Math Problem Statement

Task 2. Given a polynomial: f(x) = x4 - 8x3 -8x2 +8x +7

(i)Use rational theorem and synthetic division to find the zeros of the polynomial

(ii) Draw the graph using GeoGebra graphing tool.

(iii) Identify its end behavior

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Synthetic Division
Quadratic Formula
End Behavior

Formulas

Rational Root Theorem: Possible roots = ±p/q, where p is the constant term and q is the leading coefficient
Synthetic Division Process
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a

Theorems

Rational Root Theorem
Synthetic Division
Quadratic Formula

Suitable Grade Level

Grades 10-12