Find all values of c that will make the polynomial a perfect square trinomial.

Question

Find all values of c that will make the polynomial a perfect square trinomial.

144r^2-120r+c

Answer 1

As a perfect square the trinomial can be rewritten

as

(12r-a)² expand to 144r² -24ar + a²

the first part in parentheses is the square root of 144r²

the second part is the square root of c

24a = 120, so a = 120/24 = 5

The perfect square is (12r-5)² = 144r² -- 120r +25, so c=25