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Answer :
To find the degree of a polynomial, you need to identify the term with the highest power of the variable. Let's look at the polynomial provided:
[tex]\[ y = 5 - 4x^6 - 3x^9 - x^8 \][/tex]
In this polynomial, each term is separated by a plus or minus sign. Let's identify the exponents of [tex]\( x \)[/tex] in each term:
- The term [tex]\( -4x^6 \)[/tex] has an exponent of 6.
- The term [tex]\( -3x^9 \)[/tex] has an exponent of 9.
- The term [tex]\( -x^8 \)[/tex] has an exponent of 8.
- The constant term [tex]\( 5 \)[/tex] does not have an [tex]\( x \)[/tex], so its exponent can be considered as 0.
The degree of the polynomial is the highest exponent of [tex]\( x \)[/tex] in the entire expression. In this case, the highest exponent is 9, which comes from the term [tex]\( -3x^9 \)[/tex].
Therefore, the degree of the polynomial [tex]\( y = 5 - 4x^6 - 3x^9 - x^8 \)[/tex] is 9.
[tex]\[ y = 5 - 4x^6 - 3x^9 - x^8 \][/tex]
In this polynomial, each term is separated by a plus or minus sign. Let's identify the exponents of [tex]\( x \)[/tex] in each term:
- The term [tex]\( -4x^6 \)[/tex] has an exponent of 6.
- The term [tex]\( -3x^9 \)[/tex] has an exponent of 9.
- The term [tex]\( -x^8 \)[/tex] has an exponent of 8.
- The constant term [tex]\( 5 \)[/tex] does not have an [tex]\( x \)[/tex], so its exponent can be considered as 0.
The degree of the polynomial is the highest exponent of [tex]\( x \)[/tex] in the entire expression. In this case, the highest exponent is 9, which comes from the term [tex]\( -3x^9 \)[/tex].
Therefore, the degree of the polynomial [tex]\( y = 5 - 4x^6 - 3x^9 - x^8 \)[/tex] is 9.
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