Answer:
x+2
5x-2
Step-by-step explanation:
There is only 2 binomials that will multiply together that will give the given trinomial.
ax^2+bx+c
5x^2+8x-4
Goal: Find two numbers that multiply to be a*c and add up to be b.
We will use this goal to factor our trinomial.
a=5
b=8
c=-4
--------
a*c=-20
b=8
Can you think of two numbers that multiply to be -20 and add up to be 8? I hope you said 10 and -2.
So we are going to replace 8x with -2x+10x.
5x^2+8x-4
5x^2-2x+10x-4
We are going to pair the first terms together and the second two terms together like so:
(5x^2-2x)+(10x-4)
Now we are going to factor each pair.
x(5x-2)+2(5x-2)
(5x-2)(x+2)
So (x+2) is a factor of the given trinomial and (5x-2) is a factor of the given trinomial.
