Question
X squared minus 3x - 28
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 - 3x - 28 \), we need to find two numbers that multiply to \(-28\) (the constant term) and add up to \(-3\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(-7\) and \(4\) because:
\[
-7 \times 4 = -28
\]
\[
-7 + 4 = -3
\]
Therefore, we can factor the expression as follows:
\[
x^2 - 3x - 28 = (x - 7)(x + 4)
\]
Thus, the factored form of the quadratic expression is:
\[
(x - 7)(x + 4)
\]
If you want to find the roots of the equation \( x^2 - 3x - 28 = 0 \), you can set each factor equal to zero:
1. \( x - 7 = 0 \) ⟹ \( x = 7 \)
2. \( x + 4 = 0 \) ⟹ \( x = -4 \)
So the solutions or roots of the equation are \( x = 7 \) and \( x = -4 \).
The numbers that satisfy these conditions are \(-7\) and \(4\) because:
\[
-7 \times 4 = -28
\]
\[
-7 + 4 = -3
\]
Therefore, we can factor the expression as follows:
\[
x^2 - 3x - 28 = (x - 7)(x + 4)
\]
Thus, the factored form of the quadratic expression is:
\[
(x - 7)(x + 4)
\]
If you want to find the roots of the equation \( x^2 - 3x - 28 = 0 \), you can set each factor equal to zero:
1. \( x - 7 = 0 \) ⟹ \( x = 7 \)
2. \( x + 4 = 0 \) ⟹ \( x = -4 \)
So the solutions or roots of the equation are \( x = 7 \) and \( x = -4 \).