Solving and Writing Polynomial Equations

True or False

When a polynomial equation has the following factors, (x+3)(x+3)(x-2), we say that x = -3 has a multiplicity of 3.

• True

• False

When a polynomial has a repeated root, if the root is repeated an odd amount of times (ex. 1,3,5,...) then the graph

Solve the following equation. x⁴ + 4x³ + 3x² = 0

• x = 0, x = 3, x = 1

• x = -3, x = -1

• x = 3, x = 1

• x = 0, x = -3, x = -1

Solve the polynomial equation and determine which graphis correct.

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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

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

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

Solve by using Rational Root Theorem: 
x³ - 7x - 6 = 0

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

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

1, -6, 4

• x³+x²-26x+24

• x³+9x²-14x+24

• x³-x²+14x+24

• x³-x²+26x+24

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

1, 2 − √—3

• x³-3x²-3x -1

• x³+3x²+3x -1

• x³-5x²+5x -1

• x³+5x²-5x -1