Question

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

Explanation:

Step1: Apply distributive property (FOIL for trinomial)

Multiply \(-3x\) by each term in \(-2x^2 + 5x + 5\) and \(1\) by each term in \(-2x^2 + 5x + 5\).
\(-3x\times(-2x^2)=6x^3\), \(-3x\times5x=-15x^2\), \(-3x\times5=-15x\)
\(1\times(-2x^2)=-2x^2\), \(1\times5x=5x\), \(1\times5=5\)

Step2: Combine like terms

Combine the \(x^2\) terms: \(-15x^2 - 2x^2=-17x^2\)
Combine the \(x\) terms: \(-15x + 5x=-10x\)

Step3: Write the polynomial in standard form

Arrange the terms in descending order of exponents: \(6x^3 - 17x^2 - 10x + 5\)

Answer:

\(6x^3 - 17x^2 - 10x + 5\)