Question

question
factor completely.
$3x^2 - 20x + 25$

Explanation:

Step1: Use the AC method for factoring. For the quadratic \(ax^2 + bx + c\), find two numbers that multiply to \(a\times c\) and add to \(b\). Here, \(a = 3\), \(b=-20\), \(c = 25\). So \(a\times c=3\times25 = 75\). We need two numbers that multiply to 75 and add to -20. Those numbers are -15 and -5.

\(3x^2-15x - 5x + 25\)

Step2: Group the terms.

\((3x^2 - 15x)+(-5x + 25)\)

Step3: Factor out the GCF from each group.

\(3x(x - 5)-5(x - 5)\)

Step4: Factor out the common binomial factor \((x - 5)\).

\((3x - 5)(x - 5)\)

Answer:

\((3x - 5)(x - 5)\)