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What is the degree of the polynomial given below?

[tex]\[F(x) = 2x^3 - 3x^4 + 5x - 2\][/tex]

A. 2
B. 5
C. 4
D. 3

Sagot :

GinnyAnswer
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
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