which following trinomial is a perfect square?
A. x^2 + 2x - 3
B. x^2 - 4x - 4
C. x^2 + x + 1/4
D. x^2 - x -56
question B & C 1-term and 3-term is perfect square. how do figure which is perfect square?
automatically rule out A and D, last terms are not perfect squares
Also rule out B, since both front and back must be positive.
So it could only be C , if any at all.
take √ of both first and last, multiply those results, then double to get the middle term.
looks like C is it!
(x+1/2)^2 = x^2 + x + 1/4
To determine if a trinomial is a perfect square, we need to consider the number of terms and the pattern of the constants.
A perfect square trinomial always has three terms.
One way to check if a three-term trinomial is a perfect square is to factor it and see if the factors are the same.
For example, let's check options B and C:
B. x^2 - 4x - 4: We can see that this trinomial doesn't look like a perfect square because the constant term (-4) is not a perfect square. factoring it gives us: (x - 2)(x - 2), which means the trinomial is (x-2)^2. So, option B is a perfect square.
C. x^2 + x + 1/4: Now let's check option C. We can see that this trinomial is formed by squaring a binomial. factoring it gives us: (x + 1/2)(x + 1/2), which means the trinomial is (x + 1/2)^2. So, option C is a perfect square.
Therefore, the correct answers are B and C.