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=−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=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=−8 and x=0
1 answer
1. Put the quadratic in standard form by moving the \(56x\) term to the left side of the equation:
\[ 7x^2 - 56x = 0 \]
2. Factor out the GCF, which in this case is \(7x\), since both terms are divisible by \(7x\):
\[ 7x(x - 8) = 0 \]
3. Set each factor equal to zero:
\[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]
4. Solve each equation for \(x\) to find the solutions:
\[ x = 0 \quad \text{from} \quad 7x = 0 \]
\[ x = 8 \quad \text{from} \quad x - 8 = 0 \]
Therefore, the solutions to the equation are \(x = 0\) and \(x = 8\).
The correct representation in the given options 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 \(x = 8\)
The incorrect options include suggesting that the solutions are \(x = -7\) or \(x = -8\), which are not correct for this equation. Only \(x = 0\) and \(x = 8\) satisfy the equation \(7x^2 = 56x\).