Questions: Question 7 Find the last term (or the c ) to make the trinomial into a perfect square: [ x^2+frac65 x+frac925 ] When this is factored, it becomes:

Solution Steps

To determine if the given trinomial is a perfect square, we need to check if it can be written in the form \((ax + b)^2\). For a trinomial \(x^2 + bx + c\) to be a perfect square, the middle term \(b\) should be twice the product of the square root of the first term and the square root of the last term. We can verify this by comparing the given trinomial with the expanded form of \((x + d)^2\).

1. Identify the coefficients of the trinomial.
2. Check if the middle term is twice the product of the square root of the first and last terms.
3. If it is, then the trinomial is a perfect square and can be factored accordingly.

The given trinomial is

\[ x^2 + \frac{6}{5} x + \frac{9}{25} \]

To determine if this trinomial is a perfect square, we can express it in the form

\[ (ax + b)^2 \]

The coefficients are identified as follows:

• \(a = 1\)
• \(b = \frac{6}{5} = 1.2\)
• \(c = \frac{9}{25} = 0.36\)

We can factor the trinomial as follows:

\[ x^2 + 1.2x + 0.36 = (1.0 \cdot (x + 0.6))^2 \]

This shows that the trinomial can be expressed as a perfect square.

Final Answer