### Home > CCA2 > Chapter 1 > Lesson 1.1.3 > Problem1-36

1-36.

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: Homework Help ✎

 Step 1: $x^2−10x+21=0$, so $(x+7)(x+3)=0$. Step 2: Therefore, $x+7=0$ or $x+3=0$. Step 3: So $x=−7$ 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.

She made a sign error while factoring. The correct factorization is $(x−7)(x−3)=0$.