Grade 9 : Mathematics - 2. Polynomials (Set 1)

Question 1

What is the degree of the polynomial $p(x) = 5x^4 - 3x^3 + 2x^2 - 9$?

Accepted Answer

B) 4

Answer

A) 3

Answer

C) 2

Answer

D) 5

Question 2

What is the coefficient of $x^2$ in the polynomial $p(x) = 7x^3 - 8x^2 + 4x + 12$?

Accepted Answer

B) -8

Answer

A) 8

Answer

C) 7

Answer

D) 4

Question 3

Which of the following algebraic expressions is a polynomial in one variable?

Accepted Answer

C) $4x^3 - 2x^2 + \sqrt{5}x - 7$

Answer

A) $x^2 + \frac{2}{x} + 3$

Answer

B) $3\sqrt{x} + 5x$

Answer

D) $x^2 + x^{-1} + 4$

Question 4

What is the value of the polynomial $p(x) = 3x^2 - 5x + 4$ at $x = 2$?

Accepted Answer

A) 6

Answer

B) 8

Answer

C) 10

Answer

D) 4

Question 5

Find the zero of the linear polynomial $p(x) = 4x - 20$.

Accepted Answer

C) 5

Answer

A) -5

Answer

B) 4

Answer

D) -4

Question 6

What is the degree of a non-zero constant polynomial, such as $p(x) = 7$?

Accepted Answer

B) 0

Answer

A) 1

Answer

C) Not defined

Answer

D) 2

Question 7

What is the degree of the zero polynomial $p(x) = 0$?

Accepted Answer

C) Not defined

Answer

A) 0

Answer

B) 1

Answer

D) Any real number

Question 8

According to the Remainder Theorem, what is the remainder when $p(x) = x^3 - 4x^2 + 2x + 5$ is divided by $(x - 2)$?

Accepted Answer

A) 1

Answer

B) 5

Answer

C) -1

Answer

D) 3

Question 9

If $(x - 1)$ is a factor of $p(x) = x^2 + 3x + k$, what is the value of $k$?

Accepted Answer

B) -4

Answer

A) 4

Answer

C) 3

Answer

D) -3

Question 10

Which of the following is an example of a binomial of degree 35?

Accepted Answer

A) $x^{35} + 35$

Answer

B) $35x$

Answer

C) $x^{35} + x^{20} + 5$

Answer

D) $35x^{35}$

Question 11

Factorize the quadratic polynomial $x^2 + 8x + 15$.

Accepted Answer

A) $(x + 3)(x + 5)$

Answer

B) $(x - 3)(x - 5)$

Answer

C) $(x + 1)(x + 15)$

Answer

D) $(x - 1)(x - 15)$

Question 12

Evaluate $105 imes 95$ using a suitable algebraic identity.

Accepted Answer

A) 9975

Answer

B) 9925

Answer

C) 9950

Answer

D) 9900

Question 13

Expand $(2x + 3y)^2$ using the algebraic identity $(a + b)^2 = a^2 + 2ab + b^2$.

Accepted Answer

C) $4x^2 + 12xy + 9y^2$

Answer

A) $4x^2 + 9y^2$

Answer

B) $4x^2 + 6xy + 9y^2$

Answer

D) $2x^2 + 12xy + 3y^2$

Question 14

If $x + y = 7$ and $xy = 10$, find the value of $x^2 + y^2$.

Accepted Answer

A) 29

Answer

B) 39

Answer

C) 49

Answer

D) 19

Question 15

What is the coefficient of xy in the algebraic expansion of $(x + y + 2z)^2$?

Accepted Answer

B) 2

Answer

A) 1

Answer

C) 4

Answer

D) 0

Question 16

Factorize $9x^2 - 16y^2$.

Accepted Answer

B) $(3x + 4y)(3x - 4y)$

Answer

A) $(3x - 4y)^2$

Answer

C) $(9x - 16y)(9x + 16y)$

Answer

D) $(3x + 4y)^2$

Question 17

Evaluate $102^3$ using the identity $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$.

Accepted Answer

A) 1,061,208

Answer

B) 1,060,808

Answer

C) 1,061,216

Answer

D) 1,040,408

Question 18

Which of the following values is the zero of $p(x) = 5x + 3$?

Accepted Answer

B) $-\frac{3}{5}$

Answer

A) $\frac{3}{5}$

Answer

C) $\frac{5}{3}$

Answer

D) $-\frac{5}{3}$

Question 19

Find the value of $a$ if $(x + 2)$ is a factor of $x^3 + 3x^2 + 3x + a$.

Accepted Answer

B) 2

Answer

A) 1

Answer

C) -2

Answer

D) -1

Question 20

Evaluate $99^2 - 1^2$ using the identity $a^2 - b^2 = (a - b)(a + b)$.

Accepted Answer

A) 9800

Answer

B) 9900

Answer

C) 9700

Answer

D) 10000

Grade 9 : Mathematics - 2. Polynomials (Set 1)