Let's add the given polynomials step by step.
Given polynomials:
1. \( P(x) = x^4 - 9x + 5x^7 \)
2. \( Q(x) = 5x - 10 + 3x^4 - 2x^2 \)
First, combine all the similar terms:
- Collect the \( x^7 \) terms: \( 5x^7 \)
- Collect the \( x^4 \) terms: \( x^4 + 3x^4 = 4x^4 \)
- Collect the \( x^2 \) terms: \( -2x^2 \)
- Collect the \( x \) terms: \( -9x + 5x = -4x \)
- Constant term: \( -10 \)
Now, we can write down the polynomial by summing up all these collected terms:
[tex]\[
5x^7 + 4x^4 - 2x^2 - 4x - 10
\][/tex]
Therefore, the sum of the given polynomials in standard form is:
[tex]\[
5x^7 + 4x^4 - 2x^2 - 4x - 10
\][/tex]
