Answer :
To determine the degree of a polynomial, we need to find the highest power of the variable present in the polynomial. Here's a step-by-step explanation:
1. Identify the Polynomial: The given polynomial is [tex]\( f(x) = x^6 - 4x^3 - 2x + 7 \)[/tex].
2. Look at Each Term: The polynomial consists of several terms: [tex]\( x^6 \)[/tex], [tex]\( -4x^3 \)[/tex], [tex]\( -2x \)[/tex], and [tex]\( 7 \)[/tex].
3. Determine the Exponent of Each Term:
- The term [tex]\( x^6 \)[/tex] has an exponent of 6.
- The term [tex]\( -4x^3 \)[/tex] has an exponent of 3.
- The term [tex]\( -2x \)[/tex] has an exponent of 1.
- The constant term [tex]\( 7 \)[/tex] has an exponent of 0 (since any number can be considered as multiplied by [tex]\( x^0 \)[/tex]).
4. Identify the Highest Exponent: Among the exponents [tex]\( 6, 3, 1, \)[/tex] and [tex]\( 0 \)[/tex], the highest exponent is 6.
5. Conclusion: Therefore, the degree of the polynomial [tex]\( f(x) = x^6 - 4x^3 - 2x + 7 \)[/tex] is 6.
The degree of a polynomial tells us the highest degree of any term with a non-zero coefficient. In this case, it's 6.
1. Identify the Polynomial: The given polynomial is [tex]\( f(x) = x^6 - 4x^3 - 2x + 7 \)[/tex].
2. Look at Each Term: The polynomial consists of several terms: [tex]\( x^6 \)[/tex], [tex]\( -4x^3 \)[/tex], [tex]\( -2x \)[/tex], and [tex]\( 7 \)[/tex].
3. Determine the Exponent of Each Term:
- The term [tex]\( x^6 \)[/tex] has an exponent of 6.
- The term [tex]\( -4x^3 \)[/tex] has an exponent of 3.
- The term [tex]\( -2x \)[/tex] has an exponent of 1.
- The constant term [tex]\( 7 \)[/tex] has an exponent of 0 (since any number can be considered as multiplied by [tex]\( x^0 \)[/tex]).
4. Identify the Highest Exponent: Among the exponents [tex]\( 6, 3, 1, \)[/tex] and [tex]\( 0 \)[/tex], the highest exponent is 6.
5. Conclusion: Therefore, the degree of the polynomial [tex]\( f(x) = x^6 - 4x^3 - 2x + 7 \)[/tex] is 6.
The degree of a polynomial tells us the highest degree of any term with a non-zero coefficient. In this case, it's 6.
