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Chapter 5: Problem 102

Factor. $$x^{2}+10 x+25$$

Short Answer

Expert verified
The factorized form of the given quadratic equation is \((x+5)^{2}\).

Step by step solution

01

Identify the coefficients

In the given equation \(x^{2}+10x+25\), the coefficient of \(x^{2}\) (denoted as \(a\)) is 1, the coefficient of \(x\) (denoted as \(b\)) is 10, and the constant term (denoted as \(c\)) is 25.
02

Find two numbers

For factorizing the quadratic equation, we need to find two numbers such that their sum is equal to the coefficient of \(x\) (which is \(b\) = 10) and their product is equal to the constant term (which is \(c\) = 25). 5 and 5 are two such numbers (5+5 = 10 and 5*5 = 25).
03

Write the factorization

Let's factorize the equation. Our \(p\) and \(q\) are both 5. So we can write the factorized form as \((x+5)(x+5)\) or \((x+5)^{2}\).

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