factor th trinomial if possible using integers show work
2x^2+7x+5

Question

factor th trinomial if possible using integers show work 
2x^2+7x+5

anonymous · Answer

$$2x ^{2} + 7x + 5$$ = 

(2x + a)(x + b)
First    Outside   Inside   Last   (FOIL Method)
2x*x + 2x*b   + a*x     + a*b

That gives our $$2x ^{2}$$

Then 2x*b + a*x = 7x 
and 
a*b = 5

From the second equation, we know that a and b are some combination of 1 and 5 (because these are the only two integers which, when multiplied, equal 5).

If we set a=1 and b=5 we have:
(2x + 1)(x + 5)

Let's see.

2x^2 + 10x + 1x + 5=2x^+11x+5...

That doesn't work.  Let's try the other way.
(2x+5)(x+1)

2x^2+2x + 5x + 5=2x^2+7x+5  

Looks good too me! 

Was that enough work shown?

anonymous · Answer

Or are you supposed to use the quadratic equation?

anonymous · Answer

yeah thats good thank you

myininaya · Answer

a=2
b=7
c=5
find two factors of a*c that add up to be b
a*c=2(5)
b=7=2+5
now replace middle term the bx term with 2x+5x
so we have 2x^2x+2x+5x+5
now factor by grouping

myininaya · Answer

2x(x+1)+5(x+1)
(x+1)(2x+5)