Math Problem Statement

What is the sum of the given polynomials in standard form?

(x2 – 3x) + (–2x2 + 5x – 3)

–3x2 + 8x – 3

x2 – 2x – 3 

3x2 – 8x + 3 

x2 + 2x – 3

Solution

To find the sum of the given polynomials, let's first rewrite each polynomial clearly and then add them together term by term.

Given polynomials:

  1. x23xx^2 - 3x
  2. 2x2+5x3-2x^2 + 5x - 3
  3. 3x2+8x3-3x^2 + 8x - 3
  4. x22x3-x^2 - 2x - 3
  5. 3x28x+33x^2 - 8x + 3
  6. x2+2x3-x^2 + 2x - 3

We will now add the corresponding coefficients of each term together.

Combining Like Terms

x2x^2 terms: 1x2+(2x2)+(3x2)+(x2)+3x2+(x2)=1231+31=3x21x^2 + (-2x^2) + (-3x^2) + (-x^2) + 3x^2 + (-x^2) = 1 - 2 - 3 - 1 + 3 - 1 = -3x^2

xx terms: 3x+5x+8x2x8x+2x=3+5+828+2=2x-3x + 5x + 8x - 2x - 8x + 2x = -3 + 5 + 8 - 2 - 8 + 2 = 2x

Constant terms: 0+(3)+(3)+(3)+3+(3)=333+33=90 + (-3) + (-3) + (-3) + 3 + (-3) = -3 - 3 - 3 + 3 - 3 = -9

Summing Up

The sum of the given polynomials in standard form is: 3x2+2x9-3x^2 + 2x - 9

Would you like any more details or have any questions about this solution?

Here are 5 numbered questions you can ask:

  1. How do you simplify the sum of polynomials step-by-step?
  2. Can you explain the process of combining like terms in polynomials?
  3. What are the key differences between polynomials and other algebraic expressions?
  4. How do you factor the resulting polynomial from this sum?
  5. What are the applications of polynomial addition in real-life scenarios?

Tip: When adding or subtracting polynomials, always align like terms (terms with the same power of xx) to simplify the process.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Polynomials
Combining Like Terms
Standard Form

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9