Question

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? 6x + 11 6x − 11 6x2 + 11 6x2 − 11

Answer 1

24x³ - 54x² + 44x - 99 =
(24x³ + 44x) - (54x² + 99) =
4x(6x²+11) - 9 (6x² + 11) =
(4x-9)(6x²+11)

Answer: (6x²+11)

Answer 2

The common factor that is missing from both sets of parentheses is:

`6X^2+11`

Explanation:

We are given a polynomial of degree 3 as:

`24x^3-54x^2+44x-99`

Now we have to factor the given polynomial using grouping.

We proceed in the following steps:

• 
  `24x^3-54x^2+44x-99`

• 
  `24x^3 + 44x-54x^2-99`

• 
  `4x(6x^2+11)-9(6x^2+11)`

( Since we take out the common terms in each of the following groups and obtain an common factor in both the groupings)

Hence, the common factor that is missing is:

`6x^2+11`