Question

You are familiar with the following types of factoring:
factoring out the Greatest Common Factor (GCF)
factoring by grouping
factoring trinomials of the form x2 + bx + c and ax2 + bx + c
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.

Answer 1

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.

Answer 2

for part 1 , do you have any ideas?

Answer 3

No I'm not so good at these... :/

Answer 4

Alright so in the form

\[ax^2+bx+c=0\]
if you

if you multiply a by c which in this case you get

\[2*15=30\]

now we need to find the factors of this number that add up to b or 13

this would be

\[10*3=30\]
\[10+3=13\] now you just split the bx into the factors 10 and a 3

\[2x^2+10x+3x+15=0\]

Answer 5

group the first two terms, and the last 2

\[(2x^2+10x)+(3x+15)=0\]

Answer 6

take the GCF of each parenthesis

\[2x(x+5)+3(x+5)=0\]

if you get the same thing in parenthesis, your factored polynomial whats inside the parenthesis and whats outside so
\[(2x+3)(x+5)=2x^2+13x+15\]

Answer 7

Thank you so much!!! :)

Answer 8

make sense? so part 2 what do you think you should do?