To determine the degree of the polynomial [tex]\( 5x^3 - 2x^2 + 3 \)[/tex], we need to identify the highest power of the variable [tex]\( x \)[/tex] present in the polynomial.
Here’s a detailed breakdown:
1. Identify the terms: The polynomial [tex]\( 5x^3 - 2x^2 + 3 \)[/tex] consists of three terms: [tex]\( 5x^3 \)[/tex], [tex]\( -2x^2 \)[/tex], and [tex]\( 3 \)[/tex].
2. Determine the exponents:
- For the term [tex]\( 5x^3 \)[/tex], the exponent of [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex].
- For the term [tex]\( -2x^2 \)[/tex], the exponent of [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex].
- For the constant term [tex]\( 3 \)[/tex], it can be considered as [tex]\( 3x^0 \)[/tex] where the exponent of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
3. Find the highest exponent: The degrees of the terms are [tex]\( 3 \)[/tex], [tex]\( 2 \)[/tex], and [tex]\( 0 \)[/tex]. Among these, the highest exponent is [tex]\( 3 \)[/tex].
Therefore, the degree of the polynomial [tex]\( 5x^3 - 2x^2 + 3 \)[/tex] is [tex]\( 3 \)[/tex].
So the correct option is [tex]\( 3 \)[/tex].
