High School

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Perform the operation:

[tex]\left(3x^3 - 7x^2 + 5x - 2\right) + \left(2x^2 - 9x + 8\right)[/tex]

A. [tex]3x^3 - 9x^2 + 14x - 10[/tex]
B. [tex]3x^3 - 5x^2 - 4x + 6[/tex]
C. [tex]5x^5 - 16x^3 + 13x - 2[/tex]
D. [tex]-14x^4 + 3x^3 - 45x^2 - 16[/tex]

Answer :

Sure! Let's work through the addition of these two polynomials step-by-step:

We have two polynomials that we are adding together:

1. [tex]\(3x^3 - 7x^2 + 5x - 2\)[/tex]
2. [tex]\(2x^2 - 9x + 8\)[/tex]

Here's how we add them:

Step 1: Align the polynomials by their terms:

- [tex]\(3x^3 - 7x^2 + 5x - 2\)[/tex]
- [tex]\(0x^3 + 2x^2 - 9x + 8\)[/tex]

Step 2: Add the coefficients of the like terms:

- For [tex]\(x^3\)[/tex] terms: [tex]\(3 + 0 = 3\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(-7 + 2 = -5\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(5 - 9 = -4\)[/tex]
- For the constant terms: [tex]\(-2 + 8 = 6\)[/tex]

Step 3: Write down the resulting polynomial:

The result of adding these two polynomials is:

[tex]\[3x^3 - 5x^2 - 4x + 6\][/tex]

So, the answer is [tex]\[3x^3 - 5x^2 - 4x + 6\][/tex].

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