Algebra II factoring help.?

Question

I'm typically good at math but algebra always gets me.

Find the value of c that makes the trinomial a perfect square. Then write the trinomial as a perfect square.

1.   X^2 - 10x + c.                   2. X^2 +60x + c

There's more for my homework but hopefully seeing the work for these two will be enough.
Thanks for your time and help :)

Axel · Accepted Answer

Hi Nathaniel

Solution 1:

perfect square trinomial uses the identity:

(x + a)(x + a) = x^2 +2ax +a^2

from you're equation  x^2 -10x + c comparing this to the above identity
we can arrive at 2 more equation

2ax = -10x  and a^2 = c  solving the 1st equation

2ax = -10x ;  x = -5   substituting this value to the 2nd equation

a^2 = c ; c = 25  the answer

Solution 2:

same as the solution above

c = 900

Hoping you will choose my  Answer as the Best answer thanks

Jeris · Answer

1. c = 25

x^2 - 10x + 25

= (x-5)^2

2. c = 900

x^2 + 60x + 900

= (x+30)^2

All you do is cut the middle number in half and square it.

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