Question

Find the value of $c$ that makes $x^2+20x+c$ a perfect square trinomial. $c=$ Write the expression as the square of a binomial. The expression is .

Answer 1

9514 1404 393

Answer:

• c = 100
• (x +10)²

Step-by-step explanation:

The square of a binomial is ...

  (x +a)² = x² +2ax + a²

Comparing this to your expression, we have ...

  2a = 20 . . . . x-coefficient

  a² = c . . . . . . constant term

Then ...

  a = 20/2 = 10

  a² = 10² = 100 = c

The square is then ...

  (x +10)²

Answer 2

Answer:

c = 100 makes this a perfect square trinomial

Step-by-step explanation:

$x^2+20x+c\\x^2+20x+100\\=(x+10)^{2}$