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A student wrongly factored a trinomial. To find the error, let's multiply the factors on the right-hand side to find the correct quadratic expression.
We can see that the constant term above is $60,$ while the constant term in the given expression is $-60.$

Let's factor the expression by ourselves. Since the leading coefficient is $1,$ we need to find two numbers whose sum is $-17$ and whose product is $-60.$ Even though $-5$ and$-12$ add to $-17,$ these are not the correct numbers as their product is **not** $-60.$ Let's look at all the factors of $-60$ to see which ones have a sum of $-17.$

Factors | $1(-60)$ | $2(-30)$ | $3(-20)$ | $4(-15)$ | $5(-12)$ | $6(-10)$ |
---|---|---|---|---|---|---|

Sum | $-59$ | $-28$ | $-17$ | $-11$ | $-7$ | $-4$ |

Since the sum of $3$ and $-20$ is $-17,$ and their product is $-60,$ these are the numbers we are looking for. With this information, we can correctly factor the given expression.