Gordon Sandoval
08/25/2024 · Senior High School
sum of \( \left(3 x^{3}-8 x^{2}+5 x+15\right) \) and \( \left(4 x^{2}+7 x-11\right) \)
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Step-by-step Solution
To find the sum of the two polynomials \( (3x^3 - 8x^2 + 5x + 15) \) and \( (4x^2 + 7x - 11) \), we will combine like terms.
1. Write the two polynomials together:
\[
(3x^3 - 8x^2 + 5x + 15) + (4x^2 + 7x - 11)
\]
2. Combine the like terms:
- The \( x^3 \) term: \( 3x^3 \)
- The \( x^2 \) terms: \( -8x^2 + 4x^2 = -4x^2 \)
- The \( x \) terms: \( 5x + 7x = 12x \)
- The constant terms: \( 15 - 11 = 4 \)
3. Putting it all together, we get:
\[
3x^3 - 4x^2 + 12x + 4
\]
Thus, the sum of the two polynomials is:
\[
\boxed{3x^3 - 4x^2 + 12x + 4}
\]
Quick Answer
The sum of the two polynomials is \( 3x^3 - 4x^2 + 12x + 4 \).
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