Question

1. $3\

$$\begin{bmatrix} 0 & 5 \\\\ -4 & 5 \\end{bmatrix}$$

$
$\

$$\begin{bmatrix} 0 & 15 \\\\ -12 & 15 \\end{bmatrix}$$

$
simplify each expression. (5pts each)

1. factor out a gcf

$3x^2 - 6x + 42$

1. factor the trinomial

$x^2 - 3x - 28$

Explanation:

Step1: Solve scalar multiplication

Multiply each matrix element by 3:

$$3
LATEXBLOCK0
=
LATEXBLOCK1
=
LATEXBLOCK2
$$

Step2: Factor out GCF from trinomial

Identify GCF = 3, factor it out:
$$3x^2 - 6x + 42 = 3(x^2 - 2x + 14)$$

Step3: Factor quadratic trinomial

Find two terms that multiply to -28 and add to -3:
$$x^2 - 3x - 28 = (x - 7)(x + 4)$$

Answer:

3)

$$\begin{bmatrix} 0 & 15 \\ -12 & 15 \end{bmatrix}$$

1. $3(x^2 - 2x + 14)$
2. $(x - 7)(x + 4)$