How to find the roots of a polynomials by factoring
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- čas přidán 14. 03. 2015
- 👉 Learn how to find all the zeros of a polynomial. 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.
To find the zeros of a polynomial, we first equate the polynomial to 0 and then use our knowledge of techniques of factoring polynomials to factor the polynomial. After we have factored the polynomial, we can then use the zero-product property to evaluate the factored polynomial and hence obtain the 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 term is equal to 0.
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Organized Videos:
✅Zeros of a Polynomial by Factoring
• Zeros of a Polynomial ...
✅Zeros and Multiplicity of Polynomials | Learn About
• Zeros and Multiplicity...
✅How to Find all of the Zeros by Sum and Difference of Two Cubes
• How to Find all of the...
✅How to Find all of the Zeros by Grouping
• How to Find all of the...
✅How to Find all of the Zeros in Factored Form
• How to Find all of the...
✅How to Find all of the Zeros by Factoring 5th Degree
• How to Find all of the...
✅How to Find all of the Zeros by Difference of Two Squares
• How to Find all of the...
✅How to Find all of the Zeros by Factoring 4th Degree
• How to Find all of the...
✅How to Find all of the Zeros of a 3rd Degree Polynomial
• How to Find all of the...
✅How to Find all of the Zeros Without Factoring
• How to Find all of the...
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I still dont get it.
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1:22 what technique was used? I've never seen it before
It is middle term split up . You can look that up on CZcams.
That's like a basic thing to learn in quad eqn
🤣🤣🤣🤣🤣 I also
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Sanaol naintindihan. Hayss.
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Ang hirap kumuha ng roots, tangenang yan.
Okay one question plsss answer it for me if you know it,
If the answer we got is 3 we can write in a factor form as(X-3) right? What about if we get a zero how to we write it in a factor form????
Yes if it’s positive 3 then it would be (x-3) the zero is the same (x+0) or (x-0) it doesn’t matter in the end because 0+0=0 and 0-0=0
factor of 0 is just (x+0), or (x)
Just saved me from failing a test
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i still don’t get it.
i hate online school tremendously
HOW MANY REAL ROOT DOES THE POLINOMIAL X^4+3X^2+5 HAVE?
4
How would you do x^6-7x^3-8 = 0
raise it to three instead of (what he did) 2.
(x^3-8)(x^3+1)
@@hubertmonzon7223 yes that only factors to 2 factors. But the end result would be 6 factors if done correctly.
I just found that there is another formula
It is an interesting equation, it´s solutions are vertices of two equilateral triangles in the complex plane. You have to know and be comfortable with complex numbers, are you? If you are, then: Let y = x^3 , then the equation transforms to : y^2 - 7y - 8 = 0. A quadratic equation where you can use the quadratic formula. Once you get the two solutions of "y" you have to find the cubic root of "y", Three solutions for each, for a total of six solutions. Solutions X = -1, -2, -1 ± (3)^(1/2)*sqrt(-1) , +.5 ± 1*sqrt(-1)
@@youtubeaccount0x073 2 real solutions, 4 complex solution. it is 6 solutions not factors. (some factors are quadratic, and have 2 solutions)
saving my algebra 2 grade
find roots of x^4-2x^3+2x^2+1=0 .... please
What if the only thing they have in common is a 1?
For example: x^3 + 4x^2 - 20x - 48
my question exactly
rational root theorem.
for any polynomial, a possible rational root can be expressed as (+-)(p/q), where p is a factor of the constant term, and q is a factor of the coefficient of the largest degree term.
in this case, the constant term in -48, but since the theorem accounts for plus or minus, we can just factor 48.
1x48
2x24
3x16
4x12
6x8
since the coefficient of the largest term is just one, we don't need it, so the numbers listed above, and there negative counterparts, are possible roots for the polynomial. after plugging in many numbers, and after a lot of trial and error, we can figure out one root of the polynomial is -2. now that we know one root of the polynomial is -2, we know one factor of the polynomial is (x+2). this means we can divide the polynomial by (x+2), end up with a quadratic, and factor that normally. although that is pretty easy, I will also demonstrate how to do that.
dividing polynomials, and demonstrating it using a keyboard and mouse, in a CZcams comment section is too hard, so just watch a CZcams video on that.
if we divide the polynomial, we get x^2+2x-24
lets use CTS
x^2+2x=24
x^2+2x+1=25
(x+1)^2=25
x+1=5 x+1=-5
x=4 x=-6
so there you go. using rational root theorem we can figure out the roots of the polynomial, and they come to be -2, 4, and -6.
if you have any other questions feel free to reply.
Bonus fact: Both of those factors from the x^4 factorization could also have been factored again, because each factor was a difference of squares.
But, in this case, it was faster to just take the root of both sides because they were simple squares.
I need this now on reverse, I have to find 2 possibilities for p(x) if it has 3 roots x= 5, x= -10 and x= 0 😭😭😭 I don't know how to
Still need help?--
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"And guess what? That works now" hehehe
Boom
@@brianmclogan 😂🤣
Thanks for replying
Wow
How about 3x³+24x²+48x
just take out a 3x, and solve like a quadratic
Sir can I ask why u didn't factor the (x^2-4) and (x^2-4) with the factoring technique sum of the difference of two squares? In that case u can get all real roots? Can I get u'r response to end my confusion???
he used plus and minus, but i agree with you, he shouldve factored
Not sure you are right on x = -2 or x=2, it should have been 2
should have dropped the pen at the last
Love from India 🥰
HOW DID HE GET A 4 IN THE BEGINNING GUYS IM SO CONFUSED
Guys can someone answer my Question
Find the roots of each equation by factoring
1. 15a³ - 9a² = 0
2. 8x⁴ = 6x³
3. 12a² + 12a = 0
4. x² + 3× - 4x - 12 = 0
I cant understand this, my teacher is too lazy to teach us and just gives us works without teaching 😩
This is an SAT question lol
According to other sites there is no x = 2 and -2 for an answer
Together +&- are normal to come
I feel so stupid I've been learning this for weeks now and I still don't get it. Idk why my brain doesn't get it.
First pretend to understand it the second time you will understand
I heard a bit of an accent come out of him at the very beginning of the video. Anyone else notice?
No wonder drop out rates are high...
Man this is so confusing .
bro why u always walk out after u solve the equation?