Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2+2x

Question

Find the constant term that should be added to make the following expression a perfect-square trinomial.  X^2+2x

Answer 1

Hi Adeline;

We will factor this into two parenthetical expressions.

For the FOIL...

FIRST must be (x)(x)=x²

OUTER and INNER must be identical to create a perfect square, and must add up to 2x to satisfy the original expression.

(x+1)(x+1)

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(1)=1x=x

INNER...(1)(x)=1x=x

LAST...(1)(1)=1

x²+x+x+1

x²+2x+1

The constant is 1.