Score: 0 of 1 point Add the polynomials: $$ \left(9 x^{4}+10 x^{3}+3 x+6\right)+\left(5 x^{4}+10 x^{3}+2 x^{2}+6\right) $$ The resulting polynomial is: Enter your answer

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UpStudy AI · Accepted Answer

1. Write down the given polynomials:
   $$
   \left(9x^4 + 10x^3 + 3x + 6\right) \quad \text{and} \quad \left(5x^4 + 10x^3 + 2x^2 + 6\right)
   $$

2. Group and add the like terms:

- For $$ x^4 $$ terms: 
     $$
     9x^4 + 5x^4 = 14x^4
     $$
     
   - For $$ x^3 $$ terms:
     $$
     10x^3 + 10x^3 = 20x^3
     $$
     
   - For $$ x^2 $$ terms: 
     $$
     2x^2 \quad (\text{only one term})
     $$
     
   - For $$ x $$ terms: 
     $$
     3x \quad (\text{only one term})
     $$
     
   - For the constant terms:
     $$
     6 + 6 = 12
     $$

3. Combine all the summed terms to write the resulting polynomial:
   $$
   14x^4 + 20x^3 + 2x^2 + 3x + 12
   $$
The resulting polynomial is $$ 14x^4 + 20x^3 + 2x^2 + 3x + 12 $$.

Score: 0 of 1 point Add the polynomials: \( \left(9 x^{4}+10 x^{3}+3 x+6\right)+\left(5 x^{4}+10 x^{3}+2 x^{2}+6\right) \) The resulting polynomial is: Enter your answer

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