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Add these polynomials and simplify. Enter your response in standard form.

[tex]\[
\left(x^4 - 9x + 5x^7 \right) + \left(5x - 10 + 3x^4 - 2x^2 \right)
\][/tex]

Sagot :

GinnyAnswer
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]
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