Question

1. $(4x^2 + 3x + 2)(3x^2 + 2x - 1)$
2. $(x - 2)(3x + 1)(x + 3)$

mixed review.

1. $(x^5 + 3x - 5x^3 + 2) - (x^2 + 4x^3 + x^5) + (x - 3x^2 + 6)$
2. $(3x^2 - 2x + 4)(2x + 3)$
3. $(6 + 4x^2 - 5x^3 + 9x + x^5) + (2x^3 - 2x^2 + 7 - 3x) - (x^3 + 8 - 4x^2 + 3x^5 - 10x)$
4. $(x - 3)(3x + 5) - (x - 4)(2x + 7)$

Explanation:

Let's solve problem 12: \((3x^2 - 2x + 4)(2x + 3)\)

Step 1: Apply the distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial.
\[

$$\begin{align*} &(3x^2)(2x) + (3x^2)(3) + (-2x)(2x) + (-2x)(3) + 4(2x) + 4(3)\\ &= 6x^3 + 9x^2 - 4x^2 - 6x + 8x + 12 \end{align*}$$

\]

Step 2: Combine like terms

Combine the \(x^2\) terms and the \(x\) terms.
\[

$$\begin{align*} &6x^3 + (9x^2 - 4x^2) + (-6x + 8x) + 12\\ &= 6x^3 + 5x^2 + 2x + 12 \end{align*}$$

\]

Answer:

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