Question

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 thin k would be the easiest way to create a trinomial that can be factored? Provide one unique example.

Answer 1

Part 1:
You have to multiply the 2 and the 15, getting 30. Now, you find two numbers that also have a product of 30, but have a sum of 13. Those numbers are 10 and 3.

Separate the 13x into 10x and 3x ~ thus making your four term polynomial.

2x² + 10x + 3x + 15

Next factor by grouping. You factor the 2x² + 10x, and you factor the 3x + 15

2x(x + 5) + 3(x + 5)

Both 2x and 3 are multiplied by (x + 5). You can combine them into a binomial that's multiplied by (x + 5).

And then you have your answer:(2x + 3)(x + 5)

Part 2:
For this one, I needed to multiply a times c and then split it into two separate numbers, then you add them together and make that b.

Answer 2

is this correct?