Question

select the correct answer.
what is the simplest form of this expression?
$(2x - 3)(3x^2 + 2x - 1)$
a. $6x^3 - 2x^2 - 8x + 3$
b. $6x^3 - 5x^2 - 8x + 3$
c. $6x^3 - 9x^2 - 4x + 3$
d. $6x^3 - 5x^2 - 6x + 2$

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(2x\) by each term in \(3x^2 + 2x - 1\) and \(-3\) by each term in \(3x^2 + 2x - 1\).
\(2x(3x^2 + 2x - 1)=6x^3 + 4x^2 - 2x\)
\(-3(3x^2 + 2x - 1)=-9x^2 - 6x + 3\)

Step2: Combine like terms

Add the two results together:
\((6x^3 + 4x^2 - 2x)+(-9x^2 - 6x + 3)\)
Combine \(x^2\) terms: \(4x^2 - 9x^2=-5x^2\)
Combine \(x\) terms: \(-2x - 6x=-8x\)
So the expression becomes \(6x^3 - 5x^2 - 8x + 3\)

Answer:

B. \(6x^3 - 5x^2 - 8x + 3\)