Let’s Factor The Polynomial….Step-by-Step….

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Math help with factoring using the difference of two squares. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at tcmathacademy....
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[@thinkaboutit..ministries]

I've been wanting to review my basic mathematics as a stepping stone to try and understand some more advanced concepts. Thanks so much for your channel!!!

[@marklyles3335]

I TUTOR MATH. I always brush-up to stay sharp. You are not alone!

[@lx95020]

I would have been an engineer if I would have had you as my math teacher..... I gave up on math when I started to struggle. I wasn't aware I was missing a few rules.

[@luvsicksaturn]

its never too late :)

[@devonwilson5776]

Greetings. Yes we can. When we factor X^4-81, we should get
(X-3)(X+3)(X^2+9).
This comes from the property that
a^2-b^2= (a-b)(a+b). Therefore,
X^4-81 can be represented as
(X^2-9)(X^2+9)= (X-3)(X+3)(X^2+9).

[@leetrask6042]

X^2 +9 can be factored into x+3i times x-3i this we get two imaginary roots.

[@bobwineland9936]

Patience definitely is a virtue and much required when a teacher such as yourself teaches.
Thank you so much for what you do.
This problem requires 4 solutions. X=3, X=(-3), X= 3i, X=-3i.

[@danieldennis9831]

Yes. because on of the rules of polynomials is a²-b²=(a+b)(a-b) because (a+b)(a-b) is a²+ab-ab+b² so if you changed x^4-81 to x^4+9x²-9x²-81 it factors. x²(x²+9)-9(x²+9)=(x²-9)(x²+9)=0 which splits to x²-9=0 x²+9=0 which becomes x²=9 and x²=-9 which becomes x=3,-3,3i,-3i.

[@jameseveridgeii1765]

quick question. has anyone here signed up for the math academy? if so how was your experience? i am trying to decide if i should enroll or not. so far i have nothing but good things to say about these videos, its always refreshing to see an instructor take the time to walk through each step instead of assuming that students should already know the basics.

[@Kleermaker1000]

Could have been a nice polynomial equation: (X^2 + 9)(X + 3)(X - 3) = 0, with X^2 = - 9. :)

[@kennethwright870]

X^4 = 81
(X^2)^2=81
Sqrt each side gives:
X^2=+-9
Sqrt each side provides:
X=+-3

[@chrisdissanayake6979]

(X^2 + 9) (X^2 - 9)
(X^2 + 9)(X^2 + 3)(X^2-3)
Thank you 🙏🏽

[@leavventuredellelolewwe7492]

Thanks for your Channel Sir 👍

[@bashiirsiciid606]

Very very good.

[@prof.lsteele6570]

Ok, I think I get it. Need to practice obviously. But tell me, why do you factor in the first place? What does it achieve?

[@alanhurdle3949]

Ty

[@amoh_raz6716]

I like this channel 👍👍😍 i just pretendes to myself that I'm in class 😂😂

[@kalyanbasak6494]

Namaskar sir, Answer (X+3)(X-3)(X²+9) sharing,is it corrected? thanks sir

[@MrArray1967]

I first took your expression like an equation, but there are no equal sign and then I got it.
👍🏻

[@Kame3248]

x⁴ - 81
((x²)² - 9²)
a² - b² = (a + b)(a - b), if a = x² & b = 9
(x² + 9)(x² - 9)
x² + 9 = 0
x² = -9
√(x²) = √(-9)
x = ± 3√(‐1) = ± 3i
x² - 9 = 0
x² - 3² = 0
a² - b² = (a + b)(a - b), if a = x & b = 3
(x + 3)(x - 3) = 0
x + 3 = 0
x = -3
x - 3 = 0
x = 3
Answer:
(x + 3i)(x - 3i)(x + 3)(x - 3)

[@greenmanofkent]

@@Kame3248 You are dealing with an equation; this video is dealing with an expression, not an equation.

[@gee6887]

@@Kame3248 thank you, very thorough.

[@joomratunsheik311]

Thank you sir

[@quiltanon]

(x^2-9)(x^2+9)

[@janclifford2281]

I ordered the algebra notes& never received them.

[@amoh_raz6716]

But teacher this one you've expand 😨 i was having this Idea but it seems expanded or you mean the special terms like this you just expand . GCF will only be seen in trinomial polynomial, isn't it??
Greating you from Kenya i need an explanation from you. Thanks

[@jimcraig2521]

Why doesn't X squared + 9 factor to (x + 3)(x + 3)?

[@bouchrabensellam6657]

(x+3)(x+3)= x square +6x+9
And we don’t have 6x there

[@mikedickerson1978]

The expression x^2 + 9 is actually referred to as the sum of squares. This simply means that there is a middle component that you must add between the x^2 and the 9 to make it a square expression. In this case, you have both 6x and -6x that could go into the x^2 + 9 expression. Either 6x or -6x can go into the expression to get either x^2 + 6x + 9 or x^2 - 6x + 9, because remember, 9 is the product of either 3^2 or (-3)^2.

[@rodolfomuyuela2528]

I think you must put a parentheses on - (9)square. Because without it, it will be +81 and not -81.

[@greenmanofkent]

No parentheses are required, because the order of operations rules state that the exponentiation (^9) is done first, making the expression x^4 - 81.

[@amandad6847]

So did no one else laugh when he said "I'm not trying to manipulate anyone" 🤣

[@fadakfadak5423]

You are amazing 🤩

[@hafsteinnbjargmundsson9450]

U!!]

[@bouchrabensellam6657]

The factorisation is not completed ? What about x square +9 ?

[@cain1830]

You cannot do anything else with x^2 + 9.

[@irwandasaputra9315]

x^4=3^4
x=3

[@mokooh3280]

There is insuffient info to make a call as you can make the solution anything

[@greenmanofkent]

This is not dealing with the "solution" of an equation - it is explaining with factoring an expression, and expressions do not have "solutions" (there is no '=' sign)

[@janoszala3078]

x=3=81 81-81=0 old scool

[@nueva_vida]

Poor students, very confused with so much blah blah blah just to get to the explain something so straight forward.......

[@Christopherdpenha]

John the Jackass🥹

[@cain1830]

You take too long to solve the problem.

[@jasonthompson5851]

I’m sure he can solve it quickly, but it takes a little time to teach it.

[@patriciagreen2365]

(X^2+9)(x^2-9)