Question

introduction to analyzing the equations
google classroom
analyze the given quantity and express it as th
$x^2 - 10x + 21 = \square$

Explanation:

Step1: Factor the quadratic expression

We need to find two numbers that multiply to \(21\) and add up to \(-10\). The numbers are \(-3\) and \(-7\) since \((-3)\times(-7) = 21\) and \(-3 + (-7)=-10\).
So, we can rewrite the middle term using these two numbers:
\(x^{2}-10x + 21=x^{2}-3x-7x + 21\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((x^{2}-3x)+(-7x + 21)\)
Factor out the greatest common factor from each group:
\(x(x - 3)-7(x - 3)\)
Now, factor out the common binomial factor \((x - 3)\):
\((x - 3)(x - 7)\)

Answer:

\((x - 3)(x - 7)\)