High School

Multiply the polynomials and select the expression in standard form.

$(x^5 + x - 2)2x^5$

$2x^{10} - 2x^6 - 4x^5$
$2x^{10} + 2x^6 + 4x^5$
$2x^{10} - 2x^6 + 4$
$2x^{10} + 2x^6 - 4$
$2x^{10} + 2x^6 - 4x^5$

Answer :

To multiply the polynomials [tex](x^5 + x - 2)[/tex] and [tex]2x^5[/tex], you should distribute the [tex]2x^5[/tex] to each term inside the parentheses.

Let's go through this step-by-step:

  1. Multiply [tex]x^5[/tex] by [tex]2x^5[/tex]:

    [

x^5 \times 2x^5 = 2x^{10}
]

  1. Multiply [tex]x[/tex] by [tex]2x^5[/tex]:

    [

x \times 2x^5 = 2x^6
]

  1. Multiply [tex]-2[/tex] by [tex]2x^5[/tex]:

    [

-2 \times 2x^5 = -4x^5
]

Now, combine all these expressions to write the resulting polynomial in standard form:

[tex]2x^{10} + 2x^6 - 4x^5[/tex]

The expression is written in descending order of exponents, which is the standard form for a polynomial.

The correct answer among the given options is:

  • [tex]2x^{10} + 2x^6 - 4x^5[/tex]

Therefore, the selected expression in standard form is: 2x^{10} + 2x^6 - 4x^5

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