pregunta 1-3
which expression is equivalent to (-2x^2 + 5x + 7)?
((2x + 7)(1 - x))
((2x - 7)(x + 1))
(-(2x + 7)(1 - x))
(-(2x - 7)(x + 1))

Question

Accepted Answer

# Explanation:
## Step 1: Expand each option
We will expand each of the given options and check which one matches $-2x^2 + 5x + 7$.

### Option 1: $(2x + 7)(1 - x)$
Using the distributive property (FOIL method):
$$
\begin{align*}
(2x + 7)(1 - x)&=2x\times1-2x\times x + 7\times1-7\times x\
&=2x-2x^2 + 7 - 7x\
&=-2x^2+(2x - 7x)+7\
&=-2x^2-5x + 7
\end{align*}
$$
This is not equal to $-2x^2 + 5x + 7$.

### Option 2: $(2x - 7)(x + 1)$
Using the distributive property (FOIL method):
$$
\begin{align*}
(2x - 7)(x + 1)&=2x\times x+2x\times1-7\times x - 7\times1\
&=2x^2+2x-7x - 7\
&=2x^2-5x - 7
\end{align*}
$$
This is not equal to $-2x^2 + 5x + 7$.

### Option 3: $-(2x + 7)(1 - x)$
First, we know from Option 1 that $(2x + 7)(1 - x)=-2x^2-5x + 7$. Now multiply by $-1$:
$$
\begin{align*}
-(2x + 7)(1 - x)&=-1\times(-2x^2-5x + 7)\
&=2x^2 + 5x - 7
\end{align*}
$$
This is not equal to $-2x^2 + 5x + 7$.

### Option 4: $-(2x - 7)(x + 1)$
First, we know from Option 2 that $(2x - 7)(x + 1)=2x^2-5x - 7$. Now multiply by $-1$:
$$
\begin{align*}
-(2x - 7)(x + 1)&=-1\times(2x^2-5x - 7)\
&=-2x^2 + 5x + 7
\end{align*}
$$
This matches the given expression $-2x^2 + 5x + 7$.

# Answer:
$-(2x - 7)(x + 1)$ (the fourth option)

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QUESTION IMAGE

Question

Explanation:

Step 1: Expand each option

Option 1: \((2x + 7)(1 - x)\)

Option 2: \((2x - 7)(x + 1)\)

Option 3: \(-(2x + 7)(1 - x)\)

Option 4: \(-(2x - 7)(x + 1)\)

Answer: