For each polynomial, state the degree, the leading coefficient and the constant term.
Problem 1 :
2x^{3} + x^{2} - x + 3
Solution :
Given polynomial is 2x^{3} + x^{2} - x + 3
Since, the highest power of 2 is 3.
Therefore, the degree of the given polynomial is 3.
Leading coefficient is 2. And the constant term is 3.
Problem 2 :
x^{5} - x^{3} + x - 2
Solution :
Given polynomial is x^{5} - x^{3} + x - 2
Since, the highest power of 1 is 5.
Therefore, the degree of the given polynomial is 5.
Leading coefficient is 1. And the constant term is -2.
Problem 3 :
9x^{4} + x^{2}
Solution :
Given polynomial is 9x^{4} + x^{2 }
Since, the highest power of 9 is 4.
Therefore, the degree of the given polynomial is 4.
Leading coefficient is 9. And the constant term is 0.
Problem 4 :
5 - 2x
Solution :
Given polynomial is 5 - 2x
Since, the highest power of -2 is 1.
Therefore, the degree of the given polynomial is 1.
Leading coefficient is -2. And the constant term is 5.
Problem 5 :
7x^{6}
Solution :
Given polynomial is 7x^{6}
Since, the highest power of 7 is 6.
Therefore, the degree of the given polynomial is 6.
Leading coefficient is 7. And the constant term is 0.
Problem 6 :
5 - 2x + x^{2}
Solution :
Given polynomial is 5 - 2x + x^{2}
Since, the highest power of 1 is 2.
Therefore, the degree of the given polynomial is 2.
Leading coefficient is 1. And the constant term is 5.
Problem 7 :
9 - x^{2} + x^{4} - x^{6}
Solution :
Given polynomial is 9 - x^{2} + x^{4} - x^{6}
Since, the highest power of -1 is 6.
Therefore, the degree of the given polynomial is 6.
Leading coefficient is -1. And the constant term is 9.
Problem 8 :
3
Solution :
3 is a single variable. So, no highest power of polynomial.
3 is a constant term.
Problem 9 :
x^{3} - 2x^{5}
Solution :
Given polynomial is x^{3} - 2x^{5 }
Since, the highest power of -2 is 5.
Therefore, the degree of the given polynomial is 5.
Leading coefficient is -2. And the constant term is 0.
Problem 10 :
√3x^{2} + √2x + 1
Solution :
Given polynomial is √3x^{2} + √2x + 1
Since, the highest power of √3 is 2.
Therefore, the degree of the given polynomial is 2.
Leading coefficient is √3. And the constant term is 1.
Problem 11 :
5x^{3} + 3x^{4}/2
Solution :
Given polynomial is 5x^{3} + 3x^{4}/2
Since, the highest power of 3/2 is 4.
Therefore, the degree of the given polynomial is 4.
Leading coefficient is 3/2. And the constant term is 0.
Problem 12 :
x^{4}/3 + x^{2}/2 + 1/5
Solution :
Given polynomial is x^{4}/3 + x^{2}/2 + 1/5
Since, the highest power of 1/3 is 4.
Therefore, the degree of the given polynomial is 4.
Leading coefficient is 1/3. And the constant term is 1/5.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM