Solve the quadratic equation 84a? + 16x = 0 by factoring out the
GCF. (1 point)
To factor out the GCF from the quadratic equation, we need to find the greatest common factor of the terms.
The terms in the equation are 84a² and 16x.
The prime factorization of 84a² is 2² * 3 * 7 * a².
The prime factorization of 16x is 2⁴ * x.
The GCF of 84a² and 16x is 2² = 4.
Therefore, we can factor out 4 from the equation:
4(21a² + 4x) = 0
To solve the quadratic equation 84a^2 + 16x = 0 by factoring out the GCF, we need to find the greatest common factor of the terms 84a^2 and 16x.
The GCF of 84a^2 and 16x is 4.
So, we can rewrite the equation as:
4(21a^2 + 4x) = 0.
Now, we have factored out the GCF of the equation.
To solve the quadratic equation 84a^2 + 16x = 0 by factoring out the greatest common factor (GCF), we need to find the common factor of the terms 84a^2 and 16x.
Step 1: Find the GCF
To find the GCF, we need to factor out the common factors of both terms.
For 84a^2, we can write it as 2 * 2 * 3 * 7 * a * a. The common factors are 2 and a^2.
For 16x, we can write it as 2 * 2 * 2 * 2 * x. The common factor is 2.
Step 2: Write the equation in factored form
Now that we have found the GCF, we can write the equation in factored form.
The GCF is 2. So we can divide both terms by 2 to factor it out:
2(42a^2 + 8x) = 0
The equation is now in factored form.
Step 3: Solve for a and x
To solve the equation, we set each factor equal to zero and solve for a and x:
2 = 0
This is not possible, as 2 is not equal to zero.
42a^2 + 8x = 0
This is our remaining equation. To solve for a and x, we can further simplify it if possible or use other methods such as the quadratic formula.
However, since you only asked to factor out the GCF, we have already completed the required steps.