3х^2-24х+21

To work with the expression \(3x^2 - 24x + 21\), we can either factor it or solve for its roots.

Factoring

1. First, we can factor out the greatest common factor (GCF) from the expression: \[ 3(x^2 - 8x + 7) \]

2. Next, we can factor the quadratic \(x^2 - 8x + 7\). We need two numbers that multiply to \(7\) and add to \(-8\). These numbers are \(-1\) and \(-7\).

3. Thus, we can factor it further: \[ 3(x - 1)(x - 7) \]

Final factored form

So the expression \(3x^2 - 24x + 21\) can be factored as: \[ 3(x - 1)(x - 7) \]

Finding Roots

If you want to find the roots of the equation \(3x^2 - 24x + 21 = 0\), you can set the factored form equal to zero: \[ 3(x - 1)(x - 7) = 0 \]

From this, we can find two solutions:

1. \(x - 1 = 0 \Rightarrow x = 1\)
2. \(x - 7 = 0 \Rightarrow x = 7\)

Summary

• The expression factors to \(3(x - 1)(x - 7)\).
• The roots (solutions) of the equation \(3x^2 - 24x + 21 = 0\) are \(x = 1\) and \(x = 7\).