Ch.8 -Polynomials & Factoring

Factor out GCF

100

Factor out the GCF.

4x³ - 12x² + 2x

2x(2x² - 6x + 1)

200

Factor out the GCF

24x⁴ + 4x³y - 28x²y³

4x²(6x² + xy - 7y³)

300

Factor out the GCF.

18x⁴ + 30x³ + 12x

6x(3x³ + 5x² + 2)

400

Factor out the GCF

24x⁵y + 8x⁴y - 16x²y³

8x²y(3x³ + x² - 2y²)

500

Factor out the GCF

24x⁴y⁴ + 48x³y³ + 60x²y³

12x²y³(2x²y + 4x + 5)

Factoring trinomials when a = 1

100

What is the factored form of x² - 11x + 24?

(x - 8)(x - 3)

200

What is the factored form of x² + 16x + 64?

(x + 8)²   or   (x + 8)(x + 8)

300

What is the factored form of y² + 9y - 36?

(y + 12)(y - 3)

400

What is the factored form of x² - 225?

(x - 15)(x + 15)

500

What is the factored form of x² - 18x - 63?

(x - 21)(x + 3)

Factoring trinomials when a>1

100

What is the factored form of 6x² + 13x + 5?

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

200

What is the factored form of 10x² + 9x + 2?

(5x + 2)(2x + 1)

300

What is the factored form of 4x² - 28x + 49?

(2x - 7)²  or (2x - 7)(2x - 7)

400

What is the factored form of 8x² + 34x - 30?

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

500

What is the factored form of 9y² + 3y - 30?

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

Word Problems

100

The area of a parallelogram is x² - 14x + 24.  The base of the parallelogram is x - 2.  What is an expression for the height of the parallelogram?  (Hint: A = bh)

x - 12

200

The area of a rectangular table is y² + 7y - 8.  The table's length is y + 8.  What is the table's width?

y - 1

300

A rectangular skateboard park has an area of 

x² + 15x + 54.  

What are the possible dimensions of the park?

(x + 6) and (x + 9)

400

A rectangle has a width of x + 6 and a length of 3x - 4.

What is the area of the rectangle?

3x² + 14x - 24

500

A cereal box in the shape of a rectangular prism has a volume of 18x³ - 3x² - 6x.  What are the three possible expressions for the dimensions of the cereal box?

3x, (2x + 1), (3x - 2)