Factors of Polynomials

Solving Word Problems Involving Factors of Polynomials

Multiple Choice

Which of the following is the title/name of this pattern

ax²+ax+a?

• Quadratic Trinomial

• Difference of Two Squares

• Common Factor

• Perfect Square Trinomial

• Sum and Difference of Two Cubes

Multiple Choice

Which of the following is the title/name of this pattern

x²+2xy+y²?

• Quadratic Trinomial

• Difference of Two Squares

• Common Factor

• Perfect Square Trinomial

• Sum and Difference of Two Cubes

Multiple Choice

Which of the following is the title/name of this pattern

x²-y²?

• Quadratic Trinomial

• Difference of Two Squares

• Common Factor

• Perfect Square Trinomial

• Sum and Difference of Two Cubes

Multiple Choice

Which of the following is the title/name of this pattern

x³-y³?

• Quadratic Trinomial

• Difference of Two Squares

• Common Factor

• Perfect Square Trinomial

• Sum and Difference of Two Cubes

Multiple Choice

Which of the following is the title/name of this pattern

ax²+bx+c?

• Quadratic Trinomial

• Difference of Two Squares

• Common Factor

• Perfect Square Trinomial

• Sum and Difference of Two Cubes

Choose the appropriate answer with the given mathematical statements below:

e.g. expression -> 2x+3

equation -> 2x+3=6

Multiple Choice

Choose the appropriate answer with the given mathematical statements below:

12x³-3x

• Equation & Factored Form

• Equation & Not Factored Form

• Expression & Factored Form

• Expression & Not Factored Form

Multiple Choice

Choose the appropriate answer with the given mathematical statements below:

7(x-3)

• Equation & Factored Form

• Equation & Not Factored Form

• Expression & Factored Form

• Expression & Not Factored Form

Multiple Choice

Choose the appropriate answer with the given mathematical statements below:

-6x²=-24

• Equation & Factored Form

• Equation & Not Factored Form

• Expression & Factored Form

• Expression & Not Factored Form

Multiple Choice

Choose the appropriate answer with the given mathematical statements below:

x(2x+1)=10

• Equation & Factored Form

• Equation & Not Factored Form

• Expression & Factored Form

• Expression & Not Factored Form

Multiple Choice

Choose the appropriate answer with the given mathematical statements below:

3x+12

• Equation & Factored Form

• Equation & Not Factored Form

• Expression & Factored Form

• Expression & Not Factored Form

Factor completely.

Multiple Choice

Factor Completely.

x²-3x-10

• (x-2)(x+5)

• (x+2)(x+5)

• (x-2)(x-5)

• (x+2)(x-5)

Multiple Choice

Factor Completely.

x²+3x-10

• (x-2)(x+5)

• (x+2)(x+5)

• (x-2)(x-5)

• (x+2)(x-5)

Multiple Choice

Factor Completely.

x²+7x+10

• (x-2)(x+5)

• (x+2)(x+5)

• (x-2)(x-5)

• (x+2)(x-5)

Multiple Choice

Factor Completely.

x²-7x+10

• (x-2)(x+5)

• (x+2)(x+5)

• (x-2)(x-5)

• (x+2)(x-5)

Multiple Choice

Factor Completely.

8x³+125

• (2x-5)(2x-5)

• (2x+5)(2x-5)

• (2x-5)(4x²+10x+25)

• (2x+5)(4x^2-10x+25)

Multiple Choice

Factor Completely.

4x²-20x+25

• (2x-5)(2x-5)

• (2x+5)(2x-5)

• (2x-5)(4x²+10x+25)

• (2x+5)(4x^2-10x+25)

Multiple Choice

Factor Completely.

8x³-125

• (2x-5)(2x-5)

• (2x+5)(2x-5)

• (2x-5)(4x²+10x+25)

• (2x+5)(4x^2-10x+25)

Multiple Choice

Factor Completely.

