Question

enter the correct answer in the box.
what standard form polynomial expression represents the perimeter of this quadrilateral?
$4x^3 + 2x^2$
$3x^2 - 4x + 3$
$x^3 - 2x$
$x^2 + 6x - 11$
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Explanation:

Step1: Recall perimeter formula

Perimeter of a quadrilateral is the sum of all its four sides. So we need to add the four given polynomial expressions: \(4x^3 + 2x^2\), \(3x^2 - 4x + 3\), \(x^3 - 2x\), and \(x^2 + 6x - 11\).

Step2: Combine like terms for \(x^3\) terms

The \(x^3\) terms are \(4x^3\) and \(x^3\). Adding them: \(4x^3 + x^3 = 5x^3\).

Step3: Combine like terms for \(x^2\) terms

The \(x^2\) terms are \(2x^2\), \(3x^2\), and \(x^2\). Adding them: \(2x^2 + 3x^2 + x^2 = 6x^2\).

Step4: Combine like terms for \(x\) terms

The \(x\) terms are \(-4x\), \(-2x\), and \(6x\). Adding them: \(-4x - 2x + 6x = 0x\) (which simplifies to 0, so we can ignore this term).

Step5: Combine constant terms

The constant terms are \(3\) and \(-11\). Adding them: \(3 - 11 = -8\).

Step6: Combine all terms

Putting it all together, the polynomial in standard form (descending powers of \(x\)) is \(5x^3 + 6x^2 - 8\).

Answer:

\(5x^3 + 6x^2 - 8\)