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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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: \[ \boxed{3x^3 - 4x^2 + 12x + 4} \]

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The sum of the two polynomials is \( 3x^3 - 4x^2 + 12x + 4 \).
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