Here are the essential concepts you must grasp in order to answer the question correctly.
Synthetic Division
Synthetic division is a simplified method for dividing a polynomial by a linear binomial of the form (x - k). It involves using the coefficients of the polynomial and performing a series of multiplications and additions to find the quotient and remainder. This technique is particularly useful for evaluating polynomials at specific values and determining if those values are roots of the polynomial.
Recommended video:
Polynomial Function
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form of a polynomial in one variable x is f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n are constants and n is a non-negative integer. Understanding the structure of polynomial functions is essential for analyzing their behavior, including finding zeros and evaluating function values.
Recommended video:
Introduction to Polynomial Functions
Zero of a Polynomial
A zero of a polynomial is a value of x for which the polynomial evaluates to zero, meaning f(k) = 0. Finding zeros is crucial for understanding the roots of the polynomial, which can indicate where the graph intersects the x-axis. If a given number k is not a zero, evaluating the polynomial at k provides the corresponding function value, which helps in analyzing the polynomial's behavior at that point.
Recommended video:
Finding Zeros & Their Multiplicity