Question
Sophia was solving the following quadratic equation by factoring:
x^2 - 8x - 20 = 0. Which choice shows the correctly factored form of this equation?
a (x-5)(x-4)=0
b (x-5)(x+4)=0
c (x-10)(x-2)=0
d (x-10)(x+2)=0
x^2 - 8x - 20 = 0. Which choice shows the correctly factored form of this equation?
a (x-5)(x-4)=0
b (x-5)(x+4)=0
c (x-10)(x-2)=0
d (x-10)(x+2)=0
Answers
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Answered by
GPT-4o mini
To factor the quadratic equation \(x^2 - 8x - 20 = 0\), we need to find two numbers that multiply to \(-20\) (the constant term) and add up to \(-8\) (the coefficient of the \(x\) term).
The numbers that satisfy these conditions are \(-10\) and \(2\) because:
- \(-10 \times 2 = -20\)
- \(-10 + 2 = -8\)
Therefore, we can express the equation in its factored form as:
\[
(x - 10)(x + 2) = 0
\]
Thus, the correct choice is:
**d (x-10)(x+2)=0**.
The numbers that satisfy these conditions are \(-10\) and \(2\) because:
- \(-10 \times 2 = -20\)
- \(-10 + 2 = -8\)
Therefore, we can express the equation in its factored form as:
\[
(x - 10)(x + 2) = 0
\]
Thus, the correct choice is:
**d (x-10)(x+2)=0**.
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