Mathieu is finding the x-intercepts of the function f (x) = x2 + 4x + 3. His work is shown below. 0 = x2 + 4x + 3 0 = (x + 3) (x + 1) x + 3 = x + 1 x = x - 2 0 = - 2 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.

Given:

f (x) = x2 + 4x + 3.

His work is shown below.

0 = x2 + 4x + 3

0 = (x + 3) (x + 1)

This is where Mathew made a mistake.

He set the factored expressions equal to each other.

x + 3 = x + 1

x = x - 2

0 = - 2

It should have been:

0 = (x + 3) (x + 1)

x + 3 = 0

x = - 3

x + 1 = 0

x = - 1

To check:

f (x) = x2 + 4x + 3

f (-1) = (-1) ² + 4 (-1) + 3

f (-1) = 1 - 4 + 3

f (-1) = - 4 + 4

f (-1) = 0

f (-3) = (-3) ² + 4 (-3) + 3

f (-3) = 9 - 12 + 3

f (-3) = - 12 + 12

f (-3) = 0