Find the last term (or the c ) to make the tri

Ask by O'Quinn Huff. in the United States

Dec 05,2024

Question

Find the last term (or the c ) to make the tri $$ x^{2}+\frac{16}{3} x+\square $$

UpStudy AI · Accepted Answer

To find the last term (the constant term, denoted as $$ c $$) that makes the expression $$ x^2 + \frac{16}{3} x + c $$ a perfect square trinomial, we can use the formula for completing the square.

A perfect square trinomial can be expressed in the form:

$$
(x + a)^2 = x^2 + 2ax + a^2
$$

In our case, we have:

$$
x^2 + \frac{16}{3} x + c
$$

Here, we can identify $$ 2a $$ with $$ \frac{16}{3} $$. To find $$ a $$, we solve for $$ a $$:

$$
2a = \frac{16}{3} \implies a = \frac{16}{6} = \frac{8}{3}
$$

Now, we need to find $$ c $$, which is $$ a^2 $$:

$$
c = a^2 = \left(\frac{8}{3}\right)^2 = \frac{64}{9}
$$

Thus, the last term $$ c $$ that makes the expression a perfect square trinomial is:

$$
\boxed{\frac{64}{9}}
$$
The last term $$ c $$ is $$ \frac{64}{9} $$.

Find the last term (or the c ) to make the tri

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