Solving Quadratic Equations Using Common Factors Quick Check

Question

2 of 52 of 5 Items
Question
Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point)
Responses

Put the quadratic in standard form x−8=0
Factor out the GCF No GCF
Set each factor equal to zero x−8=0
The solutions are x=8 Put the quadratic in standard form x minus 8 equals 0 Factor out the GCF No GCF Set each factor equal to zero x minus 8 equals 0 The solutions are x equals 8

Put the quadratic in standard form 7x2−56x=0
Factor out the GCF 7x(x−8)=0
Set each factor equal to zero 7x=0 and x−8=0
The solutions are x=0 and x=8Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals 0 and x equals 8

Put the quadratic in standard form 7x2−56x=0
Factor out the GCF 7x(x−8)=0
Set each factor equal to zero 7x=0 and x−8=0
The solutions are x=−7 and x=8 Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals negative 7 and x equals 8

Put the quadratic in standard form 7x2+56x=0
Factor out the GCF 7x(x+8)=0
Set each factor equal to zero 7x=0 and x+8=0
The solutions are x=−8 and x=0 Put the quadratic in standard form 7 x squared plus 56 x equals 0 Factor out the GCF 7 x left parenthesis x plus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x plus 8 equals 0 The solutions are x equals negative 8 and x equals 0
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Answer 1

To solve the quadratic equation \(7x^2 = 56x\), we need to follow these steps:

1. Put the quadratic in standard form: \[ 7x^2 - 56x = 0 \]

2. Factor out the GCF (Greatest Common Factor): The GCF of \(7x^2\) and \(56x\) is \(7x\): \[ 7x(x - 8) = 0 \]

3. Set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]

4. Solve for \(x\): From \(7x = 0\): \(x = 0\)

   From \(x - 8 = 0\): \(x = 8\)

So the correct response showing the right steps is:

• Put the quadratic in standard form: \(7x^2 - 56x = 0\)
• Factor out the GCF: \(7x(x - 8) = 0\)
• Set each factor equal to zero: \(7x = 0\) and \(x - 8 = 0\)
• The solutions are: \(x = 0\) and \(x = 8\)

Thus, the second option provided is the correct one.

Final Answer: Put the quadratic in standard form: \(7x^2 - 56x = 0\) Factor out the GCF: \(7x(x - 8) = 0\) Set each factor equal to zero: \(7x = 0\) and \(x - 8 = 0\) The solutions are: \(x = 0\) and \(x = 8\)