Math Problem Statement

A polynomial function P and its graph are given.

P(x) = 3x3 + x2 − 7x − 5

The x y-coordinate plane is given. The curve enters the window in the third quadrant, goes up and right becoming less steep, changes direction at the point (−1, 0), goes down and right becoming more steep, passes through the approximate point (−0.1, −4.2), goes down and right becoming less steep, crosses the y-axis at y = −5, changes direction at the approximate point (0.8, −8.4), goes up and right becoming more steep, crosses the x-axis at approximately x = 1.7, and exits the window in the first quadrant. 

(a)

List all possible rational zeros of P given by the Rational Zeros Theorem. (Enter your answers as a comma-separated list.)

x =     (b)

From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)

x =    

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Graph Analysis

Formulas

P(x) = 3x^3 + x^2 − 7x − 5
Rational Zeros Theorem: Possible Rational Zeros = factors of constant term / factors of leading coefficient

Theorems

Rational Zeros Theorem

Suitable Grade Level

Grades 10-12