Question

\\(8x^3 + 3x - 11) + (5x^2 - 8x + 3) + (3x^3 - 2x^2 + 2)\\

answer

Explanation:

Remove parentheses

We begin by removing the parentheses surrounding each polynomial. Since all the operations between the polynomials are addition, we can write the expression without changing any signs.

$$ (8x^3 + 3x - 11) + (5x^2 - 8x + 3) + (3x^3 - 2x^2 + 2) = 8x^3 + 3x - 11 + 5x^2 - 8x + 3 + 3x^3 - 2x^2 + 2 $$

Group like terms

Using Polynomial Addition, we group the terms with the same exponent of \(x\) together, starting from the highest degree down to the constant terms.

• Cubic terms (\(x^3\)): \(8x^3 + 3x^3\)
• Quadratic terms (\(x^2\)): \(5x^2 - 2x^2\)
• Linear terms (\(x\)): \(3x - 8x\)
• Constant terms: \(-11 + 3 + 2\)

Combine the coefficients

Using Polynomial Simplification, we add or subtract the coefficients for each group of like terms.

• Cubic: \((8 + 3)x^3 = 11x^3\)
• Quadratic: \((5 - 2)x^2 = 3x^2\)
• Linear: \((3 - 8)x = -5x\)
• Constant: \(-11 + 3 + 2 = -6\)

Write the final polynomial

We combine the simplified groups to write the final polynomial in standard form.

$$ 11x^3 + 3x^2 - 5x - 6 $$

Answer:

\((8x^3 + 3x - 11) + (5x^2 - 8x + 3) + (3x^3 - 2x^2 + 2) =\) <blank>\(11x^3 + 3x^2 - 5x - 6\)</blank>