## 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.