Question

the polynomial $24x^3 - 54x^2 + 44x - 99$ is factored by grouping.
$24x^3 - 54x^2 + 44x - 99$
$24x^3 + 44x - 54x^2 - 99$
$4x(\\_\\_\\_\\_) - 9(\\_\\_\\_\\_)$
what is the common factor that is missing from both sets of parentheses?
\\(\bigcirc\\) $6x + 11$
\\(\bigcirc\\) $6x - 11$
\\(\bigcirc\\) $6x^2 + 11$
\\(\bigcirc\\) $6x^2 - 11$

Explanation:

Step1: Factor first group

Take \(24x^3 + 44x\), factor out \(4x\): \(24x^3\div4x = 6x^2\), \(44x\div4x = 11\), so \(24x^3 + 44x = 4x(6x^2 + 11)\).

Step2: Factor second group

Take \(-54x^2 - 99\), factor out \(-9\): \(-54x^2\div(-9)=6x^2\), \(-99\div(-9)=11\), so \(-54x^2 - 99 = -9(6x^2 + 11)\).

Answer:

C. \(6x^2 + 11\)