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Chapter 5: Problem 69

Factor. $$25 x^{2}+30 x+9$$

Short Answer

Expert verified
The factored form of \(25x^{2}+30x+9\) is \((5x+3)^{2}\)

Step by step solution

01

Identify the Quadratic Form

A quadratic trinomial can be written in the form \( ax^{2}+bx+c \), where a, b, and c are constants. The given quadratic trinomial \(25x^{2}+30x+9\) can be arranged in this form. Here, \(a = 25\), \(b = 30\), and \(c = 9\).
02

Factor the Quadratic

Checking for perfect square trinomials, which will be in the form of \(a^{2}+2ab+b^{2}\), \(25x^{2}+30x+9\) is the perfect square trinomial since \(a = 5x\), \(b = 3\), and the trinomial can be written as \((5x)^{2}+2*5x*3+(3)^{2}\), which is \((5x+3)^{2}\).
03

Write the Final Answer

The factored form of the given quadratic trinomial \(25x^{2}+30x+9\) is \((5x+3)^{2}\)

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