Question

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

Answer 1

B

Explanation:

Answer 2

B.

Explanation:

So
`2x^2+5x+3` will have two factors if one factor in the form
`(ax+b)` is given.

The other factor will also be in the form of
`(cx+d)`.

So we have

`(x+1)(cx+d)`:

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).