8. Factor the trinomial, 49c^2-126c+81 __ Select the correct choice below and fill indiny answer boxes within your choice. ()A. 49c^2-126c+81= square form.) B. The polynomial is prime.

Question

Answer 1

To factor the trinomial

, we can use the method of factoring by grouping.First, let's rewrite the trinomial in standard form:

Next, we need to find two numbers that multiply to give the product of the coefficient of

(which is 49) and the constant term (which is 81), and add up to give the coefficient of

(which is -126).The product of 49 and 81 is:

We need to find two numbers that multiply to 3969 and add up to -126. After some trial and error, we find that these numbers are -63 and -63, since:

Now we can rewrite the middle term (-126c) using these two numbers:

Next, we group the terms in pairs and factor out the common factors:

Factor out the common factors from each group:

Now we can factor out the common binomial factor \((7c - 9)\):

So the factored form of the trinomial

is:

Therefore, the correct choice is:A. \(49c^2 - 126c + 81 = (7c - 9)^2\)

Question