Question

Find the value of c that makes the expression a perfect square trinomial.

x2 + 4x + c

Answer 1

the value of c that makes the expression a perfect square binomial is c=4 .

Explanation:

Here we have , an expression x2 + 4x + c or ,
`x^2 + 4x + c` . We need to find the value of c that makes the expression a perfect square binomial. Let's find out:

We have ,
`x^2 + 4x + c`

⇒
`x^2+4x+c`

⇒
`x^2+2(2)x+c`

Now , we know that
`(a+b)^2=a^2+2(a)(b)+b^2`

Comparing above equation , to
`x^2+2(2)x+c` we get ;

⇒
`x^2+2(2)x+c` {
`c=2^2` }

⇒
`x^2+2(2)x+2^2`

⇒
`(x+2)^2`

Therefore , the value of c that makes the expression a perfect square binomial is c=4 .