Polynomial Operations

Monomial X Polynomial

100

6(7x-3)

Expand

42x-18

200

-4(4x+9)

Expand

-16x-36

300

3(x+5)-7

Expand and Simplify

3x+8

400

5(8x-3y)+ 2(4y+x)

Expand and Simplify

42x-7y

500

a(b-c)+b(c-a)+c(a-b)

Expand and Simplify

0

Multiplying Binomials

100

(x+6)(x-2)

Expand and Simplify

x²+4x-12

200

(a+7)(3a-5)

Expand and Simplify

3a²+16a-35

300

(6-5b)(6-5b)

Expand and Simplify

36-60b+25b²

400

(a-7)²

Expand and Simplify

a²-14a+49

500

(x²+7y²)(2x²-5y²)

Expand and Simplify

2x⁴+9x²y²-35y⁴

Multiplying Polynomials

100

(x-9)(x+9)

Expand and simplify

x²-81

200

(x-8)²

x²-16x+64

300

(3x-1)(x-3)-2x(x-1)

Expand and Simplify

x²-8x+3

400

5(2x-3)(2x+5) + 3(x+7)(x+2)

Expand and Simplify

23x²+47x-33

500

3(1+3y)(4-y) - (3y-2)(3y-5)

Expand and Simplify

-18y²+54y+2

Problem Solving

100

A square metal plate of side 25 cm is heated so that each side increases in length by x cm

Simplify the expression for the area of the heated plate

625+50x+x² cm²

200

A rectangular prism has length (5x-2) cm, width 

(3x-1) cm and height (3x+1) cm.

Write and simplify an expression for the volume of the rectangular prism

45x³-18x²-5x+2 cm³

300

Dice for a Children's board game are cubes with an edge length of (3x-2) mm. 

The manufacturer packages dice in cubic containers containing 64 dice

Determine the volume of the container in cm³ if x=4.

64cm³

400

The volume of the rectangular prism can be written as the polynomial expression ax³+bx²+cx where a,b and c are integers.

The value of a+c, to the nearest whole number is

A. 191

B. 195

C. 4

D. 247

A

500

A box is in the shape of a rectangular prism. The length of the box is y cm. The width is 2 cm less than the length, and the height is 2 cm more than the length. If the volume of the box can be written in the form V= ay³+by²+cy+d where a,b,c and d are integers, then how many of the parameters a,b,c and d are equal to zero

A.0

B.1

C.2

D.3

C

Miscellaneous

100

2x²+6x+x⁴

What is the degree of this Polynomial

4

200

Which of the following expansions is correct?

A. -2x²(3x³+5) = -6x⁶- 10x²
B. -7x(2-3x) = -14x -21x²
C. -5x³(4+x) = -20x³-5x³
D. -9x²(1-x) = -9x²+ 9x³

D

300

When (x+y)(x-y) is expanded, how many terms are in the simplified product

A.1

B.2

C.3

D.4

B

400

Triangle PQR is isosceles and right angled at Q. Side PQ measures 2x+8 cm. If the area of the triangle can be expressed in the form ax²+bx+ c cm², then the value of b is

A. 32
B. 16
C. 8
D. 6

B

500

The expression 6x(4-3x) -5x(x-4) - (9x+2) can be written in the form ax²+bx+c. The value of abc is

A.1

B. 1450

C.1610

D.2048

C