Grade 9 : Mathematics - 2. Polynomials (Set 3)

Question 1

What is the degree of the polynomial $p(x) = 4x^4 - 3x^3 + 7x^5 - 2x + 9$?

Accepted Answer

C) 5

Answer

A) 4

Answer

B) 3

Answer

D) 1

Question 2

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

Accepted Answer

C) $2y^3 - \frac{3}{5}y + \sqrt{7}$

Answer

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

Answer

B) $3\sqrt{x} + x^2 - 5$

Answer

D) $z + \frac{1}{\sqrt{z}} + 4$

Question 3

Find the zero of the polynomial $p(x) = 5x - 15$.

Accepted Answer

B) 3

Answer

A) -3

Answer

C) $\frac{1}{3}$

Answer

D) 15

Question 4

If $p(x) = 2x^3 - 3x^2 + 4x - 5$, find the value of $p(-2)$.

Accepted Answer

A) -41

Answer

B) -21

Answer

C) -13

Answer

D) 19

Question 5

Using the Remainder Theorem, find the remainder when $p(x) = x^3 - 4x^2 + 6x - 8$ is divided by $(x - 3)$.

Accepted Answer

A) 1

Answer

B) -1

Answer

C) 3

Answer

D) -3

Question 6

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

Accepted Answer

A) $\frac{3}{2}$

Answer

B) $-\frac{3}{2}$

Answer

C) 3

Answer

D) $\frac{2}{3}$

Question 7

Factorize the quadratic polynomial $6x^2 + 17x + 5$ by splitting the middle term.

Accepted Answer

B) $(2x + 5)(3x + 1)$

Answer

A) $(2x + 1)(3x + 5)$

Answer

C) $(6x + 1)(x + 5)$

Answer

D) $(2x - 1)(3x - 5)$

Question 8

Expand $(2a - 3b + 4c)^2$ using algebraic identities.

Accepted Answer

A) $4a^2 + 9b^2 + 16c^2 - 12ab - 24bc + 16ca$

Answer

B) $4a^2 - 9b^2 + 16c^2 - 12ab + 24bc - 16ca$

Answer

C) $4a^2 + 9b^2 + 16c^2 + 12ab - 24bc + 16ca$

Answer

D) $4a^2 + 9b^2 - 16c^2 - 12ab - 24bc + 16ca$

Question 9

Evaluate $104 imes 96$ using a suitable algebraic identity.

Accepted Answer

A) 9984

Answer

B) 9976

Answer

C) 9986

Answer

D) 10016

Question 10

If $x + \frac{1}{x} = 5$, find the value of $x^2 + \frac{1}{x^2}$.

Accepted Answer

B) 23

Answer

A) 25

Answer

C) 27

Answer

D) 21

Question 11

If $x + \frac{1}{x} = 4$, find the value of $x^3 + \frac{1}{x^3}$.

Accepted Answer

A) 52

Answer

B) 64

Answer

C) 48

Answer

D) 56

Question 12

If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?

Accepted Answer

C) $3abc$

Answer

A) 0

Answer

B) abc

Answer

D) $(a+b+c)^3$

Question 13

Without actually calculating the cubes, find the value of $(-12)^3 + 7^3 + 5^3$.

Accepted Answer

A) -1260

Answer

B) -420

Answer

C) 1260

Answer

D) 0

Question 14

Factorize the cubic polynomial $p(x) = x^3 - 2x^2 - x + 2$ completely into linear factors.

Accepted Answer

A) $(x - 1)(x + 1)(x - 2)$

Answer

B) $(x - 1)(x - 1)(x + 2)$

Answer

C) $(x + 1)(x + 1)(x - 2)$

Answer

D) $(x - 1)(x + 2)(x - 3)$

Question 15

A rectangular park has an area modeled by the expression $A(x) = 2x^2 + 11x + 12$ square meters.

If the width of the park is $(x + 4)$ meters, what is its length in terms of $x$?

Accepted Answer

A) $(2x + 3)$ meters

Answer

B) $(2x - 3)$ meters

Answer

C) $(x + 3)$ meters

Answer

D) $(2x + 4)$ meters

Question 16

Find the coefficient of $x^2$ in the expansion of $(3x - 4)^3$.

Accepted Answer

A) -108

Answer

B) 108

Answer

C) -36

Answer

D) -144

Question 17

Polynomial ID	Polynomial Expression $P(x)$	Recorded Value at $x = 2$
P1	$x^3 - 3x + 1$	3
P2	$2x^2 - 5x + 3$	1
P3	$x^4 - 2x^2 - 5$	3
P4	$3x^3 - 4x^2 + 2$	14

A student calculated $P(2)$ for four polynomials as shown in the table. Which Polynomial ID contains an incorrect valuation?

Accepted Answer

D) P4

Answer

A) P1

Answer

B) P2

Answer

C) P3

Question 18

If $(x + 1)$ and $(x - 1)$ are factors of $p(x) = ax^3 + x^2 - 2x + b$, find the values of $a$ and $b$.

Accepted Answer

A) $a = 2, b = -1$

Answer

B) $a = -2, b = 1$

Answer

C) $a = 2, b = 1$

Answer

D) $a = 1, b = 2$

Question 19

If $x + y + z = 9$ and $xy + yz + zx = 26$, find the value of $x^2 + y^2 + z^2$.

Accepted Answer

A) 29

Answer

B) 31

Answer

C) 55

Answer

D) 81

Question 20

What must be added to the polynomial $x^4 + 2x^3 - 2x^2 + x - 1$ so that the resulting polynomial is exactly divisible by $x^2 + 2x - 3$?

Accepted Answer

A) $x - 2$

Answer

B) $-x + 2$

Answer

C) $2x - 1$

Answer

D) $-2x + 2$

Grade 9 : Mathematics - 2. Polynomials (Set 3)