Find the last term (or the c ) to make the trinomial into a perfect square:

When this is factored, it becomes:

Question

Find the last term (or the c ) to make the trinomial into a perfect square: $$ x^{2}+\frac{16}{9} x+ $$ When this is factored, it becomes:

UpStudy AI · Accepted Answer

To make the trinomial $$ x^{2} + \frac{16}{9} x + c $$ into a perfect square, we need to find the value of $$ c $$ such that the expression can be factored as $$ (x + a)^2 $$.

A perfect square trinomial can be expressed in the form:

$$
(x + b)^2 = x^2 + 2bx + b^2
$$

In our case, we have:

$$
x^2 + \frac{16}{9} x + c
$$

Here, we can identify $$ 2b $$ with $$ \frac{16}{9} $$. To find $$ b $$, we solve for $$ b $$:

$$
2b = \frac{16}{9} \implies b = \frac{16}{18} = \frac{8}{9}
$$

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

$$
c = b^2 = \left(\frac{8}{9}\right)^2 = \frac{64}{81}
$$

Thus, the trinomial becomes:

$$
x^2 + \frac{16}{9} x + \frac{64}{81}
$$

Now, we can factor it:

$$
x^2 + \frac{16}{9} x + \frac{64}{81} = \left(x + \frac{8}{9}\right)^2
$$

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

$$
\frac{64}{81}
$$

And when factored, it becomes:

$$
\left(x + \frac{8}{9}\right)^2
$$
The last term $$ c $$ is $$ \frac{64}{81} $$, and the factored form is $$ \left(x + \frac{8}{9}\right)^2 $$.

Find the last term (or the c ) to make the trinomial into a perfect square:

When this is factored, it becomes:

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Find the last term (or the c ) to make the trinomial into a perfect square: When this is factored, it becomes:

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When this is factored, it becomes: