To determine the degree of a polynomial, you need to identify the term with the highest power of [tex]\( x \)[/tex] in the expression. The degree of the polynomial is that highest power.
Let's examine the given polynomial:
[tex]\[ F(x) = 2x^3 - 3x^4 + 5x - 2 \][/tex]
1. Identify each term in the polynomial:
- [tex]\( 2x^3 \)[/tex]
- [tex]\( -3x^4 \)[/tex]
- [tex]\( 5x \)[/tex]
- [tex]\( -2 \)[/tex]
2. Determine the power of [tex]\( x \)[/tex] in each term:
- For [tex]\( 2x^3 \)[/tex], the power is [tex]\( 3 \)[/tex].
- For [tex]\( -3x^4 \)[/tex], the power is [tex]\( 4 \)[/tex].
- For [tex]\( 5x \)[/tex], the power is [tex]\( 1 \)[/tex].
- For [tex]\( -2 \)[/tex], the power is [tex]\( 0 \)[/tex] (since [tex]\( -2 \)[/tex] can be written as [tex]\( -2x^0 \)[/tex]).
3. Identify the highest power of [tex]\( x \)[/tex] in these terms:
- The highest power is [tex]\( 4 \)[/tex] (from the term [tex]\( -3x^4 \)[/tex]).
Therefore, the degree of the polynomial [tex]\( F(x) = 2x^3 - 3x^4 + 5x - 2 \)[/tex] is [tex]\( 4 \)[/tex].
Hence, the correct answer is:
C. 4
