Math Problem Statement

Given two polynomials A(x) = 3x^3 + 4x^2 - 5x + 2 and B(x) = x^4 - 3x^3 - 6x^2 + x, solve the following: 1. Compute A(-1) and A(3). 2. Find A(x) - B(x). 3. Determine the value of x such that A(x) = B(x).

Solution

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Please hold on for a moment.The image contains mathematical problems with two main sections. Here’s a breakdown of the key points in the questions:

Problem 1 (Bài 3):

It asks you to:

  1. a) Find the expressions for A(x)A(x) and B(x)B(x) and simplify the sum of two functions F(x)+G(x)F(x) + G(x).
  2. b) Compute the value A(1)A(-1).
  3. c) Find the value of A(3)A(3).
  4. Solve the equation A(x)=B(x)A(x) = B(x).

The functions provided are:

  • A(x)=3x3+4x25x+2A(x) = 3x^3 + 4x^2 - 5x + 2
  • B(x)=x43x36x2+xB(x) = x^4 - 3x^3 - 6x^2 + x

Problem 2 (Bài 2):

It involves simplifying or combining two functions (likely involving polynomials).

Let me guide you through these steps:

  1. Simplifying A(x)+B(x)A(x) + B(x): You simply add the two expressions together.
  2. Finding A(1)A(-1): You substitute x=1x = -1 into A(x)A(x) and compute the result.
  3. Finding A(3)A(3): Substitute x=3x = 3 into A(x)A(x).
  4. Solving A(x)=B(x)A(x) = B(x): Set the expressions for A(x)A(x) and B(x)B(x) equal to each other and solve for xx.

I will now work through these calculations.

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Algebraic Manipulation
Equation Solving

Formulas

Polynomial addition/subtraction: (P(x) ± Q(x)) = sum/difference of corresponding terms.
Substitution: f(a) = replace x with a in f(x).
Equation solving: Find x where f(x) = g(x).

Theorems

Basic Polynomial Arithmetic
Fundamental Theorem of Algebra

Suitable Grade Level

Grades 9-12