Practice: The Factor Theorem

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25
• 25
• 113
• -113

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656
• p(2) = 652
• p(2) = -64
• p(2) = -368

f(x) is a polynomial. f(2) = 0

Identify a factor of f(x)

• (x - 2)

• (x + 2)

• (2x - 1)

• (2x + 1)

f(x) is a polynomial. f(-5) = 0

Identify a factor of f(x)

• (x - 5)

• (x + 5)

• (5x - 1)

• (5x + 1)

f(x) is a polynomial. f(3) = 0

Identify a factor of f(x)

• (x - 3)

• (x + 3)

• (3x - 1)

• (3x + 1)

Using the factor theorem, determine whether (x + 3) is a factor of

2x³ + x² - 9x + 18

• (x + 3) is a factor

• (x + 3) is not a factor

Using the factor theorem, determine whether (x - 1) is a factor of

2x³ + x² - 9x + 18

• (x - 1) is a factor

• (x - 1) is not a factor

Using the factor theorem, determine whether (x - 2) is a factor of

2x³ - 3x² - 3x + 2

• (x - 2) is a factor

• (x - 2) is not a factor

f(x) is a polynomial. f(-0.5) = 0

Identify a factor of f(x)

• (x - 2)

• (x + 2)

• (2x - 1)

• (2x + 1)

f(x) is a polynomial. f(-¹/₃) = 0

Identify a factor of f(x)

• (x - 3)

• (x + 3)

• (3x - 1)

• (3x + 1)