Question

question
factor.
$x^2 - 13x + 30$
answer attempt 1 out of 2
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Explanation:

Step1: Find two numbers that multiply to 30 and add to -13.

We need two numbers \( m \) and \( n \) such that \( m \times n = 30 \) and \( m + n = -13 \). The numbers are -10 and -3 because \( (-10) \times (-3) = 30 \) and \( (-10) + (-3) = -13 \).

Step2: Factor the quadratic using these numbers.

The quadratic \( x^2 - 13x + 30 \) can be factored as \( (x - 10)(x - 3) \) since \( x^2 + (m + n)x + mn=(x + m)(x + n) \), here \( m=-10 \), \( n = -3 \).

Answer:

\((x - 10)(x - 3)\)