Question

jenna constructs the model to represent $3x^2 + 11x - 4$. what factors does jenna need to model for the sides? \
\
| | factor 1 \
factor 2 | $+x^2$ | $+x^2$ | $+x^2$ | $-x$ \

$+x$	$+x$	$+x$	$-$ \
$+x$	$+x$	$+x$	$-$ \
$+x$	$+x$	$+x$	$-$ \
$+x$	$+x$	$+x$	$-$ \

\
$\circ$ $(3x + 1)$ and $(x - 4)$ \
$\circ$ $(3x - 1)$ and $(x + 4)$ \
$\circ$ $(3x - 2)$ and $(x + 2)$ \
$\circ$ $(3x + 2)$ and $(x - 2)$

Explanation:

Step1: Recall factoring quadratic

To factor \(3x^2 + 11x - 4\), we can also multiply the factors in each option and see which gives the original quadratic.

Step2: Test Option 1: \((3x + 1)(x - 4)\)

Expand: \(3x \cdot x + 3x \cdot (-4)+1 \cdot x + 1 \cdot (-4)=3x^2 - 12x + x - 4 = 3x^2 - 11x - 4\) (not correct).

Step3: Test Option 2: \((3x - 1)(x + 4)\)

Expand: \(3x \cdot x + 3x \cdot 4+(-1) \cdot x + (-1) \cdot 4 = 3x^2+12x - x - 4=3x^2 + 11x - 4\) (matches the quadratic).

Step4: Test Option 3: \((3x - 2)(x + 2)\)

Expand: \(3x \cdot x + 3x \cdot 2+(-2) \cdot x + (-2) \cdot 2=3x^2 + 6x - 2x - 4 = 3x^2 + 4x - 4\) (not correct).

Step5: Test Option 4: \((3x + 2)(x - 2)\)

Expand: \(3x \cdot x + 3x \cdot (-2)+2 \cdot x + 2 \cdot (-2)=3x^2 - 6x + 2x - 4=3x^2 - 4x - 4\) (not correct).

Answer:

B. \((3x - 1)\) and \((x + 4)\)