Finding Zeros of Polynomials Made Easy #maths #algebra #studyhacks

Added: 2026-06-02

[00:00:00]Let's go and find the zeros of this polomial function raised to the fifth power. First thing I'm going to do is I'm going to replace y with zero. The reason being we want to be able to find the values of x that are going to satisfy the equation when it's equal to zero. The next thing I want to do is see if I can factor out any common terms.

[00:00:14]Hopefully recognize that all three of these terms are divisible by x. So I can go ahead and factor that out and rewrite it as a product.

[00:00:22]All right. The next thing I recognize here is that this is a tromial. And I know from my practice of quadratic tromials that all tromials can be factored or if they can be factored or actually they can they can always be factored down into a product of two binomials.

[00:00:35]Okay, so I'm going to write down my products of two binomials. I know my first two terms always multiply to give me an x 4th. Now for quadratic tromials, x * x gave me x^2. But in this example, I need them to multiply to give me an x^2 or x 4th. So I'm going to raise the power of my two factors to x^2 * x^2.

[00:00:51]That's critically important because again remember our inner and our outer need to both be the same term if our middle term is going to be an x^2 which in this case it's -4x^2. Now I look at this and I say what two numbers multiply to give me 3 and add to give me a4.

[00:01:03]Ladies and gentlemen I only have one option x - 3 and x - 1. Now you can see I have a product of factors equal to zero. So I can apply the zero product property.

[00:01:14]So by taking each factor setting equal 0 I can now go and solve. So I have 1 0 x= 0 add three take the square root include plus or minus so x= plus or minus the square roo of 3 add 1 take the square root x is going to equal plus or minus one now I have found all five zeros with a multiplicity of one of this polomial function