What Should Be Added To 3x² +4x³+7x -3 To Get 9-5x³+4x²+5??

Mar 9, 2025 by ADMIN 61 views

What Should Be Added to 3x² + 4x³ + 7x - 3 to Get 9 - 5x³ + 4x² + 5?

Introduction

In algebra, finding the difference between two polynomials is a common operation. However, the inverse operation, which is finding the value that needs to be added to a polynomial to get another polynomial, is also an essential concept. This article will guide you through the process of finding the value that needs to be added to the polynomial 3x² + 4x³ + 7x - 3 to get 9 - 5x³ + 4x² + 5.

Understanding the Problem

To solve this problem, we need to understand that we are looking for a value, let's call it 'p(x)', that when added to the polynomial 3x² + 4x³ + 7x - 3, will result in the polynomial 9 - 5x³ + 4x² + 5. In other words, we need to find the value of 'p(x)' such that:

(3x² + 4x³ + 7x - 3) + p(x) = 9 - 5x³ + 4x² + 5

Breaking Down the Problem

To solve this problem, we can start by simplifying the equation by combining like terms. We can then isolate the term 'p(x)' by subtracting the polynomial 3x² + 4x³ + 7x - 3 from both sides of the equation.

Step 1: Simplify the Equation

First, let's simplify the equation by combining like terms. We can start by combining the terms with the same power of x.

(3x² + 4x³ + 7x - 3) + p(x) = 9 - 5x³ + 4x² + 5

Combine like terms:

(3x² + 4x³ + 7x - 3) + p(x) = (9 - 5x³ + 4x² + 5)

Step 2: Isolate the Term 'p(x)'

Now, let's isolate the term 'p(x)' by subtracting the polynomial 3x² + 4x³ + 7x - 3 from both sides of the equation.

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3)

Step 3: Simplify the Equation

Now, let's simplify the equation by combining like terms.

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3)

Combine like terms:

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3)

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3

Introduction

Understanding the Problem

(3x² + 4x³ + 7x - 3) + p(x) = 9 - 5x³ + 4x² + 5

Breaking Down the Problem

Step 1: Simplify the Equation

First, let's simplify the equation by combining like terms. We can start by combining the terms with the same power of x.

(3x² + 4x³ + 7x - 3) + p(x) = 9 - 5x³ + 4x² + 5

Combine like terms:

(3x² + 4x³ + 7x - 3) + p(x) = (9 - 5x³ + 4x² + 5)

Step 2: Isolate the Term 'p(x)'

Now, let's isolate the term 'p(x)' by subtracting the polynomial 3x² + 4x³ + 7x - 3 from both sides of the equation.

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3)

Step 3: Simplify the Equation

Now, let's simplify the equation by combining like terms.

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3)

Combine like terms:

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3)

p(x) = (9 - 5x³ + 4x² + 5) - (3x² + 4x³ + 7x - 3