Factorization Techniques
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Factorization Techniques — Free MYP5 Mathematics (Standard) 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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3QuestionGrouping and Advanced PatternsAssessment Practice
2 marks~3 minCriterion C
A landscape architect models a rectangular garden plot with area given by x3+3x2+2x+6x^3 + 3x^2 + 2x + 6 square metres, where x>0x > 0.
a
Show that x3+3x2+2x+6=(x+3)(x2+2)x^3 + 3x^2 + 2x + 6 = (x + 3)(x^2 + 2) using the grouping method. [1]
b
Given that x=3x = 3, the architect claims one side length exceeds 11 m. Justify whether this claim is correct. [1]
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4QuestionFactoring Difference of SquaresAssessment Practice
5 marks~8 minCriterion B
A tile manufacturer cuts square ceramic tiles of side length aa cm, then removes a smaller square of side length bb cm from one corner to create an L-shaped tile for border edging.
a
Show that (a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2 by expanding the left-hand side algebraically. State the property used at each step. [2]
b
Construct an area model for the L-shaped tile. Show that the remaining area can be expressed both as a2−b2a^2 - b^2 and as (a+b)(a−b)(a+b)(a-b). [2]
c
A tile is described as "large" if its L-shaped area exceeds 300 cm2300\ \text{cm}^2. Given a=20a = 20 and b=5b = 5, justify whether this tile qualifies as large. [1]
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