Here are two expressions whose product is a new expression, : 1. What could we put in the boxes to make be a polynomial?

Question

Here are two expressions whose product is a new expression, :

1. What could we put in the boxes to make be a polynomial?

2. What could we put in the boxes to make not be a polynomial?

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Khánh Gia 4 years 2021-07-28T06:51:56+00:00 1 Answers 121 views 0

Answers ( )

    0
    2021-07-28T06:53:09+00:00

    Answer:

    1. Fill in the box with 1

    2. Fill in the box with -2

    Step-by-step explanation:

    Expression:

    (-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A

    Solving (1): Fill in the box to make it a polynomial.

    To make it a polynomial, we simply fill in the box with a positive integer (say 1)

    Fill in the box with 1

    (-2x^3 + [1]x)(x^{[1]}+1.5) = A

    Remove the square brackets

    (-2x^3 + x)(x^1+1.5) = A

    (-2x^3 + x)(x+1.5) = A

    Open bracket

    -2x^4 - 3x^3 + x^2 + 1.5x = A

    Reorder

    A = -2x^4 - 3x^3 + x^2 + 1.5x

    The above expression is a polynomial.

    This will work for any positive integer filled in the box

    Solving (2): Fill in the box to make it not a polynomial.

    The powers of a polynomial are greater than or equal to 0.

    So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial

    Fill in the box with -2

    (-2x^3 + [-2]x)(x^{[-2]}+1.5) = A

    Remove the square brackets

    (-2x^3 - 2x)(x^{-2}+1.5) = A

    Reorder

    A = (-2x^3 - 2x)(x^{-2}+1.5)

    Open brackets

    A = -2x-3x^3-2x^{-1}-3x

    Collect Like Terms

    A = -3x^3-2x-3x-2x^{-1}

    A = -3x^3-5x-2x^{-1}

    Notice that the least power of x is -1.

    Hence, this is not a polynomial.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )