Which of the following is a requirement for a trinomial to be factored as a perfect square? a. the coefficient for the x term must be twice the square root of the first term. b. the coefficient for the x term must be twice the square root of the last term. c. the coefficient for the x term must be twice the product of the square roots of the first and last terms. d. the coefficient for the x term must be half the product of the square roots of the first and last terms.

Step-by-step explanation:

The right answer is B.

A perfect square has the form , if we develop this expression would be

Notice when a trinomial is a perfect square, the second term is twic the square root of the third term, becase , and twice means , now in our example, .

Therefore, the right answer is B.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.