Types of Polynomials

Q.

Question 2
Write whether the following statements are true or false. Justify your answer.

i. A Binomial can have atmost two terms.

ii. Every polynomial is a Binomial.

iii. A binomial may have degree 5.

iv. Zero of a polynomial is always 0.

v. A polynomial cannot have more than one zero.

vi. The degree of the sum of two polynomials each of degree 5 is always 5.

Q.

Identify constant, linear, quadratic, cubic and quartic polynomials from the following.

(i) $-7+x$

(ii) $6y$

(iii) $-z^3$

(iv) $1-y-y^3$

(v) $x-x^3+x^4$

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

(viii) $-6x^2$

(viii) $-13$

(ix) $-p$

Q.

An expression that contains only one term is called a __.

Q. Every real number is a zero of the __________ polynomial.

1. Zero
2. Linear
3. Cubic
4. Quadratic

Q.

Which among the following is a binomial?

1. $x^2-x+1$
2. $2x^2$
3. $x^3+1$​
4. $x^4+x^2-2$

Q.

Which of the following expressions is a polynomial in one variable?
(a) $x+\frac{2}{x}+3$
(b) $3\sqrt{x}+\frac{2}{\sqrt{x}}+5$
(c) $\sqrt{2}{x}^2-\sqrt{3}x+6$
(d) $x^{10}+y^5+8$

Q.

Which of the following is a quadratic polynomial ?
(a) $x+4$
(b) $x^3+x$
(c) $x^3+2x+6$
(d) $x^2+5x+4$

Q.

A polynomial with only two terms is known as a .

1. Binomial

2. Quadratic polynomial
3. Cubic polynomial
4. Trinomial

Q. Which of the following is a constant polynomial?

1. $4x^3+2x^2+3$
2. $x^3+8$
3. $x^0+1$
4. $x^2-4$

Q. A polynomial with 2 terms is known as a .

1. binomial
2. quadratic polynomial
3. trinomial
4. cubic polynomial

Q.

The equation of X-Axis is

1. x = 0

2. y = 0

3. x = y = 0

4. xy = 0

Q.

Classify the following as linear, quadratic and cubic polynomials: $x^2+x$.

Q.

Which of the following is a binomial ?
(a) $x^2+x+3$
(b) $x^2+4$
(c) $2x^2$
(d) $x+3+\frac{1}{x}$

Q.

Which of the following is a linear polynomial ?
(a) $x+x^2$
(b) $x+1$
(c) $5x^2-x+3$
(d) $x+\frac{1}{x}$

Q.

Which of the following graphs may correspond to the equation y = k where k is a negative rational number.

1. 

2. 

3. 

4. 

Q.

Classify the following as linear, quadratic and cubic polynomials: $x-x^3$.

Q.

State true or false every polynomial is a binomial

Q. What can be the maximum number of distinct terms in a polynomial with a single variable of degree 1?

1. 1
2. 2
3. 3
4. 4

Q.

Identify the numerical coefficients of terms (other than constants) in the following expressions: $0.1y+0.01y^2$

Q.

If $a(x{)}^2+bx+c$ is a monomial in $x$ , what can be said about $a$, $b$ and $c$?

1. Atleast one of a, b and c is non - zero.

2. Only one among a, b and c is zero.

3. Only one among a, b and c is non - zero.

4. All three should be non - zero

Q.

Polynomials having only three terms are called ________

1. trinomials

2. binomial

3. monomial

4. multinomial

Q. $x^{10}+y^3+t^{50}$ is a polynomial in:

[1 mark]
[NCERT]
[Types of Polynomials]

1. None of the above
2. Three Variables
3. One Variable
4. Two Variables

Q. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:

(i) 3x² − 4x + 15

(ii) y² + 2$\sqrt{3}$

(iii) $3\sqrt{x}+\sqrt{2}x$

(iv) $x-\frac{4}{x}$

(v) x¹² + y³ + t⁵⁰

Q.

Which of the following expressions are polynomials in one variable and which are not?

State reasons for your answer. (i) $y^2+\sqrt{2}$ (ii) $3\sqrt{t}+t\sqrt{2}$ and (iii) $x^{10}+y^3+t^{50}$.

Q. Which of the following is a binomial?

1. $x^2-2x-1$
2. $x+1$
3. $x^3+x+1$
4. $x^2$

Q.

If $a(x{)}^2+bx+c$ is a monomial in $x$ , what can be said about $a$, $b$ and $c$?

1. Atleast one of a, b and c is non - zero.

2. All three should be non - zero

3. Only one among a, b and c is zero.

4. Only one among a, b and c is non - zero.

Q. Give one example each of a binomial of degree $35$ and of a monomial of degree $100$.

Q. The degree of the algebraic expression \lbrack(x2 – 3x)2 ÷ 3x2\rbrack is = ?

Q.

The factor theorem states that if there is a polynomial of degree greater than or equal to one and ‘a’ be a real number. If P(a) = 0 then x – a is the factor of the polynomial P(x). Is this true or false?

1. True

2. False

Q.

1.The graph of a Linear equation is always - answer

2.the equation of the x axis is answer

3.the equation of the y axis is answer