Question

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

\\(x - 1)(-4x^2 + x - 5)\\

Explanation:

Distribute the first term

Using the Distributive Property with Polynomials and Polynomial Multiplication, we multiply \(x\) by each term in the trinomial:

$$ x \cdot (-4x^2 + x - 5) = -4x^3 + x^2 - 5x $$

Distribute the second term

Next, we distribute the \(-1\) to each term in the trinomial:

$$ -1 \cdot (-4x^2 + x - 5) = 4x^2 - x + 5 $$

Combine the distributed parts

We write the sum of the two distributed parts:

$$ (-4x^3 + x^2 - 5x) + (4x^2 - x + 5) $$

Group and combine like terms

Using Polynomial Simplification, we group terms with the same exponent and combine their coefficients:

$$
LATEXBLOCK0
$$

Answer:

\(-4x^3 + 5x^2 - 6x + 5\)