Final answer:
To find factors of the cubic equation x³-7x²+7x-15, use the Rational Root Theorem to test possible rational roots and then employ polynomial division or synthetic division. Simplify the process by eliminating terms where possible. Remember that math provides many paths to the same answer.
Step-by-step explanation:
To find the factors of the cubic equation x³-7x²+7x-15, we need to apply various algebraic techniques. Since this is a higher-degree polynomial, the methods involve looking for rational roots and then using polynomial division or synthetic division to simplify it further once a factor is found. One technique is to use the Rational Root Theorem to test possible factors, which are the divisors of the constant term (in this case, ±15) divided by the leading coefficient (in this case, 1). If any of these possible factors are indeed roots, they can be used to factor the polynomial further.
Another method to solve a quadratic equation like x² +0.0211x -0.0211 = 0 is to apply the quadratic formula, but sometimes simplification can make the process easier, as it's often best to eliminate terms wherever possible to simplify the algebra. When factoring, always check the answer to see if it is reasonable.
It's also important to remember that math provides many paths to the same answer, which can be used to check and reinforce the solution you've found. This can include checking your factors against the original equation to ensure they work.