Factor completely [tex]2x^3 + x^2 - 18x - 9[/tex].

The completely factored form of 2x³ + x² - 18x - 9 is (2x + 1)(x - 3)(x + 3).
We have,
To factor completely the expression 2x³ + x² - 18x - 9, we can follow these steps:

Step 1: Group the terms in pairs:

(2x³ + x²) + (-18x - 9)

Step 2: Factor out the greatest common factor from each pair:

x²(2x + 1) - 9(2x + 1)

Step 3: Observe that we have a common binomial factor of (2x + 1).

Factor it out:
(2x + 1)(x² - 9)

Step 4: The binomial (x² - 9) is a difference of squares and can be further factored as:

(2x + 1)(x - 3)(x + 3)
Therefore,
The completely factored form of 2x³ + x² - 18x - 9 is (2x + 1)(x - 3)(x + 3).
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Answered by swapnalimalwadeVT | 2024-06-24

2 x 3 + x 2 − 18 x − 9 = x 2 ( 2 x + 1 ) − 9 ( 2 x + 1 ) = ( 2 x + 1 ) ( x 2 − 9 ) = ( 2 x + 1 ) ( x 2 − 3 2 ) = ( 2 x + 1 ) ( x − 3 ) ( x + 3 )

Answered by Anonymous | 2024-06-25

The polynomial 2 x 3 + x 2 − 18 x − 9 can be completely factored as ( 2 x + 1 ) ( x − 3 ) ( x + 3 ) . We achieved this by grouping the terms, factoring out common factors, and recognizing a difference of squares. The final expression represents the polynomial in its simplest factored form.
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Answered by Anonymous | 2024-08-26