I need help finding the perfect square?

Question

What value of c makes the polynomial a perfect square?

x^2 + 5x + c

Do I plug numbers in for x and then factor it out?

Answer 1

What you'll need to do is a method called "completing the square." What you do is take the coefficient of the x^1 term, divide it by two, and then square it. and that becomes your c term. In this case, you divide 5 by 2, yeilding 2.5. then squaring 2.5 = 6.25 = c. To double check this method to make sure the answer is correct, you simply try to factor the polynomial - if it factors, you've done it correctly.

ex: x^2 = 5x + 6.25 factors to (x+2.5) * (x+2.25) = (x + 2.25)^2

hope that helps!

Answer 2

x² + 5x + c

Complete the square by making c = 6.25
which is (5/2)²

x² + 5x + 6.25

(x + 2.5)²

(x+ 2.5)(x + 2.5)
.