FACTORING but it keeps getting HARDER!!! 🧠 (how far can you get???)

[@Utesfan100]

Factoring expressions involving radicals, as seen in evaluating derivatives of radicals using the limit definition, should be on this list. The last one is close to x^4+4, which shows that the sum of squares can sometimes be factored (by completing the square on the middle term).

[@robertveith6383]

@ JensenMath -- An alternative beginning to Level 7 is to group them as: 3x^5 - 24x^2 + x^4 - 8x - 4x^3 + 32 = 3x^2(x^3 - 8) + x(x^3 - 8) - 4(x^3 - 8) = (x^3 - 8)(3x^2 + x - 4) = etc.

[@IAMswayingwillow]

I love the way this was presented it makes it fun and it was something I needed to learn

[@Fire_Axus]

your feelings are irrational

[@adw1z]

Doing before seeing the answers: 1. 12x^2 (2 + 3x^3) 2. (x+7)(x-4) 3. 2(2x^2 + 3x - 20) = 2(2x^2 +8x - 5x -20) = 2(x+4)(2x-5) 4. (2x^2-3y)(x^2-9y) 5. y^2 (x^4 - 3x^3) - z^4 (9x^2 - 27x) = y^2 x^3 (x-3) - 9z^4 x (x - 3) = x ( (yx)^2 - 9z^4) (x-3) = x(xy + 3z^2 )(xy - 3z^2)(x-3) 6. (x^3 - 27)(x^3 + 1) = (x-3)(x+3)(x^2 + 3x + 9)(x^2 - x + 1) 7. Notice (1,3,-4) and (-8,-24,32): = x^3 (3x^2 + x - 4) - 8(3x^2 +x-4) = (x-2)(x^2 + 2x + 4)(3x^2 +x-4) = (x-2)(x-1)(3x+4)(x^2 + 2x + 4) 8. plugging in -1 gives 0, so equating coeffs: = (x+1)(3x^3 + bx^2 + cx -12) b + 3 = 2, b = -1 ; c - 12 = -32 , c = -20 = (x+1)(3x^3 - x^2 - 20x -12) Plugging in -2 makes second factor 0; = (x+1)(x+2)(3x^2 + dx - 6) 2d - 6 = -20, d = -7 = (x+1)(x+2)(3x^2 -7x - 6) = (x+1)(x+2)(x-3)(3x+2) 9. (2x+3y)^2 - (3m + 4n)^2 = (2x+3y+3m+4n)(2x+3y-3m-4n) 10. (2x+3)^3 - 64y^3 = (2x+3-4y)(4x^2 + 12x + 9 + 8xy + 12y + 16y^2) Can only complete the square on second factor, not simplify further? 11. x^4 + 4x^2 + 16 If u = x^2, then u^2 + 4u + 16 has no real roots. Therefore factorising will most likely take the form: (x^2 + ax + b)(x^2 + cx + d), where a,c non-zero x^3: a + c = 0 so a = -c ; now form is: (x^2 + ax + b)(x^2 -ax + d); x: -ab + ad = 0 so a(d-b) = 0 so d = b ==> form is (x^2 + ax + b)(x^2 -ax + b) x^2 : 4 = -a^2 + 2b Have b^2 = 16 so b = +-4 and since a^2 = 2b - 4 > 0, b = 4 and so a = +-2 ==> x^4 + 4x^2 + 16 = (x^2 + 2x + 4)(x^2 - 2x + 4) Edit: I missed the trick in the last part: (x^2 +4)^2 - (2x)^2 and difference of 2 squares. I should’ve seen this!

[@KeplerYubified]

these videos are so good - i love them - next can you do COMPOUND AREA BUT IT KEEPS GETTING HARDER

[@pietergeerkens6324]

Thank you. Very nice problems for a morning "factoring kata". If one knows the Sophie Germain identity (for #11) then IMHO #7 & #8 are the most challenging (or, alternatively, the most work) as 9 and 10 get simpler again.

[@ramzfn3543]

jensen math is the best! I love you dude your awesome:)

[@djfghjif]

im in grade 7 and learnt factoring until level 6. how you explain it is really clear and makes it look easier. appreciate it

[@sel5595]

what? my little brother is in grade 7 and they are learning ab patterns 💀💀

[@Mathmaniac-vw9ip]

@@sel5595 bro, we learned that in grade 5 💀

[@alexfrosa2163]

This was easy for those who did the Kumon maths program. The beginning of level J is full of such factoring tricks and challenges!

