Question

factorize 47 th question

Answer 1

Hello,
The polynomial is :-
$4 {x}^{3} + 20 {x}^{2} + 33x + 18$
It is a cubic polynomial.
Hence to solve it or factorize it we need to use the trial and error method.

P(x) = 4x³+20x²+33x+18
P(-1) = 4(-1)³+20(-1)²+33(-1)+18
= - 4+20-33+18 = - 37 + 38 =1
P(-2) = 4(-2)³+20(-2)²+33(-2)+18
= - 32 + 80 - 66 -+18
= - 98+98 =0
So p(-2) =0
By factor theorem we can say that
X+2 is a factor of p(x)

Now,
We will divided p(x) by (x+2)

See the division in the attachment :

So p(x) = (x+2)(4x²+12x+9)

Now we will do middle term splitting of the second product of p(x) that is (4x²+12x+9)

See the attachment for splitting...

After splitting we got

P(x) = (x+2)(2x+3)(2x+3)

This is the factorization of 47 th number

Hope this will be helping you ✌️