Fill in the blanks to write x2+14x+24=0

Question

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 add up to 14 (the coefficient of \( x \)) and multiply to 24 (the constant term).

The numbers that satisfy these conditions are 12 and 2, since:

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

Thus, we can write the factored form of the equation as:

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

So the filled blanks would be:

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