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------------------------------------------------ What are the degree and leading coefficient of the polynomial [tex]4x + 23x^4 + 2 - 12x^5[/tex]?

Degree: [tex]\square[/tex]

Leading coefficient: [tex]\square[/tex]

To determine the degree and the leading coefficient of the polynomial [tex]\(4x + 23x^4 + 2 - 12x^5\)[/tex], follow these steps:

1. Identify the Terms: Write down the terms of the polynomial and their respective powers and coefficients:
- [tex]\(4x\)[/tex] has a degree of 1 and a coefficient of 4.
- [tex]\(23x^4\)[/tex] has a degree of 4 and a coefficient of 23.
- [tex]\(2\)[/tex] is a constant term and can be seen as [tex]\(2x^0\)[/tex], which has a degree of 0 and a coefficient of 2.
- [tex]\(-12x^5\)[/tex] has a degree of 5 and a coefficient of -12.

2. Determine the Degree: The degree of the polynomial is the highest power of [tex]\(x\)[/tex] present in any term, which in this case is 5 from the term [tex]\(-12x^5\)[/tex].

3. Identify the Leading Coefficient: The leading coefficient is the coefficient of the term with the highest degree. Since [tex]\(-12x^5\)[/tex] is the term with the highest degree, its coefficient, [tex]\(-12\)[/tex], is the leading coefficient.

So, for the polynomial [tex]\(4x + 23x^4 + 2 - 12x^5\)[/tex]:
- The degree is [tex]\(5\)[/tex].
- The leading coefficient is [tex]\(-12\)[/tex].