how to factorise 4 term polynomial
Answers
Answer:
1.Break up the polynomial into sets of two.
2.You can go with (x3 + x2) + (–x – 1). Put the plus sign between the sets, just like when you factor trinomials.
3.Find the GCF of each set and factor it out.
4.The square x2 is the GCF of the first set, and –1 is the GCF of the second set. Factoring out both of them, you get x2(x + 1) – 1(x + 1).
5.Factor again as many times as you can.
6.The two terms you’ve created have a GCF of (x + 1). When factored out, you get (x + 1)(x2 – 1).
7.However, x2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).
If this method doesn’t work, you may have to group the polynomial some other way. Of course, after all your effort, the polynomial may end up being prime, which is okay.
For example, look at the polynomial x2 – 4xy + 4y2 – 16. You can group it into sets of two, and it becomes x(x – 4y) + 4(y2 – 4). This expression, however, doesn’t factor again. Bells and whistles should go off inside your head at this point, telling you to look again at the original. You must try grouping it in some other way. In this case, if you look at the first three terms, you’ll discover a perfect-square trinomial, which factors to (x – 2y)2 – 16. Now you have a difference of squares, which factors again to [(x – 2y) – 4][(x – 2y) + 4].
Step-by-step explanation:
by taking x-1=0
so, x = 1
in the equation in polynomial where u find x put one at place of x and when u solve it completely and result is 0 ...
so divide the equation from x-1
if u don't get 0 so take -1 at the place of x and the 2 then -2 while u get 0. and so on
as like in image
