Question

which algebraic expression is a polynomial with a degree of 4? a: 5x4 b: x5 – 6x4 14x3 x2 c :9x4 – x3 – d:2x4 – 6x4

Answer 1

Answer: the option C. c) 9x⁴– x³– ...

Explanation:

1) A polynomial of one variable is an expression of the kind:

$a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0$

2) The order of the polynomial is the highest exponent of the variable, this is n

3) When the expression has one term it is called a monomial, when the expression has two terms it is called a binomial, when the expression has 3 terms it is called a trinomial.

Usually expressions of that kind with two or more terms are referred as polynomial, but one term is referred as monomial.

4) For the given expressions you have:

a) 5x⁴: it is a monomial (one term), which is usually not referred as polynomial properly.

b) x⁵ – 6x⁴ + 14x³ + x²: it is a polynomial with degree 5 (the highest power).

c) 9x⁴– x³– ... : altough the expression is incomplete, assuming that the next terms are monomials with degree less than 4, then this is a polynomial with degree 4, and is the right answer choice.

d) 2x⁴ – 6x⁴: since both terms have the same power, they can be simplified into one term, - 4x⁴, and it is a monomial.

Answer 2

For polynomials having two or more variables, degree can be of a term or of the polynomial. The degree of a term is the sum of the exponents in a specific term while the degree of a polynomial is the highest value of all the degree of a term in the given polynomial. From the choices given, the algebraic expression with a degree of 4 is option C, 9x^4 – x^3.