Question

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

This table outlines the steps to solve a quadratic equation, showing the progression from standard form to the final solutions.
Steps Solution
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

Table with 2 columns and 5 rows.Row 1: Column 1, 'Steps'; Column 2, 'Solution' Row 2: Column 1, 'Put the quadratic in standard form'; Column 2, 'x minus 8 is equal to 0' Row 3: Column 1, 'Factor out the GCF'; Column 2, 'No GCF' Row 4: Column 1, 'Set each factor equal to zero'; Column 2, 'x minus 8 is equal to 0' Row 5: Column 1, 'The solutions are'; Column 2, 'x is equal to 8'

This table outlines the steps to solve a quadratic equation, showing the progression from standard form to the final solutions.
Steps Solution
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

Table with 2 columns and 5 rows.Row 1: Column 1, 'Steps'; Column 2, 'Solution' Row 2: Column 1, 'Put the quadratic in standard form'; Column 2, '7 x squared minus 56 x is equal to 0' Row 3: Column 1, 'Factor out the GCF'; Column 2, '7 x open paren x minus 8 close paren is equal to 0' Row 4: Column 1, 'Set each factor equal to zero'; Column 2, '7 x is equal to 0 and x minus 8 is equal to 0' Row 5: Column 1, 'The solutions are'; Column 2, 'x is equal to negative 7 and x is equal to 8'

This table outlines the steps to solve a quadratic equation, showing the progression from standard form to the final solutions.
Steps Solution
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

Table with 2 columns and 5 rows.Row 1: Column 1, 'Steps'; Column 2, 'Solution' Row 2: Column 1, 'Put the quadratic in standard form'; Column 2, '7 x squared plus 56 x is equal to 0' Row 3: Column 1, 'Factor out the GCF'; Column 2, '7 x open paren x plus 8 close paren is equal to 0' Row 4: Column 1, 'Set each factor equal to zero'; Column 2, '7 x is equal to 0 and x plus 8 is equal to 0' Row 5: Column 1, 'The solutions are'; Column 2, 'x is equal to negative 8 and x is equal to 0'

This table outlines the steps to solve a quadratic equation, showing the progression from standard form to the final solutions.
Steps Solution
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=8

Table with 2 columns and 5 rows.Row 1: Column 1, 'Steps'; Column 2, 'Solution' Row 2: Column 1, 'Put the quadratic in standard form'; Column 2, '7 x squared minus 56 x is equal to 0' Row 3: Column 1, 'Factor out the GCF'; Column 2, '7 x open paren x minus 8 close paren is equal to 0' Row 4: Column 1, 'Set each factor equal to zero'; Column 2, '7 x is equal to 0 and x minus 8 is equal to 0' Row 5: Column 1, 'The solutions are'; Column 2, 'x is equal to 0 and x is equal to 8'

Answer 1

The correct table is the last one (the one that gives the solutions x = 0 and x = 8).

Work: 7x^2 = 56x → 7x^2 − 56x = 0 → factor 7x(x − 8) = 0 → 7x = 0 or x − 8 = 0 → x = 0 or x = 8.