1.
The graph of a polynomial function is tangent to its?
Correct Answer
C. X-axis
Explanation
The graph of a polynomial function is tangent to its x-axis because when a polynomial function is tangent to the x-axis, it means that the function intersects the x-axis at exactly one point and does not cross it. This occurs when the polynomial function has a root or zero, which is a value of x that makes the function equal to zero. Therefore, the graph of the polynomial function will touch the x-axis at this root, resulting in a tangent.
2.
How many possible roots than fourth-degree polynomials can have?
Correct Answer
A. 4
Explanation
A fourth-degree polynomial can have a maximum of four roots. This is because a polynomial of degree n can have at most n distinct roots. In this case, since the polynomial is of degree four, it can have up to four roots. Therefore, the correct answer is 4.
3.
Is a linear function a polynomial?
Correct Answer
C. Always
Explanation
A linear function is always a polynomial. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. A linear function is a polynomial of degree 1, meaning it has one variable raised to the power of 1 and no other variables or exponents. Therefore, it falls under the category of polynomials.
4.
What do you call a polynomial of five degrees?
Correct Answer
D. None of the above
Explanation
The correct answer is "none of the above" because a polynomial of five degrees is called a quintic polynomial. "Pentanomial" refers to a polynomial with five terms, "heptanomial" refers to a polynomial with seven terms, and "hexanomial" refers to a polynomial with six terms. None of these terms accurately describe a polynomial of five degrees.
5.
What is the graph of a polynomial function?
Correct Answer
B. Continuous
Explanation
A polynomial function is a mathematical function that consists of terms involving variables raised to non-negative integer powers. The graph of a polynomial function is continuous, meaning that it has no breaks or gaps. It is a smooth curve that can be traced without lifting the pencil from the paper. This is because polynomial functions are defined for all real numbers, and there are no restrictions or interruptions in their domain. Therefore, the correct answer is continuous.
6.
What are the x-intercepts of polynomials?
Correct Answer
D. Roots
Explanation
The x-intercepts of a polynomial are the values of x where the polynomial intersects the x-axis. These points are also known as the roots of the polynomial. Therefore, the correct answer is "roots".
7.
What do you call a polynomial with two as the highest degree 4?
Correct Answer
B. Quadratic
Explanation
A polynomial is an algebraic expression with multiple terms. The highest degree in a polynomial refers to the exponent of the term with the highest power. In this case, the polynomial has a highest degree of 4, which means the term with the highest power is x^4. A quadratic polynomial is a polynomial with a highest degree of 2, so it does not fit the description given. Therefore, the correct answer is quadratic.
8.
What is the degree of this given, x+2=0?
Correct Answer
B. 1
Explanation
The degree of a given equation is determined by the highest power of the variable present in the equation. In this case, the equation x+2=0 is a linear equation, meaning it has a degree of 1. The highest power of the variable x is 1, as there is no x^2 or any higher power term present in the equation. Therefore, the degree of the given equation x+2=0 is 1.
9.
Which is a polynomial of degree 1?
Correct Answer
A. X+1
Explanation
The expression "x+1" is a polynomial of degree 1 because it consists of a variable (x) raised to the power of 1 (degree 1) and a constant term (1). The other options, "5+5", "polynomial has no degree 1", and "quadratic", do not meet the criteria of being a polynomial of degree 1.
10.
What is the constant term in this equation, x+25?
Correct Answer
C. 25
Explanation
The constant term in an equation is the term that does not contain any variables. In the equation x+25, the constant term is 25 because it does not have any variable attached to it.
11.
How do you define the maximum number of roots in a polynomial?
Correct Answer
A. Equal to the highest degree of a polynomial
Explanation
The maximum number of roots in a polynomial is determined by the highest degree of the polynomial. The degree of a polynomial represents the highest power of the variable in the polynomial expression. Since each root of a polynomial corresponds to a factor of the polynomial, the maximum number of roots can be equal to the degree of the polynomial.
12.
What theorem states that if x-c is a factor of f(x), then it becomes f(c)?
Correct Answer
B. Remainder theorem
Explanation
The remainder theorem states that if (x-c) is a factor of f(x), then it becomes f(c).
13.
What do you call the shortcut method in dividing polynomials?
Correct Answer
C. Synthetic division
Explanation
Synthetic division is a shortcut method used to divide polynomials. It is a process that simplifies the long division of polynomials by using coefficients and remainders. This method is particularly useful when dividing by linear factors. By using synthetic division, one can quickly find the quotient and remainder of the division, making it an efficient technique for dividing polynomials.
14.
What do you call a four-degree polynomial?
Correct Answer
D. Bi-quadratic
Explanation
A four-degree polynomial is called a bi-quadratic polynomial. This is because the prefix "bi-" means two, and a bi-quadratic polynomial has two quadratic terms.
15.
What are the roots of G(x)= (x+2)(x-5)(x-1)?
Correct Answer
A. -2,5,1
Explanation
The roots of a polynomial are the values of x that make the polynomial equal to zero. In this case, the polynomial G(x)=(x+2)(x-5)(x-1) will be equal to zero when any of the factors (x+2), (x-5), or (x-1) are equal to zero. By setting each factor equal to zero and solving for x, we find that the roots are x=-2, x=5, and x=1. Therefore, the correct answer is -2, 5, 1.
16.
Is the graph of the polynomial function smooth?
Correct Answer
C. Yes, continuous, and curve
Explanation
The graph of a polynomial function is smooth because it is continuous and has no breaks or jumps. Additionally, the graph of a polynomial function is typically curved, as it can have various shapes such as parabolas, cubic curves, or higher-degree curves. Therefore, the correct answer is "yes, continuous, and curve."
17.
How do you define the turning points of the graph of polynomial functions?
Correct Answer
C. N-1
Explanation
The turning points of a graph of a polynomial function are defined as the points where the graph changes direction from increasing to decreasing or vice versa. In this case, the correct answer is n-1, which suggests that the number of turning points in the graph is equal to n-1. This means that the graph will have one less turning point than the degree of the polynomial function.