Fill in the blanks to write x2+14x+24=0 in its factored form.(2 points) (x+ )(x+ )=0

Answer 1

To factor the quadratic equation \(x^2 + 14x + 24 = 0\), we need to find two numbers that multiply to 24 (the constant term) and add up to 14 (the coefficient of \(x\)).

The numbers that satisfy this are 12 and 2, since:

• \(12 \cdot 2 = 24\)
• \(12 + 2 = 14\)

So, we can write the equation in its factored form as:

\[ (x + 12)(x + 2) = 0 \]

Thus, filling in the blanks gives us:

\[ (x + 12)(x + 2) = 0 \]