Explain how to find all the possible positive values of b such that x^2 + bx + 6 can be factored into binomial factors. Write the possible trinomials.

Question

jim_thompson5910 · Answer

did you mean this `x^2 + bx + 6` ?

amberlykhan · Answer

Yeah

jim_thompson5910 · Answer

ok what are all the possible ways to multiply 2 numbers to get 6?

here is one way: 2*3 = 6
what are some others?

amberlykhan · Answer

1 * 6

amberlykhan · Answer

-2 * -3
-1 * -6

jim_thompson5910 · Answer

good, each pair of factors will add up to b

so if we go with the pair 2 and 3, then
b =2+3 = 5

that means x^2 + 5x + 6 is one possibility

amberlykhan · Answer

ok i understand that but what are binomial factors i got confused there

amberlykhan · Answer

wait

jim_thompson5910 · Answer

binomial means 2 terms

so anything where you have 2 terms added or subtracted

example: x+5, or 2x-7

amberlykhan · Answer

is it like (x +2) (x +3)

jim_thompson5910 · Answer

x^2 + 5x + 6 factors into (x+2)(x+3)

notice how the 2 and 3 are there

x+2 is one binomial factor
x+3 is the other

jim_thompson5910 · Answer

yes correct, that's one factorization

amberlykhan · Answer

sorry my computer was lagging

amberlykhan · Answer

thanks for clearing that up for me!