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Answer :
To find the degree of a polynomial, you simply look for the term with the highest exponent on the variable. The degree of the polynomial is that exponent.
Let's examine the given polynomial:
[tex]\[ 7x^6 - 6x^5 + 2x^3 + x - 8 \][/tex]
1. Identify each term in the polynomial:
- [tex]\( 7x^6 \)[/tex]
- [tex]\( -6x^5 \)[/tex]
- [tex]\( 2x^3 \)[/tex]
- [tex]\( x \)[/tex] which is the same as [tex]\( 1x^1 \)[/tex]
- [tex]\( -8 \)[/tex] is a constant term (can be considered as [tex]\( -8x^0 \)[/tex])
2. Look at the exponents for each of these terms:
- The exponent for [tex]\( 7x^6 \)[/tex] is 6.
- The exponent for [tex]\( -6x^5 \)[/tex] is 5.
- The exponent for [tex]\( 2x^3 \)[/tex] is 3.
- The exponent for [tex]\( x \)[/tex] is 1.
- The exponent for the constant term [tex]\( -8 \)[/tex] is 0.
3. The highest of these exponents is 6.
Therefore, the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex] is 6.
Let's examine the given polynomial:
[tex]\[ 7x^6 - 6x^5 + 2x^3 + x - 8 \][/tex]
1. Identify each term in the polynomial:
- [tex]\( 7x^6 \)[/tex]
- [tex]\( -6x^5 \)[/tex]
- [tex]\( 2x^3 \)[/tex]
- [tex]\( x \)[/tex] which is the same as [tex]\( 1x^1 \)[/tex]
- [tex]\( -8 \)[/tex] is a constant term (can be considered as [tex]\( -8x^0 \)[/tex])
2. Look at the exponents for each of these terms:
- The exponent for [tex]\( 7x^6 \)[/tex] is 6.
- The exponent for [tex]\( -6x^5 \)[/tex] is 5.
- The exponent for [tex]\( 2x^3 \)[/tex] is 3.
- The exponent for [tex]\( x \)[/tex] is 1.
- The exponent for the constant term [tex]\( -8 \)[/tex] is 0.
3. The highest of these exponents is 6.
Therefore, the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex] is 6.
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