To analyze the polynomial x² – 6x – 27, let’s first express it in its standard form, which is already done. The polynomial is a quadratic expression.
Next, we can attempt to factor the quadratic. To do this, we look for two numbers that multiply to give us the product of the coefficient of x² (which is 1) and the constant term (-27), so we need two numbers that multiply to -27 and add to -6.
The numbers that fulfill these criteria are -9 and +3. This means we can factor the expression as follows:
x² – 6x – 27 = (x – 9)(x + 3)
This gives us the factored form of the polynomial. In summary, the expression can be viewed in two different ways:
- As a four-term polynomial: x² – 6x – 27
- As a factored expression: (x – 9)(x + 3)