Module 5 polynomial roots

Front

Is (x-4) a factor of (x^3 + x^2 - 16x - 16)?

Back

Yes, (x-4) is a factor.

Front

What describes the leading term based on end behavior: negative coefficient, even degree?

Back

The leading term has a negative coefficient and an even degree.

Front

What are the zeros of the polynomial function y = (x + 2)(x - 7)^3?

Back

The zeros are -2 and 7 with multiplicity 3.

Front

Which binomial is a factor of f(x) = x^3 - 6x^2 + 3x + 10?

Back

The factor is x + 1.

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

The zeros are 0, 6, and -5.

Front

Define a polynomial root.

Back

A polynomial root is a value of x that makes the polynomial equal to zero.

Front

What is the relationship between factors and roots of a polynomial?

Back

Factors of a polynomial correspond to its roots; if (x - r) is a factor, then r is a root.

Front

Explain the concept of multiplicity in polynomial roots.

Back

Multiplicity refers to the number of times a root appears; a root with multiplicity 3 means it is a solution three times.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of f(x) if and only if f(c) = 0.