Questions: Use the table to answer the question. (x+3)(x+4)=0 x-3=0 x+4=0 x=3 x=-4 While using the Zero Product Property to find the values of x that make the quadratic equation (x+3)(x+4) equals 0, Oliver completed the work provided in the table. Is Oliver's work accurate? (1 point) No, he should have a third column where he should set x=0. No, x-3=0 in the second row should be x+3=0. Yes, the work is accurate. No, x+4=0 in the second row should be x-4=0.

Use the table to answer the question.

(x+3)(x+4)=0
x-3=0 x+4=0
x=3 x=-4

While using the Zero Product Property to find the values of x that make the quadratic equation (x+3)(x+4) equals 0, Oliver completed the work provided in the table. Is Oliver's work accurate? (1 point)
No, he should have a third column where he should set x=0.
No, x-3=0 in the second row should be x+3=0.
Yes, the work is accurate.
No, x+4=0 in the second row should be x-4=0.

Transcript text: Use the table to answer the question. \[ \begin{array}{c} (x+3)(x+4)=0 \\ x-3=0 \quad x+4=0 \\ x=3 \quad x=-4 \end{array} \] While using the Zero Product Property to find the values of $x$ that make the quadratic equation $(x+3)(x+4)$ equals 0 , Oliver completed the work provided in the table. Is Oliver's work accurate? (1 point) No, he should have a third column where he should set $x=0$. No, $x-3=0$ in the second row should be $x+3=0$. Yes, the work is accurate. No, $x+4=0$ in the second row should be $x-4=0$.

Solution

Solution Steps

To determine if Oliver's work is accurate, we need to apply the Zero Product Property correctly. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. For the equation $(x+3)(x+4)=0$, we should set each factor equal to zero and solve for $x$. This means setting $x+3=0$ and $x+4=0$, and solving these equations will give the correct values of $x$.

Solution Approach

Apply the Zero Product Property to the equation $(x+3)(x+4)=0$.
Set each factor equal to zero: $x+3=0$ and $x+4=0$.
Solve each equation to find the values of $x$.

Step 1: Apply the Zero Product Property

To solve the equation $(x+3)(x+4)=0$, we apply the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:

$x + 3 = 0$
$x + 4 = 0$

Step 2: Solve Each Equation

Now, we solve each equation for $x$:

From $x + 3 = 0$: \[ x = -3 \]
From $x + 4 = 0$: \[ x = -4 \]

Step 3: Verify Oliver's Work

Oliver's work included the equations $x - 3 = 0$ and $x + 4 = 0$. The first equation $x - 3 = 0$ is incorrect because it should be $x + 3 = 0$. The second equation $x + 4 = 0$ is correct. Therefore, Oliver's work is not accurate.