College

Subtract the polynomials and simplify:

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

and

[tex]\[ 8x^5 - 7x^3 + 7x^6 - 4x \][/tex].

Options:

A. [tex]\( -2x^5 + 3x^3 - 8x^6 + x \)[/tex]

B. [tex]\(\square\)[/tex] I don't know

Answer :

Let's subtract the polynomials step by step. We'll start with the given polynomials:

1. First polynomial: [tex]\(-6x^5 - 4x^3 - x^6 - 3x\)[/tex]
2. Second polynomial: [tex]\(8x^5 - 7x^3 + 7x^6 - 4x\)[/tex]

To subtract the second polynomial from the first, we need to subtract each corresponding term:

- Subtract the [tex]\(x^6\)[/tex] terms:

[tex]\(-x^6 - 7x^6 = -1x^6 - 7x^6 = -8x^6\)[/tex]

- Subtract the [tex]\(x^5\)[/tex] terms:

[tex]\(-6x^5 - 8x^5 = -6x^5 - 8x^5 = -14x^5\)[/tex]

- Subtract the [tex]\(x^3\)[/tex] terms:

[tex]\(-4x^3 + 7x^3 = -4x^3 + 7x^3 = 3x^3\)[/tex]

- Subtract the [tex]\(x\)[/tex] terms:

[tex]\(-3x + 4x = -3x + 4x = 1x\)[/tex]

Now, combine all of these results to get the simplified polynomial:

[tex]\[
-8x^6 - 14x^5 + 3x^3 + x
\][/tex]

So, the resulting polynomial after subtraction and simplification is:

[tex]\[
-8x^6 - 14x^5 + 3x^3 + x
\][/tex]

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