Question

use factoring to solve the quadratic equation. check by substitution or by using a graphing utility and identifying x-intercepts.
$4x^2 + 12x = 0$
rewrite the equation in factored form.
$\square = 0$
(factor completely.)

Explanation:

Step1: Factor out GCF

Identify the greatest common factor (GCF) of $4x^2$ and $12x$, which is $4x$. Factor it out:
$4x(x + 3) = 0$

Step2: Solve for x via zero product

Set each factor equal to 0:
First factor: $4x = 0$
Second factor: $x + 3 = 0$

Step3: Calculate each x value

Solve $4x = 0$:
$x = \frac{0}{4} = 0$
Solve $x + 3 = 0$:
$x = -3$

Step4: Verify solutions (substitution)

Substitute $x=0$ into original equation:
$4(0)^2 + 12(0) = 0 + 0 = 0$ (valid)
Substitute $x=-3$ into original equation:
$4(-3)^2 + 12(-3) = 4(9) - 36 = 36 - 36 = 0$ (valid)

Answer:

Factored form: $4x(x + 3) = 0$
Solutions: $x=0$ and $x=-3$