Select each statement that is true for all polynomials. When two polynomials are added, the sum is always a polynomial. When two

Question

Select each statement that is true for all polynomials.
When two polynomials are added, the sum is always a polynomial.
When two polynomials are divided, the quotient is always a
polynomial.
When two polynomials are multiplied, the product is always a
polynomial.
When two polynomials are subtracted, the difference is always a
polynomial.

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Cherry 1 week 2021-07-22T14:54:34+00:00 1 Answers 1 views 0

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    2021-07-22T14:56:25+00:00

    Answer:

    Option 3

    Step-by-step explanation:

    Analyzing All Options:

    Option 1: Sum of 2 polynomials is always a polynomial;

    This isn’t always true; Take for instance:

    (2x^3 - 3x^2 + 4x + 5) + (-2x^3 + 3x^2 - 4x + 9)

    2x^3 - 3x^2 + 4x + 5 -2x^3 + 3x^2 - 4x + 9

    -2x^3+2x^3 + 3x^2- 3x^2 + 4x- 4x + 5  + 9

    14

    The result in this case isn’t a polynomial

    Option 2: The quotient of two polynomials is always a polynomial

    This isn’t always true; Take for instance:

    \frac{4x^2 + 2x+ 2}{2x^2 + x + 1}

    =\frac{2(2x^2 + x + 1)}{2x^2 + x + 1}

    =2

    The result in this case isn’t a polynomial

    Option 3: The multiplication of two polynomials is always a polynomial

    This is always true; Take for instance:

    (2x^3 - 3x^2 + 4x + 5) * (-2x^3 + 3x^2 - 4x + 9)

    Expand this, and you get a polynomial

    Option 4: Subtraction of 2 polynomials is always a polynomial;

    This isn’t always true; Take for instance:

    (2x^3 - 3x^2 + 4x + 5) - (2x^3 - 3x^2 + 4x + 9)

    2x^3 - 3x^2 + 4x + 5 - 2x^3 + 3x^2 - 4x - 9

    - 2x^3 + 2x^3 + 3x^2 - 3x^2 + 4x - 4x+ 5  - 9

    =-4

    This isn’t  a polynomial

    Hence;

    Option 3 answers the question

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