As you know, you need to know the first two types of factoring listed above in order to be successful in factoring trinomials of the form ax2 + bx + c.

Part 1:
In your own words, explain how a trinomial of the form 2x2 + 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping. Use complete sentences.

Part 2:
If you were an Algebra 1 instructor and were creating a test on factoring trinomials of the form ax2 + bx + c, what do you think would be the easiest way to create a trinomial that can be factored? Provide one unique example.

Question

As you know, you need to know the first two types of factoring listed above in order to be successful in factoring trinomials of the form ax2 + bx + c.

Part 1:
In your own words, explain how a trinomial of the form 2x2 + 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping. Use complete sentences.

Part 2: 
If you were an Algebra 1 instructor and were creating a test on factoring trinomials of the form ax2 + bx + c, what do you think would be the easiest way to create a trinomial that can be factored? Provide one unique example.

tennistar · Answer

Part 1: To make 2x^2 + 13x + 15 a four term polynomial, I need to multiply the first and last terms of the trinomial and get 30. Then I would find the two numbers that multiply to get 30 and add to get 13. These numbers are 10 and 3. This polynomial is ready for factoring by grouping.

tennistar · Answer

Part 2: First multiply two numbers. You choose these two numbers. The list the factors of the product and find one for the middle term. Then test to see if it works in this form. ax^2 + bx + c. Use the two multiplied numbers as a c and the number that you chose for middle terms as b. Multiply first and last term, check factors and find two that added equal the middle term, then factor by grouping.