1. What is the degree of the polynomial 3x^4 – 5x^3 + 7?
Answer:
Explanation:
The degree of a polynomial is the highest power of its variable. Here, it's 4.
2. What type of polynomial is 5x^2 – 3x + 4?
Answer:
Explanation:
A polynomial of degree 2 is called a quadratic polynomial.
3. What is the degree of a constant polynomial?
Answer:
Explanation:
A constant polynomial has no variable term, so its degree is 0.
4. Which polynomial has roots 2 and -3?
Answer:
Explanation:
Using the factor theorem, (x-2)(x+3) gives the polynomial x^2 – x – 6.
5. What is the value of a quadratic polynomial at its roots?
Answer:
Explanation:
At its roots, the value of any polynomial is 0.
6. Which of the following is a binomial?
Answer:
Explanation:
A polynomial with two terms is called a binomial.
7. What is the coefficient of x in the polynomial 3x^2 – 4x + 7?
Answer:
Explanation:
The coefficient of x is the number multiplied by x, which is -4.
8. The zero of the polynomial p(x) = x – 4 is:
Answer:
Explanation:
Setting p(x) to 0, x – 4 = 0 gives x = 4.
9. What is the degree of the zero polynomial?
Answer:
Explanation:
The zero polynomial doesn’t have a well-defined degree.
10. Which of the following is a cubic polynomial?
Answer:
Explanation:
A polynomial of degree 3 is called a cubic polynomial.
11. If p(x) = 3x^2 + ax + 5 and p(1) = 10, then the value of a is:
Answer:
Explanation:
Plugging x=1 into p(x) and setting it to 10, we get 3 + a + 5 = 10, which means a = 2.
12. The number of zeros a quadratic polynomial can have is:
Answer:
Explanation:
A quadratic polynomial can have at most 2 zeros.
13. Which polynomial is represented by the algebraic expression 5x – 3?
Answer:
Explanation:
An algebraic expression with two terms is called a binomial.
14. The zeros of the polynomial x^2 – x are:
Answer:
Explanation:
Factorizing x^2 – x as x(x – 1), we get zeros at x = 0 and x = 1.
15. A polynomial of degree n has how many zeros?
Answer:
Explanation:
By the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n zeros.
16. Which of the following is not a polynomial?
Answer:
Explanation:
A polynomial cannot have negative powers.
17. The sum of the zeros of the polynomial x^2 + 3x + 2 is:
Answer:
Explanation:
For the polynomial ax^2 + bx + c, the sum of zeros is -b/a.
18. The polynomial p(x) = x^3 – 6x^2 + 11x – 6 can be factorized as:
Answer:
Explanation:
Using factor theorem and synthetic division, we can factorize the given polynomial.
19. The zero of the polynomial p(x) = x + 5 is:
Answer:
Explanation:
Setting p(x) to 0, x + 5 = 0 gives x = -5.
20. The product of the zeros of the polynomial x^2 – 5x + 6 is:
Answer:
Explanation:
For the polynomial ax^2 + bx + c, the product of zeros is c/a.