Question

how to split two middle terms

Answer 1

it is very easy to splitter to material from first you focus on the middle term and multiply the two drugs which is between it and what and after multiplying you get the answer now split the middle term like that so that their admission is equal to the multiplication

Answer 2

Hey mate,
Here's your answer,

So by your question i guess you are asking about factorising cubic polynomial.

So here are the steps to find the factor of cubic polynomials:


$step \: 1$
Try to find the common factor of the whole polynomial or group them if possible otherwise move to step 2.


$step \: 2$
Try to find the first factor of the polynomial using the hit and trial method.


$step \: 3$
Other zeros can be obtained using synthetic or long division method.


$step \: 4$
Now factorise the quotient you got after dividing.
From that you will.get your second and third factors.


$step \: 5$
Now as the last step write all the factors together.





[ i fell that you are still facing difficulties to understand this. So here's one example and i hope this will clear your all doubts. ]


EXAMPLE:
Let's factorise

${x}^{3} - 2x - x + 2$
so let p(x) = x³ - 2x - x + 2

so as per the 2nd step as 1st step is not possible here,

let's try x = 1
{ remember we must put any value in place of x so that p(x) = 0 }

so if x = 1

p(1) = (1)³ - 2(1)² - (1) + 2
= 1 - 2 - 1 + 2
= -1 +1
= 0

so the 1st factor of this polynomial is
x = 1
=> x-1

Hence x-1 is the 1st factor of this polynomial.

lets move to step 3.

divide x³ - 2x - x + 2 from x - 1
so the quotient would be x² - x - 2

now think yourself can x² - x - 2 be factorised?
oh yeah it can be.

so we landed on step 4 now,
now let's factorise x² - x - 2 by which method??
yeah! its the middle term splitting method.


${x}^{2} - x - 2 \\ = {x}^{2} + x - 2x - 2 \\ = x(x + 1) - 2(x + 1) \\ = (x + 1)(x - 2)$
Hence the other two factors are (x+1) and (x-2)


Therefore,
the factors of this polynomial are

$(x - 1)(x + 1)(x - 2)$





So by this i end my answer

Hope you are clear about this topic now.