Question

multiply the polynomials using the distributive property and combine like terms.

\\(x + 2)(-x^2 - 6x + 4)\\

Explanation:

Distribute the first term of the binomial

Using the Distributive Property with Polynomials and Polynomial Multiplication knowledge points

$$ x \cdot (-x^2 - 6x + 4) = -x^3 - 6x^2 + 4x $$

Distribute the second term of the binomial

Using the Distributive Property with Polynomials and Polynomial Multiplication knowledge points

$$ 2 \cdot (-x^2 - 6x + 4) = -2x^2 - 12x + 8 $$

Combine all terms together

Using the Polynomial Simplification knowledge point

$$ (-x^3 - 6x^2 + 4x) + (-2x^2 - 12x + 8) = -x^3 - 6x^2 - 2x^2 + 4x - 12x + 8 $$

Group and combine like terms

Using the Polynomial Simplification knowledge point

$$
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Answer:

Multiply the polynomials using the distributive property and combine like terms.

$$(x + 2)(-x^2 - 6x + 4) =$$

<blank>\(-x^3 - 8x^2 - 8x + 8\)</blank>