = 5x - 2 pesos
Total cost = (2x + 1) + (4x + 3) + (5x - 2)
= 2x + 1 + 4x + 3 + 5x - 2
= 11x + 2 pesos
Therefore, the total cost of the three items is 11x + 2 pesos.
2. To find the length of the wood after cutting, we subtract the length to be cut from the original length:
Original length of wood = 3x + 2 feet
Length to be cut = 2x - 5 feet
Length of wood after cutting = (3x + 2) - (2x - 5)
= 3x + 2 - 2x + 5
= x + 7 feet
Therefore, the length of the wood after cutting is x + 7 feet.
3. To find the area of the rectangle, we multiply the length and width:
Length = 2x + 4 cm
Width = 5x + 2 cm
Area = (2x + 4) * (5x + 2)
= 10x^2 + 4x + 20x + 8
= 10x^2 + 24x + 8 cm²
Therefore, the area of the rectangle is 10x^2 + 24x + 8 cm².
4. To find the quotient when dividing 9b + 6b^2 + 12b^3 by 3b^2, we divide each term:
Dividend = 9b + 6b^2 + 12b^3
Divisor = 3b^2
Quotient = (9b + 6b^2 + 12b^3) / (3b^2)
= 9b / (3b^2) + 6b^2 / (3b^2) + 12b^3 / (3b^2)
= 3 / b + 2 + 4b
Therefore, the quotient is 3/b + 2 + 4b.
Step-by-step explanation:
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