A polynomial of degree 5 in x has at mosta)5 termsb)4 termsc)6 termsd)...
A polynomial of degree 5 is of the form
p(
x) =

, where
a, b, c, d, e, and
f are real numbers and
a ≠ 0.
Thus,
p(
x) can have at most 6 terms and at least one term containing

.
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A polynomial of degree 5 in x has at mosta)5 termsb)4 termsc)6 termsd)...
A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. The degree of a polynomial is determined by the highest power of the variable present in the expression.
To determine the maximum number of terms in a polynomial of degree 5, we need to consider the different combinations of variables and exponents that can be present in the polynomial.
A polynomial of degree 5 can have terms with powers ranging from 0 to 5. Let's analyze the possibilities for each power:
- Power 0: A term with a power of 0 represents a constant. For example, the term 2 is a constant term. Since a polynomial of degree 5 can have any number of constant terms, there is no restriction on the number of terms with power 0.
- Power 1: A term with a power of 1 represents a linear term. For example, the term 3x is a linear term. A polynomial of degree 5 can have at most one linear term.
- Power 2: A term with a power of 2 represents a quadratic term. For example, the term 4x^2 is a quadratic term. A polynomial of degree 5 can have at most one quadratic term.
- Power 3: A term with a power of 3 represents a cubic term. For example, the term 5x^3 is a cubic term. A polynomial of degree 5 can have at most one cubic term.
- Power 4: A term with a power of 4 represents a quartic term. For example, the term 6x^4 is a quartic term. A polynomial of degree 5 can have at most one quartic term.
- Power 5: A term with a power of 5 represents a quintic term. For example, the term 7x^5 is a quintic term. A polynomial of degree 5 can have at most one quintic term.
Based on the analysis above, we can conclude that a polynomial of degree 5 can have at most 6 terms, including constant, linear, quadratic, cubic, quartic, and quintic terms. Therefore, the correct answer is option 'C' - 6 terms.
A polynomial of degree 5 in x has at mosta)5 termsb)4 termsc)6 termsd)...