Question

mathieu is finding the x-intercepts of the function f(x)=x² + 4x + 3. his work is shown below. 1. 0 = x² + 4x + 3 2. 0 = (x + 3)(x + 1) 3. x + 3 = x + 1 4. x = x - 2 5. 0 = -2 6. there are no x-intercepts. which error did mathieu make? he factored incorrectly. he did not use the constant as the x-intercept. he set the factored expressions equal to each other. he incorrectly solved the equation x + 3 = x + 1.

Explanation:

To find the \( x \)-intercepts of a function \( f(x) \), we set \( f(x) = 0 \) and solve for \( x \). For a factored quadratic equation \( 0=(x + a)(x + b) \), we use the zero - product property, which states that if \( ab = 0 \), then either \( a=0 \) or \( b = 0 \).

Step 1: Analyze the correct method for solving \( 0=(x + 3)(x + 1) \)

Using the zero - product property, we should set each factor equal to zero separately. That is, we should have \( x+3 = 0 \) or \( x + 1=0 \), not \( x + 3=x + 1 \).

Step 2: Analyze Mathieu's error

Mathieu set \( x + 3=x + 1 \) in step 3. Let's solve \( x+3=x + 1 \):
Subtract \( x \) from both sides of the equation \( x+3=x + 1 \), we get \( 3=1 \), which is a contradiction. But the mistake was in the step of setting up the equation to solve for \( x \). The correct approach is to use the zero - product property, not to set the two factors equal to each other. So Mathieu's error was that he set the factored expressions equal to each other.

Answer:

He set the factored expressions equal to each other.