Classification of Polynomials According to Their Degree

Q.

What is the meaning of linear polynomial?

Q.

Write the general form of a quadratic polynomial.

Q.

Is x - 1/x a polynomial

Q.

Classify the following as linear, quadratic and cubic polynomial:

(i) (ii) (iii) (iv) (v)

(vi) (vii)

Q.

A polynomial of degree 3 is called a __ polynomial

Q.

Question 6
Give an example of a polynomial, which is:

(i) Monomial of degree 1.

(ii) Binomial of degree 20.

(iii) Trinomial of degree 2.

Q.

Give one example of a Quadratic Polynomial.

Q.

Identify constant, linear, quadratic and cubic polynomials from the following polynomials :

(i) f(x) = 0

(ii) g(x) = $2x^3$ - 7x + 4

(iii) h(x) = - 3x + $\frac{1}{2}$

(iv) p(x) = $2x^2$ - x + 4

(v) q(x) = 4x + 3

(vi) r(x) = $3x^3+4x^2$ + 5x - 7

Q.

Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials :

(i) $x+x^2$ + 4

(ii) 3x - 2

(iii) 2x + $x^2$

(iv) 3y

(v) $t^2$ + 1

(vi) $7t^4+4t^3$ + 3t - 2

Q.

The product of two polynomials is a_____

Q.

(i) Give an example of a monomial of degree 5.
(ii) Give an example of a binomial of degree 8.
(iii) Given an example of a binomial of degree 4.
(iv) Give an example of a monomial of degree 0.

Q. Factorize the cubic polynomial 2x^3-x^2-13x-6

Q.

Classify the following polynomials as polynomials in one-variable, two variables etc.

(i) $x^2$ - xy + $7y^2$

(ii) $x^2$ - 2tx + $7t^2$ - x + t

(iii) $t^2$ - $3t^2$ + 4t - 5

(iv) $xy+yz+zx$

Q. If x^g + ¹/_xa is a polynomial in one variable and if it's given that g = a, for what value of 'a' is this a polynomial?

Q.

A polynomial of degree ___ is called quadratic polynomial

1. 2

2. 0

3. -1

4. 1

Q. ‘4x’ is a constant polynomial.

1. True
2. False

Q.

Name the polynomial containing two nonzero terms.

Q. Classify the following polynomials as linear, quadratic and cubic polynomial.

Q.

The polynomial $a{x}^2+bx+c$ is a linear polynomial if

1. a = 0

2. b = 0

3. both a=0, b=0

4. neither a=0 nor b=0

Q. Identify polynomials in the following:

(i) f(x) = 4x³ − x² − 3x + 7

(ii) g(x) = 2x³ − 3x² + $\sqrt{x}$ − 1

(iii) p(x) = $\frac{2}{3}{x}^2-\frac{7}{4}x+9$

(iv) q(x) = 2x² − 3x + $\frac{4}{x}$+ 2

(v) h(x) = $x^4-x^{\frac{3}{2}}+x-1$

(vi) f(x) = $2+\frac{3}{x}+4x$

Q. In the question, a statement of assertion(A) is followed by a statement of reason (R) . Mark the correct choice:

Assertion: 𝐏(𝐱) = 𝐱${}^2$ − 𝐱 + 𝟑 is a quadratic polynomial.
Reason: 𝐱 + 𝟑 is not a linear polynomial.

1. The assertion is false, but the reason is true.
   
2. Both assertion and reason are true, and the reason is the correct explanation of assertion.
   
3. Both assertion and reason are true, but the reason is not the correct explanation of assertion.
   
4. The assertion is true, but the reason is false.
   

Q.

Question 1
Classify the following polynomials as polynomials in one variable, two variables etc.

(i) $x^2+x+1$

(ii) $y^3-5y$

(iii) $xy+yz+zx$

(iv) $x^2–xy+y^2+1$

Q.

A polynomial has finite values.

1. True

2. False

Q.

Find the general term for the sequence pattern $2,6,12,20,30,\dots$

Q.

What are the factors of polynomial p(x) = x² + x - 6

Q.

Find $p\left(0\right),p\left(1\right)$ and $p\left(2\right)$ for the following polynomial: $p\left(x\right)=x^3$

Q. Question 3
Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Q.

For the polynomial 5x³-root 7x²+9x-3 write the

1.Degree

2.co efficient of x³

3. Constant term

4. Name of the polynomial based on degree

Q. Which of the following correctly represents the given polynomial?

$(x^2+9)$

1. Quadratic Binomial
2. Quadratic Trinomial
3. Cubic Binomial
4. Linear Binomial

Q. Which of the following is a cubic polynomial?

1. $4x^4+5x^3+2x^2+9x+6$
2. $2x+5$
3. $2x^2+9x+6$
4. $5x^3+2x^2+9x+6$