Find all Zeros of the Polynomial Function f(x) = x^3 - 3x^2 - 4x + 12 MyMathlab Homework

TL;DR

Learn how to find the possible rational zeros of a polynomial function using the rational zero theorem and synthetic division.

Transcript

so a function f of X equals x cubed minus 3x squared minus 4x plus 12 and we're being asked to find the possible rational zeros so you start by looking at the factors of the last one so factors of 12 over the factors of the first one so factors of 1 the factors of 12 are 1 2 3 4 6 and 12 and the factors of the first one are just 1 it's always facto... Read More

Key Insights

• 0️⃣ The rational zero theorem provides a systematic way to find the possible rational zeros of a polynomial function.
• 0️⃣ Synthetic division is an efficient method to test the possible rational zeros and identify the actual zeros.
• 🧑‍🏭 The factors of the last term are divided by the factors of the leading coefficient to determine the possible rational zeros.

Summary & Key Takeaways

• To find the possible rational zeros of a polynomial function, check the factors of the last term divided by the factors of the leading coefficient.

• Use the rational zero theorem to identify the possible rational zeros.

• Use synthetic division to test several possible rational zeros and identify the actual zero.