[@G3R0George]

For level 6, could you have factored the trinomial final factors into binomial factors?

[@alokmishra4293]

No, they are unfactorise-able

[@DriftinVr]

Got them all! Very good quiz on factoring

[@antik8867]

We need more videos like this

[@robertveith6383]

@ JensenMath -- For Level 6, you misspelled "Parallel."

[@RR-bs9mr]

me who skipped to the end

[@riyabhaduri3206]

Same

[@williamraleigh7546]

Personally, I can't edge that quickly, so I like to stroke it throughout the entire video. Then I finish at the end.

[@jeremyjay380]

The last one should be fully factored as: [(x+2)(x+2)-2x][(x-2)(x-2)+2x] And yes, I did use his logic.

[@Fire_Axus]

this is easy for you because you have them figured out. also where are the non-polynomials?

[@DonDak4]

As a 12 years old , I can’t even tying my shoes

[@skyofquacks]

7:13 "Paralell Parking"

[@noahvale2627]

Difference is my favorite formula

[@bijipeter1471]

Thank you,sir

[@realfrogZ]

im 4th grade and i can do only level one. pretty good right?🙃

[@auztenz]

Yeah! This shows your interested in maths! Keep on going

[@georgestoica9744]

Can probably do all of it , just got 120 out of 120 on further mechanics

[@mehmetseyhmus]

Why did you extend it, factor it directly, it can be done even from the mind.

[@ataulhaye5801]

love these videos

[@muskyoxes]

Difficulty: any Canadian team winning the Cup

[@nkl7873]

Why was the lvl 10 more difficult than lvl 11?(i mean i solved it both and found lvl 11 easier)

[@p.g.wallychopin]

Level 11 it's actually level 1 x⁴ + 4x² + 16 = (x²)² + (4)(x²) + (4)² = (x²)² + (2)(4)(x²) + (4)² - (2x)² = (x² + 4)² - (2x)² = (x² + 2x + 4)(x² - 2x + 4)

[@Monitorbread]

me who lost all of them

[@reomikage-w4g]

its the good stuff when its get harder in level 5

[@taito404]

I'd say level 9 is easier than level 8 tbh

[@kawai8689]

On level 5 you don't need to take the x common we can do it without doing that.

[@masterofdeception9802]

maybe limits?

[@exodus_20_15]

14:50 Ouch.

[@sayedizaanahmad]

Level 6 could have been factored even more into (x-3) (x+3) (x+3) (x+1) (x-1) (x-1)

[@adw1z]

Not true, easy to see since plugging in x = 1 doesn't give 0

[@jupitertank7133]

Level 6 after fully factoring has 2 real solutions, -1 & 3 and the rest four solutions are complex pair of conjugated!!!

[@Beckham-pw4ee]

My max is level 7

[@botot0]

so nice

[@dhamakedarvlog114]

I wasn able to solve all except 8 and 11

[@zxtremedemon]

I’m in grade 8 so I think getting to level 6 is good for my grade

[@zxtremedemon]

Also, running a marathon is easier than pleasing my parents (at my age I already did that, just before the time limit.)

[@shivx3295]

nah atleast till level 9

[@riyabhaduri3206]

Level 9,11,5 is easy

[@sennpowerhv6922]

I got level 2 but not 1

[@shivx3295]

all of them were pretty easy not that tough to factor out i think even my 15 year old fiends could do them need some more difficult factoring questions

[@Morax___]

The last one shouldn't be there

[@manitmaniar616]

All levels can be done by a ninth grade

[@shivx3295]

so true even i could do it i am an 8th grader from india

[@Ricardo_S]

A get to level 10

[@Thiefy_]

…

[@rakeshsharma5973]

All of these are child level.

[@Sbbooster]

Agreed I’m 8 and did all of them😊

[@kevinchen9389]

.

[@jammymlbbgameplay]

Level 11 easy

[@cpsc4]

The level 2 needs some fixing the sum must be -3 and the product must be -28. The answers are -7 and 4

[@robertveith6383]

Level 2 does not need any fixing. The middle term is correctly given as positive 3x. Wrong. There are no "answers." There is no equation to be solved. There is just an expression to be factored.