Question

The polynomial x3 + 4x2 – 9x – 36 has 4 terms. Use factoring by grouping to find the correct factorization.

Answer 1

To factor the polynomial x^3 + 4x^2 - 9x - 36 by grouping, we grouped terms, factored out common factors, and used difference of squares to fully factor it into (x + 4)(x + 3)(x - 3).

Step-by-step explanation:

To factor the polynomial x^3 + 4x^2 − 9x − 36 by grouping, we follow these steps:

1. Group the terms into pairs: (x^3 + 4x^2) and (-9x − 36).
2. Factor out the common factor from each group: x^2(x + 4) and -9(x + 4).
3. Combine the groups as they both contain the factor (x + 4): (x + 4)(x^2 - 9).
4. The term x^2 - 9 is a difference of squares and can be further factored: (x + 3)(x - 3).
5. Therefore, the fully factored form of the polynomial is (x + 4)(x + 3)(x - 3).

By factoring by grouping, we have successfully found the correct factorization of the given polynomial.

Answer 2

x^3 + 4x^2 – 9x – 36
Factor out common terms in the first two terms and the last two terms
x^2 (x + 4) - 9 (x + 4)
factor out the common term (x + 4)
(x + 4) (x^2 - 9)
Rewrite
(x + 4) ( x^2 - 3^2)
Use the difference of squares
(x + 4) (x + 3) (x - 3)

Hope this helps :)