Question
Which of the following quadratic equations can be solved by factoring?(1 point)
Responses
A) x^2=2x+8
x squared equals 2 x plus 8
B) x^2=4x−10
x squared equals 4 x minus 10
C) −12=x^2−x
negative 12 equals x squared minus x
D) x^2+9x=8
Responses
A) x^2=2x+8
x squared equals 2 x plus 8
B) x^2=4x−10
x squared equals 4 x minus 10
C) −12=x^2−x
negative 12 equals x squared minus x
D) x^2+9x=8
Answers
GPT-4o mini
To determine which of the given quadratic equations can be solved by factoring, we first need to rearrange each equation into standard form (ax^2 + bx + c = 0).
Let's do that for each option:
A) \( x^2 = 2x + 8 \)
Rearranging gives:
\( x^2 - 2x - 8 = 0 \)
This can be factored as \( (x - 4)(x + 2) = 0 \).
B) \( x^2 = 4x - 10 \)
Rearranging gives:
\( x^2 - 4x + 10 = 0 \)
This does not factor nicely with integer values.
C) \( -12 = x^2 - x \)
Rearranging gives:
\( x^2 - x + 12 = 0 \)
This does not factor nicely with integer values.
D) \( x^2 + 9x = 8 \)
Rearranging gives:
\( x^2 + 9x - 8 = 0 \)
This factors to \( (x + 8)(x + 1) = 0 \).
So, the equations that can be factored are:
- Option A: \( x^2 - 2x - 8 = 0 \) can be factored.
- Option D: \( x^2 + 9x - 8 = 0 \) can be factored.
The responses that can be solved by factoring are A) and D). If you have to choose only one response, you can select either A or D. If allowed to choose multiple answers, then both A and D are correct.
Let's do that for each option:
A) \( x^2 = 2x + 8 \)
Rearranging gives:
\( x^2 - 2x - 8 = 0 \)
This can be factored as \( (x - 4)(x + 2) = 0 \).
B) \( x^2 = 4x - 10 \)
Rearranging gives:
\( x^2 - 4x + 10 = 0 \)
This does not factor nicely with integer values.
C) \( -12 = x^2 - x \)
Rearranging gives:
\( x^2 - x + 12 = 0 \)
This does not factor nicely with integer values.
D) \( x^2 + 9x = 8 \)
Rearranging gives:
\( x^2 + 9x - 8 = 0 \)
This factors to \( (x + 8)(x + 1) = 0 \).
So, the equations that can be factored are:
- Option A: \( x^2 - 2x - 8 = 0 \) can be factored.
- Option D: \( x^2 + 9x - 8 = 0 \) can be factored.
The responses that can be solved by factoring are A) and D). If you have to choose only one response, you can select either A or D. If allowed to choose multiple answers, then both A and D are correct.
The answer is just A) x^2=2x+8
GPT-4o mini
You are correct! The quadratic equation in option A) \( x^2 = 2x + 8 \) can be rearranged and factored easily.
When rearranged to the standard form, it becomes:
\[ x^2 - 2x - 8 = 0 \]
This can be factored into:
\[ (x - 4)(x + 2) = 0 \]
So the solutions are \( x = 4 \) and \( x = -2 \).
While option D also leads to a quadratic that can be factored, it seems the focus was on just option A in your context. Thank you for the clarification!
When rearranged to the standard form, it becomes:
\[ x^2 - 2x - 8 = 0 \]
This can be factored into:
\[ (x - 4)(x + 2) = 0 \]
So the solutions are \( x = 4 \) and \( x = -2 \).
While option D also leads to a quadratic that can be factored, it seems the focus was on just option A in your context. Thank you for the clarification!