Sani is factoring the polynomial 2x^2+5x+3. if one factor is (x+1), what is the other factor?
a. 2x-3
b. 2x+3
c. 3x-2
d. 3x+2

B.

Step-by-step explanation:

So will have two factors if one factor in the form is given.

The other factor will also be in the form of .

So we have

:

Let's use foil.

First:  x(cx)=cx^2

Outer: x(d)=dx

Inner: 1(cx)=cx

Last: 1(d)=d

---------------------Adding like terms:

cx^2+(d+c)x+d

We are comparing this to:

2x^2+     5x+3

So we see that c=2 and d=3 where the other factor is cx+d=2x+3.

Also this works since c+d=5 (we know this because 2+3=5).