### Home > A2C > Chapter 1 > Lesson 1.1.3 > Problem1-37

1-37.

Nissos and Chelita were arguing over a math problem. Nissos was trying to explain to Chelita that she had made a mistake in finding the x -intercepts of the function $y=x^2−10x+21$. "No way!" Chelita exclaimed. "I know how to find x-intercepts! You make the y equal to zero and solve for x. I know I did this right!" Here is Chelita's work:

Step 1: $x^2 − 10x + 21 = 0$, so $(x + 7)(x + 3) = 0$.
Step 2: Therefore, $x + 7 = 0\text{ or }x + 3 = 0$.
Step 3: So $x = −7\text{ or } x = −3$.
Nissos tried to explain to Chelita that she had done something wrong. What is Chelita's error? Justify and explain your answer completely.

Notice that 10x is being subtracted, not added.

Her error was that she makes a sign error while factoring.
The correct factorization is $(x − 7)(x − 3) = 0$.