Questions: Factor the trinomial completely. Select "Prime" if the polynomial cannot be factored. 9 r^2 + 30 r + 25 = Prime

Factor the trinomial completely. Select "Prime" if the polynomial cannot be factored. 9 r^2 + 30 r + 25 = Prime
Transcript text: Factor the trinomial completely. Select "Prime" if the polynomial cannot be factored. $9 r^{2}+30 r+25=$ $\square$ Prime
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Solution

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Solution Steps

To factor the trinomial completely, we need to check if it can be expressed as a product of two binomials. We can use the quadratic formula or recognize it as a perfect square trinomial.

Step 1: Identify the Trinomial

We start with the trinomial: \[ 9r^2 + 30r + 25 \]

Step 2: Factor the Trinomial

We recognize that the trinomial can be factored as a perfect square trinomial. The expression can be written as: \[ (3r + 5)^2 \]

Step 3: Verify if the Trinomial is Prime

Since we were able to factor the trinomial, it is not a prime polynomial.

Final Answer

The factored form of the trinomial is: \[ \boxed{(3r + 5)^2} \]

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