4x²-25

• (2x-5)(2x-5)

• (2x+5)(2x-5)

• (2x-5)(4x²+10x+25)

• (2x+5)(4x^2-10x+25)

Translate the following into a mathematical expression or equation

Fill in the Blanks

Translate the following into a mathematical expression or equation.

The cube of a number equals nine times the number.

Fill in the Blanks

Translate the following into a mathematical expression or equation.

Forty-nine less square of a number.

Fill in the Blanks

Translate the following into a mathematical expression or equation. (note: Let x be the side of a square)

The area of a square is numerically equal to five times its perimeter.

Fill in the Blanks

Translate the following into a mathematical expression or equation.

Ten times the square of a number equals forty.

Fill in the Blanks

Translate the following into a mathematical expression or equation.

Twice the square of a number is 32.

Fill in the Blanks

Translate the following into a mathematical expression or equation.

Twice a number increased by 8 is 14.

Fill in the Blanks

Translate the following into a mathematical expression or equation.

Twenty-five decreased by twice a number is twelve.

Fill in the Blanks

Translate the following into a mathematical expression or equation.

The square of the difference between a number and nine is 25.

Multiple Choice

Translate the following into a mathematical expression or equation.

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.

Let x be Marina’s age

Let _____ be Paul’s age

• (x-7)

• (x+7)

• 7x

• -7x

Multiple Choice

Translate the following into a mathematical expression or equation.

Ben is 4 years older than Mandy.

The sum of their ages is 30.

Let x be Mandy’s age

Let _____ be Ben’s age

• (x-4)

• (x+4)

• 4x

• -4x

Multiple Choice

Choose the appropriate answers(equation and expression) for the given problem.

• Jose (x+6)=24, Equation: x+(x+6)=24

• Jose (x-6)=24, Equation: x+(x-6)=24

• Jose (x+24)=6, Equation: x+(x+24)=6

• Jose (x-24)=6, Equation: x+(x-24)=6

Multiple Choice

Choose the appropriate answers(equation and expression) for the given problem.

• Romina (x-4), Arriane's age 5yrs ago (x+5), Romina's age 5yrs ago (x-4+5 or x+1), Equation: (x+1)=2(x+5)

• Romina (x-4), Arriane's age 5yrs ago (x-5), Romina's age 5yrs ago (x-4-5 or x-9), Equation: (x-9)=2(x-5)

• Romina (x+4), Arriane's age 5yrs ago (x+5), Romina's age 5yrs ago (x+4+5 or x+9), Equation: (x+9)=2(x+5)

• Romina (x+4), Arriane's age 5yrs ago (x-5), Romina's age 5yrs ago (x+4-5 or x-1), Equation: (x-1)=2(x-5)

Multiple Choice

Solve.

Twice the square of a number is 32. What is the number?

• -2 & 2

• -4 & 4

• -8 & 8

• -16 & 16

Multiple Choice

Solve.

The product of two consecutive even integers is 48. Find the numbers.

• -8 & 6

• -8 & -6

• 8 & -6

• 8 & 6

Multiple Choice

Solve.

Aby is 6 years older than Jonas. Six years ago, she was twice as old as he. How old is each now?

• Jona's age is 6 and Aby's age is 12

• Jona's age is 8 and Aby's age is 14

• Jona's age is 10 and Aby's age is 16

• Jona's age is 12 and Aby's age is 18

Multiple Choice

Solve.

A rectangular lawn is 2 meters longer than its width. The area of the lawn is 24 square meters. Find the length and width of the lawn.

• W = 3m and L = 5m

• W = 4m and L = 6m

• W = 5m and L = 7m

• W = 6m and L = 8m

Multiple Choice

Solve.

John’s father is twice as old as John. In 20 years, John will be two-thirds as old as his father. How old is each now?

• John's age is 40 and Father's age is 60

• John's age is 30 and Father's age is 50

• John's age is 20 and Father's age is 40

• John's age is 10 and Father's age is 30