Answer :
Let's simplify the expression [tex]\((x^4 + 4x + 7) - (5x^4 + 7x - 2)\)[/tex] step-by-step.
1. Distribute the Negative Sign:
When you subtract a polynomial, you distribute the negative sign across each term in the second polynomial. The expression becomes:
[tex]\[
x^4 + 4x + 7 - 5x^4 - 7x + 2
\][/tex]
2. Combine Like Terms:
- For the [tex]\(x^4\)[/tex] terms:
[tex]\[
x^4 - 5x^4 = -4x^4
\][/tex]
- For the [tex]\(x\)[/tex] terms:
[tex]\[
4x - 7x = -3x
\][/tex]
- For the constant terms:
[tex]\[
7 + 2 = 9
\][/tex]
3. Simplified Expression:
Putting it all together, the simplified expression is:
[tex]\[
-4x^4 - 3x + 9
\][/tex]
So, the correct answer is option C: [tex]\(-4x^4 - 3x + 9\)[/tex].
1. Distribute the Negative Sign:
When you subtract a polynomial, you distribute the negative sign across each term in the second polynomial. The expression becomes:
[tex]\[
x^4 + 4x + 7 - 5x^4 - 7x + 2
\][/tex]
2. Combine Like Terms:
- For the [tex]\(x^4\)[/tex] terms:
[tex]\[
x^4 - 5x^4 = -4x^4
\][/tex]
- For the [tex]\(x\)[/tex] terms:
[tex]\[
4x - 7x = -3x
\][/tex]
- For the constant terms:
[tex]\[
7 + 2 = 9
\][/tex]
3. Simplified Expression:
Putting it all together, the simplified expression is:
[tex]\[
-4x^4 - 3x + 9
\][/tex]
So, the correct answer is option C: [tex]\(-4x^4 - 3x + 9\)[/tex].
