Ask a New Question
Menu

Quadratic Equations Online Practice

Complete this assessment to review what you’ve learned. It will not count toward your grade.
8 of 208 of 20 Items

Question
Martin solved the quadratic equation 3x2+2x−8=0
. His work is shown below. However, he accidentally spilled ink over the step where he divided by the GCF that he found for each pair. Which of the following options shows the missing part of Martin’s work?

Several lines of equations.

(1 point)
Responses

3x(x+2)−4(x+2)=0
3 x left parenthesis x plus 2 right parenthesis minus 4 left parenthesis x plus 2 right parenthesis equals 0

x(3x+6)+4(x+2)=0
x left parenthesis 3 x plus 6 right parenthesis plus 4 left parenthesis x plus 2 right parenthesis equals 0

3x(x+2)−4(x−2)=0
3 x left parenthesis x plus 2 right parenthesis minus 4 left parenthesis x minus 2 right parenthesis equals 0

3x(x+2)+4(x+2)=0
3 x left parenthesis x plus 2 right parenthesis plus 4 left parenthesis x plus 2 right parenthesis equals 0
Remaining Attempts : 3
Skip to navigation

1 answer

To determine the missing part of Martin's work when solving the quadratic equation \(3x^2 + 2x - 8 = 0\), let’s first factor the expression.

  1. Identify the common factors of the terms in the equation.

    • The equation \(3x^2 + 2x - 8\) can be factored by grouping.
    • The first step is to look for a common factor in the terms of the equation.

  2. The goal is to re-arrange the equation into factored form. The GCF (Greatest Common Factor) can be useful.

    • Here, we could try regrouping the equation into two pairs to factor by grouping:
    • The equation does not present a direct GCF that simplifies all terms, but we can express it as: \[ 3x^2 + 2x - 8 = 0 \] \[ 3x(x + 2) - 4(x + 2) = 0 \]

  3. By factoring \( (x + 2) \) out of the equation above, the next logical step would be:

    • \( (x + 2)(3x - 4) = 0 \)

Given the options you provided, the only correct form of Martin's after factoring the equation correctly should look like this:

Option 1: \( 3x(x + 2) - 4(x + 2) = 0 \)

This shows correctly factoring out the GCF from the pairs.

So the answer to fill in the missing step in Martin's work is:

3x(x+2)−4(x+2)=0

If you have any more questions about quadratic equations or other problems, feel free to ask!