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What is the degree of the following polynomial?

[tex]3x^4y - 6xy^7 + 2x^4y^8[/tex]

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Sagot :

To determine the degree of the polynomial [tex]\( 3x^4 y - 6xy^7 + 2x^4 y^8 \)[/tex], we need to follow these steps:

### Step 1: Identify the degree of each term

1. First term: [tex]\( 3x^4 y \)[/tex]
- The term [tex]\( 3x^4 y \)[/tex] consists of [tex]\( x^4 \)[/tex] and [tex]\( y \)[/tex].
- The degrees of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in this term are 4 and 1, respectively.
- The total degree of this term is [tex]\( 4 + 1 = 5 \)[/tex].

2. Second term: [tex]\( -6xy^7 \)[/tex]
- The term [tex]\( -6xy^7 \)[/tex] consists of [tex]\( x \)[/tex] and [tex]\( y^7 \)[/tex].
- The degrees of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in this term are 1 and 7, respectively.
- The total degree of this term is [tex]\( 1 + 7 = 8 \)[/tex].

3. Third term: [tex]\( 2x^4 y^8 \)[/tex]
- The term [tex]\( 2x^4 y^8 \)[/tex] consists of [tex]\( x^4 \)[/tex] and [tex]\( y^8 \)[/tex].
- The degrees of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in this term are 4 and 8, respectively.
- The total degree of this term is [tex]\( 4 + 8 = 12 \)[/tex].

### Step 2: Determine the degree of the polynomial

The degree of a polynomial is the highest degree of its terms.

- The degrees of the individual terms are 5, 8, and 12.
- The highest degree among these is 12.

Therefore, the degree of the polynomial [tex]\( 3x^4 y - 6xy^7 + 2x^4 y^8 \)[/tex] is [tex]\( \boxed{12} \)[/tex].