What value of c makes the polynomial below a perfect square?

Question

x^2 + 6x + c?

C=?

Answer 1

 x² + 6x + c?

This expression it can be written as

(x)² + 2(x)(3) +3² - 3² + c

Mathematics formulas: (a + b)² = a² + 2ab + b²

(x + 3)²+ (c - 9)

Clearly to make the polynomial a perfect square (c - 9) should be zero.

So, c - 9 = 0

Add 9 to each side.

c = 9

Therefore c = 9.

Answer 2

The expression is x² + 6x + c.

 

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 6. so, (half the x coefficient)² = (6/2)²= 9.

Now set c equal to 9 and solve (and in this case it is c) :

c = 9.

 

The value of c is 9.