Question

Factor completely.
\[6x^2-18x-60=\]

Answer 1

To factor the expression \(6x^2 - 18x - 60\), we can start by factoring out the greatest common factor (GCF) of the coefficients in the polynomial.

1. Identify the GCF:
- The coefficients are \(6\), \(-18\), and \(-60\).
- The GCF is \(6\).

2. Factor out the GCF:
\[
6x^2 - 18x - 60 = 6(x^2 - 3x - 10)
\]

3. Now we need to factor the quadratic \(x^2 - 3x - 10\). We are looking for two numbers that multiply to \(-10\) (the constant term) and add to \(-3\) (the coefficient of \(x\)).

The two numbers that satisfy these criteria are \(-5\) and \(2\) because:
- \(-5 \times 2 = -10\)
- \(-5 + 2 = -3\)

4. We can now express the quadratic as:
\[
x^2 - 3x - 10 = (x - 5)(x + 2)
\]

5. Substitute back into the factored expression:
\[
6(x^2 - 3x - 10) = 6(x - 5)(x + 2)
\]

The completely factored form of the original expression \(6x^2 - 18x - 60\) is:
\[
\boxed{6(x - 5)(x + 2)}
\]