Resolved: "One of the steps involved when writing the..."

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Math Word Problem

Answered question

2022-03-25

One of the steps involved when writing the standard form of a polynomial is completing the ______.

Answer & Explanation

nick1337

Expert2023-04-26Added 777 answers

The step involved when writing the standard form of a polynomial is completing the square.
To write a polynomial in standard form, the terms must be arranged in descending order of degree, with the coefficient of each term written before the variable. The leading term should have a positive coefficient.
One way to obtain the standard form of a polynomial is by completing the square, which involves adding and subtracting a constant term to the polynomial so that it becomes a perfect square trinomial.
For example, consider the polynomial

x^{2} - 4 x + 3

. To complete the square, we need to add and subtract

(4 / 2)^{2} = 4

to the polynomial, as follows:

x^{2} - 4 x + 3 = x^{2} - 4 x + 4 - 1

= (x - 2)^{2} - 1 .

The resulting polynomial is in standard form, with the terms arranged in descending order of degree, and the leading term has a positive coefficient.

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