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Polynomials

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  • A rectangle with length 5p and width p + 1 is contained within a larger rectangle with dimensions 12p by 7p + 3. Which expression represents the area of the shaded region?

    84p^2 + 36p

    79p^2 + 31p
    42p^2 + 14p
    79p^2 + 41p


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  • Mrs. Campbell gave her Algebra I students a list of trinomials to factor for homework. Which of these can be factored into two binomials?

    x^2 + 3x + 2
    x^2 + 4x + 5
    x^2 + 5x + 7
    x^2 + 6x + 10


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  • Which of these could be the area of a perfect square?

    x^2 - 9x + 6
    x^2 - 6x + 9
    x^2 - 5x + 6
    x^2  - 6x + 5


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  • Which of these is the smaller solution to the quadratic equation, x^2 – 5x + 3 = 0?


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  • Which of these is NOT factorable over the set of real numbers?

    x^2 + 7x +10
    x^2 + 8x +15
    x^2 + 9x +14
    x^2 +10x +11


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  • What is the degree of the polynomial 12xy^3 – 7y^2z^5 + 5x6y – 2x^2y^2 ?

    22
    11
    7
    4


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  • Which expression is equivalent to (x – 2)^2?

    x^2 – 4
    x^2 + 4
    x^2 – 4x + 4
    x^2 + 4x – 4


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  • The area in square units of a certain rectangle is equal to the expression
    15x^2 – 32x + 16. Which of these expressions could NOT be equal to one
    side of the rectangle?

    I.    5x + 2
    II.   3x – 4
    III.  5x – 4


    I only
    II only
    III only
    I and III only


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  • A rectangle has an area of 6x^2 – x – 12 and a width of 2x – 3. Which expression represents the length of the rectangle?

    4x – 15
    4x – 9
    3x – 4
    3x + 4


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  • What is the difference between the binomials 2x + 3 and x + 3 ?

    x
    x + 3
    2x
    3x + 6


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  • Trinomials of the form ax2 + bx + c are “unfactorable” over the set of real numbers if b2 – 4ac is negative. Which trinomial or trinomials are unfactorable?

    4x2 - 36
    3x2 - 2x + 3
    x2 - 2x + 1
    5x2 + 20x


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  • Which of the following represent third-degree polynomials?

    IV only
    I and III only
    I, III, and IV only
    I, II, III, and IV


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  • The area of a rectangle can be expressed as x2 + 7x − 60. What is the factored form of x2 + 7x − 60?

    (x + 4)(x −15)
    (x + 6)(x +1
    (x +12)(x − 5)
    (x + 20)(x − 3)


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  • Which expression is the result when 2a - 5 is subtracted from 3a + 3?

    a - 2
    5a - 2
    a + 8
    -a + 8


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