Polynomials and Factoring

Factor 10m²n + 20m² - 2mn - 4m completely.

• 2(5m²n + 10m² - mn - 2m)
• 2m(5mn + 10m - n - 2)
• 2m(5m - 1)(n + 2)
• (5m - 1)(n + 2)

Subtract (16k² - 8k + 11) - (24k² + k - 10). Write the answer in STANDARD FORM.

• -8k² - 9k + 21
• -8k² - 7k + 1
• 40k² -17k + 21
• 40k² - 17k  + 1

Multiply (8x - 6y)². Write the answer in STANDARD FORM.

• 64x² + 36y²
• 64x² - 36y²
• 64x² - 96xy + 36y²
• 64x²  + 36y² - 96xy

The length of a rectangle is (7x - 3). The width of the rectangle is (5x - 2). Write a simplified algebraic expression for the AREA of the rectangle.

• 35x² - 29x + 6
• 35x² + 6
• 35x² - 15x - 14x + 6
• 35x² - 29x - 5

The length of a rectangle is (7x - 3). The width of the rectangle is (5x - 2). Write a simplified algebraic expression for the perimeter of the rectangle.

• 12x - 5
• 24x + 10
• 24x - 10
• 24x - 5

Factor 3x⁵ - 27x³ completely.

• 3x³(x² - 9)
• 3(x² - 3)(x² + 3)
• 3x³(x - 3)(x + 3)
• (x - 3)(x + 3)

Factor 121p² - 64r².

• (11p + 8r)(11p - 8r)
• (11p - 8r)(11p - 8r)
• (11p+ 8r)(11p + 8r)
• (11r + 8p)(11r - 8p)

Solve 7x² - 20x = 3.

• {-1/7, 3}
• {1/7, -3}
• {-1/7, -3}
• {1/7, 3}

Solve y² = 13y - 42. 

• {-6, -7}
• {6, 7}
• {-6, 7}
• {6, -7}

Find one of the factors of x² - 5x - 24.

• (x - 8)
• (x - 3)
• (x + 4)
• (x - 6)