factor each polynomial
r3+27
Isn't there a formula for the sum (or difference) of two perfect cubes?
it should read factor out the common factor from each polynomial
To factor the polynomial r^3 + 27, we can use a special identity called the sum of cubes. The sum of cubes formula states that:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
In this case, we have r^3 + 27, which can be rewritten as r^3 + 3^3.
Using the sum of cubes formula, we can substitute a = r and b = 3 into the formula to factor the polynomial:
r^3 + 27 = (r + 3)(r^2 - 3r + 9)
Therefore, the factored form of the polynomial r^3 + 27 is (r + 3)(r^2 - 3r + 9).