Supply the numbers to write x2+10x+16=0

Question

in its factored form. Enter the lesser number first.(1 point)
(x+

)(x+

)=0

Answer 1

To factor the quadratic equation \( x^2 + 10x + 16 = 0 \), we need to find two numbers that multiply to \( 16 \) (the constant term) and add to \( 10 \) (the coefficient of \( x \)).

The two numbers that satisfy these conditions are \( 2 \) and \( 8 \), since:

• \( 2 \times 8 = 16 \)
• \( 2 + 8 = 10 \)

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

\[ (x + 2)(x + 8) = 0 \]

So the answer is:

\((x + 2)(x + 8) = 0\), where the lesser number is \( 2 \) and the greater number is \( 8 \).