Can You Factor and Solve This Cubic Equation in Under 60 Seconds? - Fast Math Trick

[timeonly]

In the first cubic ( 10x^3 + 11x^2 - 2x - 3 ), we see that 10 & 11 and 2 & 3 pairs each differ by 1. So, immediately checked x=1 and x=-1 for roots: clearly 1 doesn't work since 10 & 11 are both + (no way to add to zero), but if we negate the coefficients of the odd-powered terms, we get -10+11+2-3 =-13+13=0 (yay!). Synthetic division verifies -1 as a root, and gives the quadratic 10x^2 + x - 3, from which we get the other 2 roots using the quadratic formula.

In the 2nd cubic ( 15x^3 - 31x^2 + 4 ), we see that neither x=1 nor x=-1 are roots. So we use other clues... p(x) has 2 sign-changes => either 2 or 0 R+ roots, and p(-x) has 1 sign-change => 1 R- root (guaranteed!!). Using the rational root theorem to get candidate rational roots +/- (1, 2, 4)/(1, 3, 5, 15), we 1st try +/- the "nicer" ones {2, 4, 1/3, 2/3}. Got lucky with +2 (not pure luck, if you notice that 15 is about 1/2 of 31, and using x=2 gives us a good chance of getting a root; using synthetic division verifies 2 as a root). Then quadratic formula to get remaining roots.

Before discovering all the wonderful interesting math problems videos on YouTube (I now subscribe to 3 or 4 different ones; I can't get enough of them!!), i never needed any techniques beyond what learned from secondary school. These interesting problems and the techniques shown by the various presenters are excellent for expanding on my math toolset! I am very grateful!! Thx.

[marceloboda]

I want to know, how can i find 3/5 when you put 1, (1/2.5)

[glasssmirror]

Please sir if you can give us a lecture to find Possible Divisors on fractions and also finding the three possible numbers which would work for the cubic equation.

[vaibhavsawroop]

How to know possible no. And how to use friction 3/5

[justme]

Hello. -There are so many permutations of factors of the constant that could sum up to the coefficient of the squared term. -How can you know you're choosing the correct ones?

[alster]

Factor/Remainder and the Rational Zero Theorems did the trick here

[edmondscott]

Seems very complicated. I would use factor theorem to find 1 root, then divide cubic expression by factor to get a quadratic.

[yosiganish]

On the last one he didn’t explain the last stage which is very important for understanding
Thank you

[neelayadagiri]

Sir plz tell what to do when constant is +1/-1 and when coefficient of x cube is 1...

[SuperYoonHo]

Wow that was amazing1 thanks a lot mr
love your videos and love your channel
its the best best best
love and prayers from south korea

[lefleurtobias]

Hi Sir. Please explain how you substituted ( 1/5.3 ) with ( 2/5 - 1/3 ). I know how to get the possible divisors, but not the penultimate step. Valuable time is lost if I do not know the manipulation to ( 2/5 - 1/3 ). I like this method a lot.

[humester]

In this case the following approach is simpler than trying to figure out so many possible divisors and then that 1/(2x5) = (3/5) – (1/2):
10 – 2 = 11 – 3
Since the sums of the alternate coefficients are equal, (x + 1) is a factor and x = -1 is a solution.
We next use synthetic division to get a quadratic equation:

-1 | 10 11 -2 -3
| -10 -1 3
| 10 1 -3 0  Remainder is zero
10x^2 + 1x – 3 = 0
10 x (-3) = -30, so we want numbers that multiply to give -30, and

add to give (+1)
30 = 5 x 6 so (-5) and (+6) fit, giving
10x^2 - 5x + 6x – 3 = 0
5x(2x – 1) + 3(2x – 1) = 0
(2x – 1)(5x + 3) = 0
Therefore, the factors are: (x + 1)(2x – 1)(5x + 3), and
the solution set is {-1, - (3/5), +(1/2)}

[planqbutter]

hi can someone help me how do u get possible divisors of a fraction like the first one??

[himeshsingh]

What if the last term is missing i.e D ??

[Pravinthapa]

How _ came 11/10= 3/5+1/2=2×3 6+5×1=5=5+6=11=11/10 may be there + not _

[antoinelebon]

Your factoring seems strange to me, because x=2 is a counter example to x+0.6 becoming 5x+3 since you have 2+(3/5)= (5*2)+3, which is false!

[youlookweirddude]

How to solve in less than 1 minutes but makes 10 minute video. Oh he's gooood

[paddle_shift]

Than you for not explaining the most important part of the solution!

[raziasiddique]

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