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

Question 1

A physics module models the height $h(t)$ of a launched projectile in meters after $t$ seconds using the mathematical model $h(t) = -5t^2 + 30t + 2$.

What is the degree of this polynomial model?

Accepted Answer

B) 2

Answer

A) 1

Answer

C) 3

Answer

D) 0

Question 2

An architect models the layout area $A(x)$ of a community garden in square meters using $A(x) = 2x^2 + 5x - 3$, where $x$ represents a design dimension.

Calculate the area of the garden when $x = 4$ meters.

Accepted Answer

A) $49m^2$

Answer

B) $45m^2$

Answer

C) $53m^2$

Answer

D) $37m^2$

Question 3

A production manager expresses total net profit using the linear function $C(x) = 4x - 28$, where $x$ is the number of units produced.

Find the zero of the polynomial function $C(x)$.

Accepted Answer

C) $x = 7$

Answer

A) $x = 4$

Answer

B) $x = -7$

Answer

D) $x = 14$

Question 4

An engineer reviews four algebraic expressions to determine which one qualifies as a valid polynomial model in $x$.

Which of the following expressions is a polynomial?

Accepted Answer

C) $4x^3 - 7x + 9$

Answer

A) $3x^2 + \frac{2}{x} - 5$

Answer

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

Answer

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

Question 5

A financial analysis system models total quarterly revenue with $R(x) = -3x^3 + 8x^2 - 12x + 150$.

What is the coefficient of $x^2$ in this revenue polynomial?

Accepted Answer

B) 8

Answer

A) -3

Answer

C) -12

Answer

D) 150

Question 6

A small business tracks profit using the expression $P(x) = 15x - 200$.

Based on the number of non-zero terms, what type of polynomial is $P(x)$?

Accepted Answer

B) Binomial

Answer

A) Monomial

Answer

C) Trinomial

Answer

D) Zero polynomial

Question 7

Consider the polynomial $p(x) = x^3 - 3x^2 + 4x - 5$.

Using the Remainder Theorem, find the remainder when $p(x)$ is divided by $(x - 2)$.

Accepted Answer

C) -1

Answer

A) 3

Answer

B) 1

Answer

D) -5

Question 8

A container volume is modeled by $V(x) = x^3 - 4x^2 + x + 6$.

Determine whether $(x - 3)$ is a factor of $V(x)$ using the Factor Theorem.

Accepted Answer

A) Yes, because $V(3) = 0$

Answer

B) No, because $V(3) = 6$

Answer

C) No, because $V(3) = -2$

Answer

D) Yes, because $V(3) = 12$

Question 9

Given the polynomial expression $p(x) = kx^2 - 3x + k$, where $k$ is a constant.

If $(x + 1)$ is a factor of $p(x)$, find the value of $k$.

Accepted Answer

B) -1.5

Answer

A) 1.5

Answer

C) 3

Answer

D) -3

Question 10

A carpet maker designs a square carpet with side length $(2x + 5)$ units.

Expand the area expression $(2x + 5)^2$ using a standard algebraic identity.

Accepted Answer

C) $4x^2 + 20x + 25$

Answer

A) $4x^2 + 25$

Answer

B) $4x^2 + 10x + 25$

Answer

D) $2x^2 + 20x + 25$

Question 11

A square courtyard has side measurement $(3x - 4)$ meters.

Find the expanded polynomial representing the area of the courtyard.

Accepted Answer

B) $9x^2 - 24x + 16$

Answer

A) $9x^2 - 16$

Answer

C) $9x^2 - 12x + 16$

Answer

D) $9x^2 + 24x - 16$

Question 12

A student needs to compute $103 imes 97$ quickly using algebraic identities.

What is the correct evaluated result using the identity $(a + b)(a - b) = a^2 - b^2$?

Accepted Answer

B) 9991

Answer

A) 9981

Answer

C) 10009

Answer

D) 9901

Question 13

A rectangular field has an area expressed by the polynomial $x^2 + 7x + 12$.

Factorize the quadratic polynomial to determine the linear dimensions of the field.

Accepted Answer

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

Answer

A) $(x + 2)(x + 6)$

Answer

C) $(x + 1)(x + 12)$

Answer

D) $(x - 3)(x - 4)$

Question 14

A rectangular playground has area represented by $2x^2 + 7x + 3$.

Factorize this expression to find possible expressions for its length and width.

Accepted Answer

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

Answer

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

Answer

C) $(x + 3)(x + 2)$

Answer

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

Question 15

Consider the constant zero polynomial $p(x) = 0$.

What is the degree of the zero polynomial?

Accepted Answer

D) Not defined

Answer

A) 0

Answer

B) 1

Answer

C) Any non-negative integer

Question 16

Let $p(x) = x + 5$ be a linear polynomial.

Calculate the simplified value of $p(x) + p(-x)$.

Accepted Answer

C) 10

Answer

A) $2x$

Answer

B) 0

Answer

D) $2x + 10$

Question 17

Applying the identity $(x + a)(x + b) = x^2 + (a + b)x + ab$.

Expand the algebraic expression $(x + 8)(x - 10)$.

Accepted Answer

A) $x^2 - 2x - 80$

Answer

B) $x^2 + 2x - 80$

Answer

C) $x^2 - 18x - 80$

Answer

D) $x^2 - 2x + 80$

Question 18

Expand the three-variable polynomial square $(x + 2y + 4z)^2$ using algebraic identities.

Which of the following represents the correct expanded expression?

Accepted Answer

B) $x^2 + 4y^2 + 16z^2 + 4xy + 16yz + 8zx$

Answer

A) $x^2 + 4y^2 + 16z^2 + 2xy + 8yz + 4zx$

Answer

C) $x^2 + 2y^2 + 4z^2 + 4xy + 16yz + 8zx$

Answer

D) $x^2 + 4y^2 + 16z^2 + 4xy + 8yz + 8zx$

Question 19

A cubic box side length is expressed as $(2x + 1)$.

Expand the cubic binomial $(2x + 1)^3$ using the identity $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$.

Accepted Answer

B) $8x^3 + 12x^2 + 6x + 1$

Answer

A) $8x^3 + 6x^2 + 6x + 1$

Answer

C) $6x^3 + 12x^2 + 6x + 1$

Answer

D) $8x^3 + 12x^2 + 4x + 1$

Question 20

Consider three numbers $a$, $b$, and $c$ such that $a + b + c = 0$.

Using the algebraic identity $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$, what is $a^3 + b^3 + c^3$?

Accepted Answer

C) $3abc$

Answer

A) 0

Answer

B) abc

Answer

D) $-3abc$

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