Given a Irrational Factor, Find All the Zeros

👉 Learn how to find all the zeros of a polynomial given one irrational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Note that when the square root of a non-perfect square is a factor of a polynomial, that the negative of the square root of the non-perfect square is also a factor of the polynomial.

To find the zeros of a polynomial when one of the zeros is known, we use synthetic division to divide the polynomial with the given zero or we use long division to divide the polynomial with the given zero expressed in factor form. This gives the other factor of the polynomial, which can be further factored by dividing with the negative of the square root of the non-perfect square and then further factored (if need be) using any of the techniques for factoring polynomials.

After we have factored the polynomial, we can then use the zero product property to evaluate the factored polynomial and hence obtain the remaining zeros of the polynomial. Recall that the zero-product property states that when the product of two or more terms is zero, then either of the terms is equal to 0.

Organized Videos:
✅Find all the Remaining Zeros Given a Factor or Zero
✅Find all the Remaining Zeros Given one irrational Zero
✅Find all the remaining zeros given one complex zero
✅Find all the remaining zeros given one rational zero

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[GusThePianist]

I just got done doing a whole round of "dang it i wrote that wrong" and "wow, i forgot the double negative again" lol I'm glad I'm not alone 😂
Great content :)

[astrochemistry]

Hello sir! I am sixth grader at Mary Evans Texas, I want to see an video (simple for my mindset) on factoring a higher degree polynomial. Thank you!