Question 1

Which of the following expressions is a polynomial in one variable?

Accepted Answer

A polynomial in one variable is an algebraic expression containing only one variable with non-negative integer exponents. In the expression 3x^2 - 5x + 7, the variable is x, and all exponents are whole numbers (2, 1, and 0). Thus, it is a polynomial in one variable. Other options contain variables u

Question 2

What is the degree of the polynomial 5x^3 - 4x^2 + 7x - 2?

Accepted Answer

The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial 5x^3 - 4x^2 + 7x - 2, the powers of x are 3, 2, 1, and 0. The highest power is 3. Therefore, the degree of the polynomial is 3.

Question 3

What is the coefficient of x^2 in the polynomial 2 - x^2 + x^3?

Accepted Answer

The coefficient of x^2 is the numerical factor multiplied by x^2 in the given polynomial. In 2 - x^2 + x^3, the term containing x^2 is -x^2, which can be written as -1 x^2. Therefore, the coefficient of x^2 is -1.

Question 4

What is the degree of a non-zero constant polynomial?

Accepted Answer

A non-zero constant polynomial is of the form p(x) = c, where c is a non-zero real number. Since it can be written as c x^0, the exponent of the variable x is 0. Hence, the degree of a non-zero constant polynomial is always 0.

Question 5

Find the value of the polynomial p(x) = 5x - 4x^2 + 3 at x = 0.

Accepted Answer

To find the value of p(x) at x = 0, substitute 0 for every occurrence of x in the polynomial: p(0) = 5(0) - 4(0)^2 + 3 = 0 - 0 + 3 = 3. Thus, the value of the polynomial at x = 0 is 3.

Polynomials