Question

Which of the trinomials below is a perfect square of a binomial?

Select the correct answer below:
a. 9x²+12x+1
b. 16x²+8x+4
c. x²−6x+4
d. 49x²+14x+1

Answer 1

The trinomial that is a perfect square is d. 49x²+14x+1, which can be factored into (7x + 1)^2.

Step-by-step explanation:

To determine which trinomial is a perfect square, we look for a pattern that fits the form (ax)^2 + 2abx + b^2, which can be factored into (ax + b)^2. Upon analyzing the options given:

• a. 9x²+12x+1 does not fit because (3x)^2 = 9x², but 1 is not (3²);
• b. 16x²+8x+4 does not fit because (4x)^2 = 16x², but 4 is not (2²);
• c. x²−6x+4 does not fit because the middle term is negative;
• d. 49x²+14x+1 does fit the pattern as (7x)^2 = 49x² and (1)^2 = 1

The correct answer is d. 49x²+14x+1, which is a perfect square of the binomial (7x + 1)^2.