part1: 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.

part2: 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

part1: 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.

part2: 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

Are you taking FLVS Algebra 1?

tennistar · Answer

I answered this exact question at FLVS Algebra 1

anonymous · Answer

yesss

tennistar · Answer

What you do is 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)

Notice how both 2x and 3 are multiplied by (x + 5)? You can combine them into a binomial that's multiplied by (x + 5) like this:

(2x + 3)(x + 5)


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Multiply a times c, split it into two numbers, add them together, and make that b.