Polynomial Division & Factor & Remainder Theorems (2)

Write f(x) in factored form if

f(x) / (x+2) = (x³ -3x² -4x +12) ÷ (x + 2)?

• (x-2) (x+2) (x+3)

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.SSE.B.3

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

• ±1, ±5, ±1/2, ±5/2
• ±1, ±2, ±5, ±1/2, ±5/2
• ±1, ±5
• ±1, ±2, ±5, ±1/2, ±5/2, ±2/5

Tags

CCSS.HSA.APR.B.2

            Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.
• No, (x-2) is  not a factor. The remainder is zero.
• Yes, (x-2) is a factor. The remainder is zero.
• No, (x-2) is  not a factor. There is a remainder. 

Tags

CCSS.HSA.APR.B.2

When a polynomial function f(x) is divided by

(x + 2), the remainder is 0.

What is f(-2)?

• -2

• 0

• 2

• cannot be determined

When setting up this synthetic division, what polynomial is being divided?

• 2x⁴ + 3x² - x + 2
• 2x⁴ + 3x³ - x² + 2
• 2x⁴ - 3x² + x - 2
• cannot be determined

Tags

CCSS.HSA.APR.D.6

A polynomial  factors as 
 f(x) =  x³(x + 1)²(x - 4). List the zeros of f(x) and their multiplicity.

• 0 multiplicity 3, 1 multiplicity 2, -4 multiplicity 1
• 0 multiplicity 3, -1 multiplicity 2, 4 multiplicity 1
•  1 multiplicity 2, -4 multiplicity 1
•  -1 multiplicity 2, 4 multiplicity 1

Tags

CCSS.HSF-IF.C.7C

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

• -4, -1, 3
• 3, -3, 4, 1
• 4, 1, -3
• 3, -4, -1, 3

Tags

CCSS.HSF-IF.C.7C

Solve by using Rational Root Theorem: 
2x³ - 11x² + 12x + 9 = 0

• -1, 1, 3
• -1, 3/2, 3 
• -1/2, 3, 3
• -1/2, 1, 3

Tags

CCSS.HSA.APR.B.2

The point (3 6) is on the graph of the polynomial f(x). What does this mean?

• this means 3 is a solution to the polynomial

• this means when divided by x - 3 it has a remainder of 6

• this means 6 is a solution to the polynomial

• this means when divided by x - 6 it has a remainder of 3

What is the remainder of  $\frac{f\left(x\right)}{x^2+2x+1}$  if 

 $f\left(x\right)=2x^5+3x^4-2x^2+5x-1$