Factoring and Polynomial Division

Which binomials are a difference  of two squares?
I. 6a²-25
II. 4x²+16
III. b²-9
IV. 49y²-64

• I only

• III only

• III and IV

• II, III, and IV

What do you call a polynomial that cannot be factored?

• nonfactorable

• Simplified

• Prime

• Proper

Given that x - 3 is a known factor. Factor the cubic polynomial: x³ - 4x² + x + 6. (Hint: Use long division 1st)

• (2x + 1)(x + 2)(x + 4)

• (2x - 1)(x + 2)(x - 2)

• (x - 3)(x + 2)(x - 1)

• (x - 3)(x + 1)(x - 2)

Factor using the GCF 35x³ - 40x² + 15x

• 5x(7x^2 + 8x + 3)

• 5x(7x^2 - 8x - 3)

• 5x(7x^2 - 8x + 3)

• 5x(7x^2 - 8x)

Factor the quadratic polynomial: x² + 5x + 6

• (x + 2)(x + 4)

• (x + 3)(x + 4)

• (x + 2)(x + 3)

• (x + 1)(x + 6)

Factor the polynomial: 3x⁴ - 12x³ + 9x²

• 3x^2(x - 1)(x + 3)

• 3x^2(x - 1)(x - 3)

• 3x^2(x + 1)(x + 3)

• 3x^2(x + 1)(x - 3)

Factor the quadratic polynomial: 2x² - 7x + 3

Hint: Use Long Diamond

• (2x + 3)(x - 1)

• (2x + 1)(x - 3)

• (2x - 1)(x + 3)

• (2x - 1)(x - 3)

Use long division to simplify: (2x^4 - 3x^3 + 5x^2 - 4x + 1) ÷ (x + 1)

• 2x^3 - 5x^2 + 10x + 14

• 2x^3 - 5x^2 + 10x - 1

• 2x^3 - 5x^2 + 10x - 14

• 2x^3 - 5x^2 + 10x + 1

P(x) = x⁴ - 2x³ + kx - 4

P(x) dividied by x-1 has a remainder of 0. What is k?

• 5

• 4

• 3

• 2

(a - b)(a + b) (special difference of square factoring formula)

• a² + b²

• a² + 4ab + b²

• a² - 2ab + b²

• a² - b²