To determine if a binomial is a factor of the quadratic expression 9x² + 643x + 8, we can apply factorization techniques or utilize the Rational Root Theorem to find potential factors.
First, we can look for factors by considering the roots of the equation 9x² + 643x + 8 = 0. This can be done using the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
where a = 9, b = 643, and c = 8. Plugging these values into the formula yields:
x = (-643 ± √(643² – 4 × 9 × 8)) / (2 × 9)
This calculation will give us the roots. If we find the roots, we can represent the quadratic as a product of binomials.
After completing the above calculations, you will see that one of the factors might be of the form (9x + m)(x + n), where m and n are some integers. Testing likely candidates for factors, such as (9x + 1) or (9x + 2), can help confirm.
Ultimately, through these methods, we can conclude which specific binomial is indeed a factor of the given quadratic expression.