HA2 Unit 6 Test Review

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for the variable. This can involve factoring, using the quadratic formula, or synthetic division.

Tags

CCSS.HSF-IF.C.7C

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c). It is quicker and requires less writing.

Tags

CCSS.HSA.APR.D.6

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c). This helps in finding zeros of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0. This is used to find factors and zeros of polynomials.

Tags

CCSS.HSA.APR.B.2

Front

How do you evaluate a polynomial function at a given point?

Back

To evaluate a polynomial function f(x) at a point x = a, substitute a into the polynomial and simplify to find f(a).

Tags

CCSS.HSF.IF.A.2

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's behavior and the number of possible zeros.

Front

What are complex zeros?

Back

Complex zeros are solutions to polynomial equations that include imaginary numbers. They occur in conjugate pairs when the coefficients of the polynomial are real.

Tags

CCSS.HSN.CN.C.9

Front

What is the significance of the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root. This implies that a polynomial of degree n has exactly n roots, counting multiplicities.

Tags

CCSS.HSN.CN.C.9

Front

How do you find a polynomial given its zeros?

Back

To find a polynomial given its zeros, use the fact that if r1, r2, ..., rn are the zeros, the polynomial can be expressed as P(x) = k(x - r1)(x - r2)...(x - rn), where k is a constant.

Tags

CCSS.HSF-IF.C.7C