Precalculus Roots of Polynomial - 01/10/24

Multiple Choice

Solve by using Rational Root Theorem: 
x³ + 3x² - 6x - 8 = 0

•  -4, -1, 2
• -4, -1, ±√2
• 1, 2, 4
• 4,-1,√2

Multiple Choice

Find all zeros.

• x= 3,1,1/3
• x= -3, -1, -1/3
• x = -3, 1, 1/3
• x = 3, -1, -1/3

Multiple Choice

Find the zeros of the polynomial given one factor.

• X= 3,4,5
• x=-3,-4,-5
• x=-3,4,5
• x= 3, -4, -5

Multiple Choice

Write a polynomial function of least degree with the given zeros.

• A
• B
• C
• D

Multiple Choice

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

Multiple Choice

List all the possible rational zeros 
h(x) = x³ - 5x²+2x+12

• 1,2,3,4,6,12
• 1,2,6,12
• 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

Multiple Choice

According to the Rational Root Theorem, what are the all possible rational roots? 
2x³ - 11x² + 12x + 9 = 0

• ±1,±2
• ±1,±3,±9
• ±1,±3±9,±1/2,±3/2,±9/2
• ±1,±2,±1/3,±2/3,±1/9,±2/9

Multiple Choice

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8
• ±1, ±2, ±4, ±8
• ±1, ±2, ±4
• 1, 2, 4, 8

Multiple Choice

Which of these is a possible rational root of the polynomials?

x³ - 6x² - x + 30

• 0

• 4

• -9

• -15

Multiple Choice

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

• x = 5, (2/3), 6, (7/4)
• x= -5, (3/2), (-4/7), 6
• x= 5, (-3/2), (4/7), -6
• x= 6, 5, -2/3, -4/7

Multiple Choice

Let f(x) = 4x² -33x -27.  Is k = 9 a zero of the function?

• yes
• no

Multiple Select

How could you determine    if x-2 is a factor of 2x³-5x²+x-2?

• Use synthetic division and see if the quotient is even
• Ask the person sitting next to me
• Use synthetic division and see if the remainder is zero
• Flip a coin
• Evaluate the polynomial using root from the factor if it is zero

Multiple Choice

If a zero of a polynomial function has multiplicity 4 that means:

• The x intercept is at (4, 0)
• The graph will "bounce back" at that zero
• The graph will "pass through" at that zero
• Zeros cannot have multiplicity of 4

Fill in the Blank

$$x^5+3x^2-4x+120$$   how many total possible  solutions?

Multiple Choice

Find all zeros.

• x= 3,1,1/3
• x= -3, -1, -1/3
• x = -3, 1, 1/3
• x = 3, -1, -1/3