Question

Which example correctly demonstrates polynomial subtraction? (1 point)
0(2x2+62+1) -1322+32+9) =22 + 3x +8

Answer 1

To demonstrate polynomial subtraction correctly, we first need to make sure both sides of the equation are simplified and combined correctly. Let's analyze the example given:

You wrote:
\(0(2x^2 + 62 + 1) - (1322 + 32 + 9) = 22 + 3x + 8\)

However, there are a few issues with this expression, such as the use of "0" and improper parentheses. Let's clarify how to perform polynomial subtraction step-by-step.

Let's define two polynomials:
- Let \(P(x) = 2x^2 + 62 + 1\)
- Let \(Q(x) = 1322 + 32 + 9\)

To subtract \(Q(x)\) from \(P(x)\):
\[
P(x) - Q(x) = (2x^2 + 62 + 1) - (1322 + 32 + 9)
\]

First, simplify \(Q(x)\):
\[
Q(x) = 1322 + 32 + 9 = 1363
\]

Now substitute back into the equation:
\[
P(x) - Q(x) = (2x^2 + 62 + 1) - 1363
\]
Resulting in:
\[
= 2x^2 + 63 - 1363 = 2x^2 - 1300
\]

Now, the equation becomes:
\[
P(x) - Q(x) = 2x^2 - 1300
\]

This does not equal \(22 + 3x + 8\) (or \(30 + 3x\)).

To correct it, a more accurate subtraction should look like this:

For instance, if we define:
1. \(P(x) = 2x^2 + 3x + 10\)
2. \(Q(x) = x^2 + 6x + 2\)

Then we can do:
\[
P(x) - Q(x) = (2x^2 + 3x + 10) - (x^2 + 6x + 2)
\]
Simplifying:
\[
= (2x^2 - x^2) + (3x - 6x) + (10 - 2)
\]
\[
= x^2 - 3x + 8
\]

So a correct example of polynomial subtraction is indeed:
\[
(2x^2 + 3x + 10) - (x^2 + 6x + 2) = x^2 - 3x + 8
\]

Let me know if you need further assistance or clarification!