Question

1. which expression is equivalent to $-6x^2 - x + 12$?

a. $(3x + 2)(3 - 4x)$
b. $(3x - 2)(4x + 3)$
c. $- (2x - 3)(4 - 3x)$
d. $- (2x + 3)(3x - 4)$

1. select all the expressions that are equivalent to $3x^2 + 11x - 20$.

a. $(4x + 3)(5x - 1)$
b. $(4x - 3)(5x + 1)$
c. $(3x + 4)(x - 5)$
d. $(3x - 4)(x + 5)$

Explanation:

Question 8

Step 1: Expand option a

Expand \((3x + 2)(3 - 4x)\) using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

This is not equal to \(-6x^{2}-x + 12\).

Step 2: Expand option b

Expand \((3x - 2)(4x + 3)\):

$$
LATEXBLOCK1
$$

This is not equal to \(-6x^{2}-x + 12\).

Step 3: Expand option c

First, expand \((2x - 3)(4 - 3x)\):

$$
LATEXBLOCK2
$$

Then multiply by \(-1\): \(-( - 6x^{2}+17x - 12)=6x^{2}-17x + 12\)
This is not equal to \(-6x^{2}-x + 12\).

Step 4: Expand option d

First, expand \((2x + 3)(3x - 4)\):

$$
LATEXBLOCK3
$$

Then multiply by \(-1\): \(-(6x^{2}+x - 12)=-6x^{2}-x + 12\)
This matches the given expression.

Step 1: Expand option a

Expand \((4x + 3)(5x - 1)\):

$$
LATEXBLOCK0
$$

This is not equal to \(3x^{2}+11x - 20\).

Step 2: Expand option b

Expand \((4x - 3)(5x + 1)\):

$$
LATEXBLOCK1
$$

This is not equal to \(3x^{2}+11x - 20\).

Step 3: Expand option c

Expand \((3x + 4)(x - 5)\):

$$
LATEXBLOCK2
$$

This is not equal to \(3x^{2}+11x - 20\).

Step 4: Expand option d

Expand \((3x - 4)(x + 5)\):

$$
LATEXBLOCK3
$$

This matches the given expression.

Answer:

d. \(-(2x + 3)(3x - 4)\)

Question 9