Factorization Techniques
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Factorization Techniques — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionChoosing Appropriate Factorization MethodsConcept Practice
2 marks~3 minCriterion A
A landscape architect is designing a rectangular garden bed. The area of the bed is given by x2+8x+15x^2 + 8x + 15 square metres, where x>0x > 0. One side of the bed measures (x+3)(x + 3) metres.
a
Factorise x2+8x+15x^2 + 8x + 15. [1]
b
The architect needs the missing side to be longer than 7 metres when x=3x = 3. Justify whether this condition is met. [1]
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2QuestionChoosing Appropriate Factorization MethodsAssessment Practice
2 marks~3 minCriterion D
A homeowner plans to tile a rectangular floor with length (x+3)(x + 3) metres and width (x+2)(x + 2) metres. Tiles cost 15 dollars per square metre.
a
Show that the total tiling cost, in dollars, is 15x2+75x+9015x^2 + 75x + 90. [1]
b
The homeowner has a budget of 300 dollars and estimates x=3x = 3. Advise the homeowner whether to proceed with the purchase, giving one mathematical reason why the actual cost could differ from this estimate. [1]
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Solutions

3QuestionFactoring Difference of SquaresAssessment Practice
4 marks~6 minCriterion C
A landscape designer plans a square garden with side length a=10a = 10 m. A square pond with side length b=2b = 2 m will be placed in one corner. The remaining garden area (excluding the pond) is modelled using the identity a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b).
a
Show that the area of the garden excluding the pond is 96 m296 \text{ m}^2, using the difference of squares identity. [1]
b
The pond's side length is remeasured as 2.12.1 m. Calculate the revised area and deduce the percentage change from the original result. [1]
c
The designer considers replacing the square pond with a circular pond of diameter 22 m. Advise the designer whether the difference of squares identity remains a valid model and whether the area calculation must be adjusted. [2]
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Solutions

4QuestionFactoring Difference of SquaresAssessment Practice
6 marks~9 minCriterion B
Consider the following numerical pattern:

1. 42−32=(4−3)(4+3)=1×7=74^2 - 3^2 = (4-3)(4+3) = 1 \times 7 = 7
2. 72−22=(7−2)(7+2)=5×9=457^2 - 2^2 = (7-2)(7+2) = 5 \times 9 = 45
3. 102−52=(10−5)(10+5)=5×15=7510^2 - 5^2 = (10-5)(10+5) = 5 \times 15 = 75
a
Calculate 122−7212^2 - 7^2 using the same method. Show all steps. [2]
b
Deduce a general formula for a2−b2a^2 - b^2 in terms of aa and bb, and apply it to factorise 25x2−16y225x^2 - 16y^2 completely. [2]
c
A student claims that 49x2−949x^2 - 9 cannot be factorised because it contains both a variable term and a constant. Justify whether this claim is correct. [2]

Solutions

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