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.

To factor the trinomial \(49c^2 - 126c + 81\), we can use the method of factoring by grouping.<br /><br />First, let's rewrite the trinomial in standard form:<br />\[49c^2 - 126c + 81\]<br /><br />Next, we need to find two numbers that multiply to give the product of the coefficient of \(c^2\) (which is 49) and the constant term (which is 81), and add up to give the coefficient of \(c\) (which is -126).<br /><br />The product of 49 and 81 is:<br />\[49 \times 81 = 3969\]<br /><br />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:<br />\[-63 \times -63 = 3969\]<br />\[-63 + (-63) = -126\]<br /><br />Now we can rewrite the middle term (-126c) using these two numbers:<br />\[49c^2 - 63c - 63c + 81\]<br /><br />Next, we group the terms in pairs and factor out the common factors:<br />\[(49c^2 - 63c) + (-63c + 81)\]<br /><br />Factor out the common factors from each group:<br />\[7c(7c - 9) - 9(7c - 9)\]<br /><br />Now we can factor out the common binomial factor \((7c - 9)\):<br />\[(7c - 9)(7c - 9)\]<br /><br />So the factored form of the trinomial \(49c^2 - 126c + 81\) is:<br />\[(7c - 9)^2\]<br /><br />Therefore, the correct choice is:<br />A. \(49c^2 - 126c + 81 = (7c - 9)^2\)