Question

question
expand the expression to a polynomial in standard form:
(4x + 3)(-x² - 5x + 9)
answer attempt 1 out of 2

Explanation:

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

Multiply \(4x\) by each term in \(-x^2 - 5x + 9\) and \(3\) by each term in \(-x^2 - 5x + 9\).
\(4x(-x^2) + 4x(-5x) + 4x(9) + 3(-x^2) + 3(-5x) + 3(9)\)

Step2: Simplify each term

\(4x(-x^2)= -4x^3\), \(4x(-5x)= -20x^2\), \(4x(9)= 36x\), \(3(-x^2)= -3x^2\), \(3(-5x)= -15x\), \(3(9)= 27\)

Step3: Combine like terms

Combine the \(x^2\) terms: \(-20x^2 - 3x^2 = -23x^2\)
Combine the \(x\) terms: \(36x - 15x = 21x\)

Step4: Write in standard form

Arrange terms from highest degree to lowest: \(-4x^3 - 23x^2 + 21x + 27\)

Answer:

\(-4x^3 - 23x^2 + 21x + 27\)