Q:

The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses?

Accepted Solution

A:
Answer: [tex]6x^2+11[/tex] Step-by-step explanation: Given the polynomial of degree 3: [tex]24x^3 - 54x^2 + 44x -99[/tex] You can observe make two groups or two terms each: [tex](24x^3 + 44x) - (54x^2 + 99)[/tex]The Greatest Common Factor (GCF), is the highest number that divides into two or more numbers without leaving remainder.  You can observe that the GCF of both set are factored out ([tex]4x[/tex] and [tex]9[/tex]), then, you can find  the common factor that is missing from both sets of parentheses with this procedure: [tex](\frac{24x^3}{4x}+\frac{44x}{4x})-(\frac{54x^2}{9}+\frac{99}{9})=(6x^2+11)-(6x^2+11)[/tex] You can observe that the common factor that is missing from both sets of parentheses is: [tex]6x^2+11[/tex]