Math Problem Statement

resuelve

Realizar las operaciones indicadas para los polinomios P(x), Q(x), y R(x).

Solution

To help solve the given problem, let's break down each part. You have three polynomial functions defined as:

  1. P(x)=6x5+4x43x+6P(x) = 6x^5 + 4x^4 - 3x + 6
  2. Q(x)=7x4+3x22x2+7Q(x) = 7x^4 + 3x^2 - 2x^2 + 7
  3. R(x)=9x55x4+6x32x2+8R(x) = 9x^5 - 5x^4 + 6x^3 - 2x^2 + 8

The instructions are to perform operations involving these functions, as shown:

  1. P(x)+Q(x)P(x) + Q(x)
  2. Q(x)+R(x)Q(x) + R(x)
  3. P(x)+R(x)P(x) + R(x)
  4. P(x)+Q(x)R(x)P(x) + Q(x) - R(x)
  5. P(x)Q(x)+R(x)P(x) - Q(x) + R(x)
  6. Q(x)R(x)Q(x) - R(x)

I’ll go through each operation step-by-step.

1. P(x)+Q(x)P(x) + Q(x)

Combine like terms: P(x)+Q(x)=(6x5)+(7x4+4x4)+(3x22x2)3x+6+7P(x) + Q(x) = (6x^5) + (7x^4 + 4x^4) + (3x^2 - 2x^2) - 3x + 6 + 7 =6x5+11x4+x23x+13= 6x^5 + 11x^4 + x^2 - 3x + 13

2. Q(x)+R(x)Q(x) + R(x)

Combine like terms: Q(x)+R(x)=(9x5)+(7x45x4)+(6x3)+(3x22x2)+7+8Q(x) + R(x) = (9x^5) + (7x^4 - 5x^4) + (6x^3) + (3x^2 - 2x^2) + 7 + 8 =9x5+2x4+6x3+x2+15= 9x^5 + 2x^4 + 6x^3 + x^2 + 15

3. P(x)+R(x)P(x) + R(x)

Combine like terms: P(x)+R(x)=(6x5+9x5)+(4x45x4)+6x32x23x+6+8P(x) + R(x) = (6x^5 + 9x^5) + (4x^4 - 5x^4) + 6x^3 - 2x^2 - 3x + 6 + 8 =15x5x4+6x32x23x+14= 15x^5 - x^4 + 6x^3 - 2x^2 - 3x + 14

4. P(x)+Q(x)R(x)P(x) + Q(x) - R(x)

Combine terms from each function and subtract R(x)R(x): [ P(x) + Q(x) - R(x) = (6x^5 - 9x^5) + (4x^4 + 7x^4 + 5x^4) + 6x^3 + 3x^2 + 7 - 8

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Math Problem Analysis

Mathematical Concepts

Polynomial Operations
Addition and Subtraction of Polynomials

Formulas

Addition and subtraction of polynomials by combining like terms

Theorems

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Suitable Grade Level

Grades 10-12