Write the product as linear factors: (x^2−4)(x^2−9).

Answer 1

The product (x^2−4)(x^2−9) can be written as linear factors as follows:

(x+2)(x-2)(x+3)(x-3)

Answer 2

Decompose the polynomial x3−2x^2−5x+6 into its linear factors, given that x−1 is a factor.

Answer 3

If x - 1 is a factor of the polynomial x^3 - 2x^2 - 5x + 6, it means that by dividing x^3 - 2x^2 - 5x + 6 by x - 1, we will get a quotient with no remainder.

Performing the long division:

x^2 -x - 6
-----------------
x - 1 | x^3 - 2x^2 - 5x + 6
- (x^3 - x^2)
--------------
- x^2 - 5x
+ (x^2 - x)
-------------
-6x + 6
+(6x - 6)
--------------
0

Therefore, the quotient is x^2 - x - 6.

So, the polynomial x^3 - 2x^2 - 5x + 6 can be factored as (x - 1)(x^2 - x - 6).