Question

Factor the GCF out of the trinomial on the left side of the equation. 2x²+6x-36=0

Answer 1

The trinomial
`\(2x^2 + 6x - 36\)` is factored by extracting the GCF of 2, resulting in 2(x - 3)(x + 6) = 0. The solutions are x = 3 and x = -6, obtained by setting each factor to zero.

To factor the GCF out of the trinomial
`\(2x^2 + 6x - 36 = 0\)`, we need to identify the greatest common factor (GCF) of the coefficients. In this case, the GCF is 2.

1. Factor out the GCF (2) from each term:

`\[2(x^2 + 3x - 18) = 0\]`

Now, we have factored out the GCF, and the equation becomes
`\(2(x^2 + 3x - 18) = 0\).`

2. Next, factor the quadratic trinomial
`\(x^2 + 3x - 18\)` into two binomials:

2(x - 3)(x + 6) = 0

So, the factored form of the quadratic equation
`\(2x^2 + 6x - 36 = 0\) is \(2(x - 3)(x + 6) = 0\).`

Now, to find the solutions, set each factor equal to zero:

`\[x - 3 = 0 \quad \text{or} \quad x + 6 = 0\]`

Solving these equations yields x = 3 and x = -6.

Therefore, the solutions to the original quadratic equation are x = 3 and x = -6.