Roots & Factors of Polynomials

What is the Fundamental Theorem of Algebra?

• Every polynomial has at least one real root.

• Every non-constant polynomial has at least one complex root.

• All polynomials can be factored into linear factors over the reals.

• The degree of a polynomial determines the number of roots it has.

What is the factored form of a polynomial?

• The factored form expresses the polynomial as a product of its linear factors.

• The factored form is the sum of the polynomial's coefficients.

• The factored form is a graphical representation of the polynomial.

• The factored form is the polynomial written in standard form.

What is the degree of a polynomial?

• The degree of a polynomial is the highest power of the variable in the polynomial expression.

• The degree of a polynomial is the number of terms in the polynomial.

• The degree of a polynomial is the sum of the coefficients of the polynomial.

• The degree of a polynomial is the lowest power of the variable in the polynomial expression.

How do you find the roots of a polynomial?

• Set the polynomial equal to zero and solve for the variable.

• Multiply the polynomial by a constant.

• Differentiate the polynomial and find critical points.

• Graph the polynomial and identify the x-intercepts.

What does it mean for a polynomial to have imaginary roots?

• Imaginary roots occur when the polynomial does not intersect the x-axis, indicating complex solutions.

• Imaginary roots are the result of a polynomial having real coefficients only.

• Imaginary roots indicate that the polynomial has at least one real solution.

• Imaginary roots occur when the polynomial intersects the x-axis at multiple points.

What is a linear factor?

• A polynomial of degree two

• A polynomial of degree one, typically in the form (x - r), where r is a root.

• A constant term in a polynomial

• A polynomial of degree three

If a polynomial has a degree of 4, what can you say about its roots?

• It can have 4 real roots, or a combination of real and imaginary roots.

• It must have exactly 4 real roots.

• It can have at most 2 real roots.

• It cannot have any real roots.

How many roots does a polynomial of degree n have?

• A polynomial of degree n has at most n roots.

• A polynomial of degree n has exactly n roots.

• A polynomial of degree n has no roots.

• A polynomial of degree n has at least n roots.

What is synthetic division used for in polynomials?

• A method for adding polynomials

• A simplified method for dividing polynomials and finding roots

• A technique for factoring polynomials

• A way to graph polynomial functions

What is a polynomial?

• A mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

• A type of equation that has only one variable.

• A constant value that does not change.

• A geometric shape defined by its vertices.