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Chapter 0: Problem 54

Factor each perfect square trinomial. $$25 x^{2}+10 x+1$$

Short Answer

Expert verified
The factored form of the trinomial \(25x^2 + 10x + 1\) is \((5x + 1)^2\).

Step by step solution

01

Identify the Perfect Square Trinomial

First, identify the trinomial as a perfect square. In this case we have \(25x^2 + 10x + 1\). Each term is a perfect square: The first term \(25x^2\) is the square of \(5x\), the last term \(1\) is the square of \(1\), and the middle term \(10x\) is twice the product of \(5x\) and \(1\). So it is indeed a perfect square trinomial
02

Factor the Perfect Square Trinomial

To factor a perfect square trinomial, take the square roots of the first and last terms, and put them inside parentheses with a plus sign between them. The factored form of \(25x^2 + 10x + 1\) will look like \((\sqrt{25x^2} 卤 \sqrt{1})^2\). Hence, the factored form will be \((5x 卤 1)^2.\)

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