Question

expand the expression to a polynomial in standard form:
(-4x + 5)(3x^2 - 2x - 1)

Explanation:

Step1: Apply distributive property (FOIL-like for polynomials)

Multiply \(-4x\) by each term in \(3x^2 - 2x - 1\) and \(5\) by each term in \(3x^2 - 2x - 1\):
\(-4x \cdot 3x^2 = -12x^3\), \(-4x \cdot (-2x) = 8x^2\), \(-4x \cdot (-1) = 4x\),
\(5 \cdot 3x^2 = 15x^2\), \(5 \cdot (-2x) = -10x\), \(5 \cdot (-1) = -5\).

Step2: Combine like terms

Combine the \(x^2\), \(x\) terms:
\(x^3\) term: \(-12x^3\),
\(x^2\) terms: \(8x^2 + 15x^2 = 23x^2\),
\(x\) terms: \(4x - 10x = -6x\),
constant term: \(-5\).

Step3: Write in standard form

Arrange terms by descending powers of \(x\):
\(-12x^3 + 23x^2 - 6x - 5\).

Answer:

\(-12x^3 + 23x^2 - 6x - 5\)