MAT 171 UNit 4 Review 1

Front

Solve the equation over the real numbers: 3x^3 - 4x^2 - 3x + 4 = 0

Back

x = -1

Front

What are the solutions to the equation: x^4 - 10x^2 + 25 = 0

Back

x = 5, x = -5

Front

What is one of the solutions to the equation: x^3 + 4x^2 - 4x - 16 = 0?

Back

x = -4

Front

Solve the equation: x^3 - x^2 - 16x + 16 = 0

Back

x = 1, x = 4, x = -4

Front

Solve the equation: 2x^3 - 3x^2 - 8x + 12 = 0

Back

x = 1, x = 2, x = -3

Front

What is the Rational Root Theorem?

Back

A theorem that provides a way to find possible rational roots of a polynomial equation.

Front

Define a polynomial function.

Back

A function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What is synthetic division?

Back

A simplified method of dividing a polynomial by a linear binomial.

Front

Explain the concept of multiplicity in roots.

Back

Multiplicity refers to the number of times a particular root is repeated in a polynomial equation.

Front

What is the difference between real and complex roots?

Back

Real roots are solutions that are real numbers, while complex roots include imaginary numbers.