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Write the polynomial [tex]$-23x^3 + x^4 - 6x^3 + 10 + 2x^2$[/tex] in standard form. Then, identify the degree and leading coefficient.

Answer :

To write the polynomial [tex]\(-23x^3 + x^4 - 6x^3 + 10 + 2x^2\)[/tex] in standard form, follow these steps:

1. Combine Like Terms:
- Look for terms that have the same power of [tex]\(x\)[/tex].
- Combine [tex]\(-23x^3\)[/tex] and [tex]\(-6x^3\)[/tex], which are like terms:
[tex]\[
-23x^3 - 6x^3 = -29x^3
\][/tex]

2. Write the Polynomial in Standard Form:
- Arrange the terms from the highest power to the lowest power:
- The terms in descending order of their exponents are:
[tex]\[
x^4, -29x^3, 2x^2, \text{and } 10
\][/tex]
- So, the polynomial in standard form is:
[tex]\[
x^4 - 29x^3 + 2x^2 + 10
\][/tex]

3. Identify the Degree of the Polynomial:
- The degree of the polynomial is the highest exponent of [tex]\(x\)[/tex] in the polynomial, which is 4.

4. Identify the Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest degree. In this polynomial, it is the coefficient of [tex]\(x^4\)[/tex], which is 1.

Therefore, the polynomial in standard form is [tex]\(x^4 - 29x^3 + 2x^2 + 10\)[/tex], the degree is 4, and the leading coefficient is 1.

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