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Solving Problems Involving Factors of Polynomials


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10 questions
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  • Q1

    Translate “The sum of two consecutive odd integers”.

    x + 2

    x + (x + 2)

    2x + 1

    x – 3

  • Q2

    The length of a rectangular frame is 4 cm more than its width. The area of the frame is 60 square cm. Translate this situation into an equation.

    2w (w – 4) = 60

    w (w – 4) = 60

    w (w + 4) = 60

    w (w - 4)2 = 60

  • Q3

    The total cost c in selling the goods is represented by 2c2 – 3c + 1. Factor  this expression.

    (2c + 1)(c – 1)     

    (2c + 1)(c + 1)

    (2c – 1)(c – 1)

    (2c – 1)(c – 2) 

  • Q4

    The side of a square is x meters long. The length of a rectangle is 3 meters longer than the side of the square and the width is 3 meters shorter. Which statement is true?

    Any relationship cannot be determined from the given information

    The area of the square is equal to the area of the rectangle

    The area of the square is less than the area of the rectangle

    A.   The area of the square is greater than the area of the rectangle.

  • Q5

    The area of the square is represented by 16x2+ 16x + 4 square units. Which expression represents the length of the side?

    (2x – 4) units

    (4x + 2) units      

    (4x – 2) units

    (2x + 4) units     

  • Q6

    All the short line segments in the figure below are perpendicular to each other and 1 inch long. What is the total area of the four shaded sections?

    Question Image

    32 square inches

    72square inches

    40square inches

    64square inches

  • Q7

    A parallelogram has the height that measures 5 meters more than its base. If the area is 36 m2, what is the height in meters?

    [area of parallelogram = (base)(height)]

    9 m

    4 m

    12 m

    12 m

  • Q8

    Pedro owns a rectangular plot that has an area of 3280 square cm. The length of the plot is 2 more than twice the width. What is the width?

    50 cm

    60 cm

    45 cm

    40 cm

  • Q9

    Elena reduces a cardboard to fit in the bulletin board. She needs the cardboard to be one-third of the area of the original. The original size is 4cm by 6cm. How many centimeters is the smaller dimension of the reduced cardboard if each dimension changes the same amount?





  • Q10

     A 4cm by 6cm canvas for painting is going to be enlarged by increasing each side by the same amount. The new area is 168 How many centimeters increased in each dimension?






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