CPM Homework Help : CCA2 Problem 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:

Step 1:

$x^2-10x+21=0$ , so $\left(x+7\right)\left(x+3\right)=0$

Step 2:

Therefore,

$x+7=0$ or $x+3=0$

Step 3:

$x=-7$ 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.

Hint:

Notice that $10x$ is being subtracted, not added.

Answer:

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