Solved Questions on Polynomials
1. Which of the following polynomials is a binomial?
a) 2x2 - 3x + 1
b) 4x3 + 2x2 - 5x + 1
c) 3x4 - 2x2 + 5x - 3
d) 7x2 - 5x
Answer: d) 7x2 - 5x
Explanation: A binomial is a polynomial with exactly two terms. In this case, option (d) has only two terms (7x2 and -5x), making it a binomial.
2. What is the degree of the polynomial 2x4 - 3x2 + 5x - 1?
a) 2
b) 3
c) 4
d) 1
Answer: c) 4
Explanation: The degree of a polynomial is determined by the highest exponent of the variable. In this case, the term with the highest exponent is 2x4, indicating that the polynomial has a degree of 4.
3. Which expression represents the sum of (4x2 - 2x + 1) and (2x2 + 3x - 5)?
a) 6x2 + x - 6
b) 6x2 + x - 4
c) 6x2 + x - 4x + 6
d) 6x2 + x + 4x - 6
Answer: b) 6x2 + x - 4
Explanation: Align the like terms and add their coefficients. In this case, the like terms are the ones with the same exponent of x. Adding the coefficients of like terms, we get 6x2 + x - 4.
4. What is the result of subtracting (6x3 - 2x2 + 5x + 3) from (4x3 + 3x2 - 2x + 1)?
a) -2x3 + 5x2 - 7x - 2
b) 2x3 - 5x2 + 7x + 2
c) -2x3 - 5x2 + 7x + 2
d) 2x3 + 5x2 - 7x - 2
Answer: a) -2x3 - 5x2 - 7x - 2
Explanation: When subtracting polynomials, you align the like terms and subtract their coefficients. In this case, the like terms are the ones with the same exponent of x. Subtracting the coefficients of like terms, we get -2x3 - 5x2 - 7x - 2.
5. The length of a rectangular field is 2x + 4 and its width is x - 2. What expression represents the perimeter of the field?
a) 6x + 4
b) 6x - 4
c) 3x + 2
d) 3x - 2
Answer: a) 6x + 4
Explanation: The perimeter of a rectangle is given by the sum of all its sides. In this case, the length is 2x + 4 and the width is x - 2. The perimeter can be found by adding the lengths of all four sides, which is 2(2x + 4) + 2(x - 2) = 6x + 4. Simplifying further, we get 6x + 4, which represents the perimeter of the field.
Practice Questions on Polynomials
1. What is the degree of the polynomial 3x2 - 7x + 5?
a) 1
b) 2
c) 3
d) 4
Answer: b) 2.
2. Which of the following is not a polynomial?
a) x2 - 3x + 4
b) 4x3 + 2x2 - 5x
c) x4 + 2x3 - 7x2 + 3x
d) 2x + 3/x
Answer: d) 2x + 3/x.
3. What is the degree of the polynomial 3x2 - 7x + 5?
a) 1
b) 2
c) 3
d) 4
Answer: b) 2.
4. The perimeter of a square is 4x + 8. What expression represents the length of one side of the square?
a) x + 2
b) x - 2
c) x + 4
d) x - 4
Answer: a) x + 2
5. What is the degree of the polynomial x3 + 3x2 - 2x + 5?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3.
6. What is the result of adding (3x2 + 2x - 1) and (-2x2 + 5x + 3)?
a) x2 + 7x + 2
b) x2 - 3x + 2
c) x2 - 3x - 4
d) x2 + 3x - 4
Answer: a) x2 + 3x - 4
7. What is the result of subtracting (5x3 + 2x2 - 3x + 1) from (3x3 - 4x2 + 5x - 2)?
a) 2x3 + 6x2 - 8x + 3
b) -2x3 - 6x2 + 8x - 3
c) 2x3 - 6x2 + 8x - 3
d) -2x3 + 6x2 - 8x + 3
Answer: b) -2x3 - 6x2 + 8x – 3
8. Which of the following is a polynomial of degree 4?
a) 2x2 - 3x + 1
b) 4x3 + 2x2 - 5x + 1
c) 3x4 - 2x2 + 5x - 3
d) 7x2 - 5x + 2
Answer: c) 3x4 - 2x2 + 5x - 3
9. Which of the following is a monomial?
a) 2x2 + 3x + 1
b) 4x3 - 2x2
c) 5x
d) 5x + 2
Answer: c) 5x
10. When a polynomial f(x) is divided by (x - 2), the remainder is 3. What is the value of f(2)?
a) 3
b) 2
c) 5
d) 0
Answer: a) 3
