Find the value of C that will make 25x^2-40x+c a perfect trinomial.
The answer is 16 because when you use FIOL for (5x-4)(5x-4) you get 25x^2 -20x-20x+16.Then you simplify to 25x^2-40x+16 to your original problem with the answer of 16 in the problem.
FIOL is multiplying...
the FIRST term
then INNER terms
then OUTER terms
finally your LAST terms.
I suppose what you mean by a perfect trinomial is a perfect square, in which case c has to be a perfect square in such a way that
25x^2-40x+c = (5x-4)^2
Can you find c?
16
16
To find the value of C that will make the quadratic 25x^2 - 40x + c a perfect trinomial, we need to understand what makes a trinomial perfect.
A perfect trinomial is a quadratic expression that can be factored into two identical binomial factors. In other words, its factors will have a common binomial term.
To determine the value of C that will make the quadratic a perfect trinomial, we can use the following steps:
Step 1: Recall the pattern for perfect trinomials
A perfect trinomial can be factored into the form (ax + b)^2, where a is the coefficient of the x^2 term, and b is half the coefficient of the x term. In this case, a = 25 and b = -20.
Step 2: Set up the equation
We know that the perfect square trinomial is (ax + b)^2. Substituting the given coefficients into the equation, we have:
(25x - 20)^2 = 25x^2 - 40x + c.
Step 3: Expand the equation
Expanding (25x - 20)^2 using the square of a binomial formula:
(25x - 20)^2 = (25x)^2 - 2 * 25x * 20 + (20)^2
= 625x^2 - 1000x + 400.
Step 4: Compare coefficients
Now we can compare the expanded form with the original quadratic expression:
25x^2 - 40x + c = 625x^2 - 1000x + 400.
By comparing the coefficients of corresponding terms:
25x^2 - 40x + c = 625x^2 - 1000x + 400.
We can see that the coefficient of x^2 is the same on both sides, so 25 = 625.
The coefficient of x is also the same, so -40 = -1000.
Finally, equating the constant terms, we have c = 400.
Therefore, the value of C that will make the quadratic 25x^2 - 40x + c a perfect trinomial is C = 400.
Well, I must say, finding the perfect value of C sounds like quite the challenge. But fear not, brave question-asker, for Clown Bot is here to help!
To find the value of C that will make 25x^2 - 40x + c a perfect trinomial, we need to use some mathematical wizardry.
Now, a perfect trinomial is in the form (ax + b)^2, where ax and b are the terms of the original trinomial. In this case, we have (5x - 4)^2.
Expanding this perfect trinomial, we get (5x - 4)(5x - 4) = 25x^2 - 40x + 16.
Ah, but you're probably thinking, "Clown Bot, that's not the answer we're looking for!" You are correct, my inquisitive friend. So, the value of C that will make 25x^2 - 40x + c a perfect trinomial is...
C = 16!
A round of applause for Clown Bot, please!