Here are a few recommended readings before getting started with this lesson.

A quadratic trinomial in the form can be factored as if there exist and such that and

Substitute expressions

Commutative Property of Multiplication

It is known that and that and are positive integers. Therefore, two positive factors of whose sum is need to be found. The positive factor pairs of will be listed and the pair with a sum of identified.

 Positive Factors of Sum and and and

As seen, the factor pair of and meet these requirements, so the values of and are and

It’s a three-day weekend and Tearrik has the day off from school. He wants to use this time to make a present for his brother’s birthday. He bought a nice frame and then chose a photo of the two of them. However, the photo does not fit in the frame, so Tearrik needs to edit it.

The editing program represents the area of the photo as and its length as Help Tearrik answer the following questions.

Two positive factors of whose sum is need to be found. Now, list the positive factor pairs of and identify the pair with a sum of

 Positive Factors of Sum and and and and

Multiply

Vincenzo is using the extra day off school to begin building a kennel for his dog. In order to use the garden area in the most effective way, he has to build it on a triangular base. He draws a plan of a right triangle whose hypotenuse is represented by the binomial

It is known that the trinomial is twice the area of the triangle and that the length of is greater than the length of

As such, the factor pairs of where one factor is negative should be listed. Then, look for the pair with a sum of

 Positive Factors of Sum and and and and

Tadeo is using the extra day off school to catch up on homework. He is almost finished with his math homework but is stuck on one problem. He reviews the notes he wrote about factoring the given quadratic trinomial with a leading coefficient of

Error: When must be a positive integer and must be a negative integer so that their sum is negative.
Factored Form:

Start by identifying the values of and for the given quadratic trinomial.

Therefore, Tadeo’s first point is correct. If it is assumed that then should be negative. In other words, Tadeo’s second point is incorrect.

The given trinomial can be factored using this information. To do so, the factor pairs of where one factor is negative and its absolute value is greater than the other factor are listed. Then, the pair with a sum of should be looked for.

 Factors of Sum of Factors and and and and and

An inter-class quiz game is being held at Davontay’s school this weekend, and he is his class’s champion. The quizmaster Paulina asks Davontay to write a quadratic trinomial and then factor it. The conversation between the quizmaster and Dovantoy is shown in the diagram.

Based on this information, only negative factor pairs of need to be listed.

 Negative Factors of and and and and and and

The sum of the factors in each pair could be the value of so Davontay’s concern is valid. There are six values for These values can be found as follows.

 Factors of Sum and and and and and and

Factor each quadratic expression with a leading coefficient Write the answer in such a way that the value of is the greater factor.

Maya and her father spent the long weekend building a trough for the animals on their farm. Her father knows that Maya has a math test coming up soon, so he decides to help her prepare for it by quizzing her about the trough they just built.

The trough’s length is centimeters longer than its width. The area covered by the trough is square centimeters.

Width: centimeters

 Factors of Sum of Factors and and and and and

Use the Zero Product Property

 Expression Width Length

The width of the trough is centimeters and the length is centimeters.

and

 Factors of Sum of Factors and and and

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