# PreCalculas math problems?

+1 vote

Hello i need some help with these problems, any help will be much appreciated.I also if need to know how to do the problem.
1.Find the linear factorization of
X^4-4X^3-10X^2+20X+25

Let f(x) =x^4-4x^3-10x^2+20x+25

Let us check for x = -1 then

f(-1) = (-1)^4-4(-1)^3-10(-1)^2+20(-1)+25

= 1-4(-1)-10(1)-20+25

= 1+4-10-20+25

= 30-30

= 0

So x+1 is a factor

by using synthetic division

-1| 1 -4 -10 20 25
| -1 5 5 -25
-----------------------
1 -5 -5 25 0

The resultant quoteint is x^3-5x^2-5x+25.

=(x^3-5x^2)+(-5x+25)

=x^2(x-5)-5(x-5)

=(x^2-5)(x-5)

=(x+sqrt5)(x-Sqrt5)(x-5)

The linear factors of x^4-4x^3-10x^2+20x+25 is (x+sqrt5)(x-Sqrt5)(x-5)(x+1)

Hence the factors are -1,5, ± Sqrt 5.

reshown Dec 28, 2012 by bradely
Let f(x) =x^4-4x^3-10x^2+20x+25

Let us check for x = -1 then

f(-1) = (-1)^4-4(-1)^3-10(-1)^2+20(-1)+25

= 1-4(-1)-10(1)-20+25

= 1+4-10-20+25

= 30-30

= 0

So x+1 is a factor

by using synthetic division

-1| 1 -4 -10 20 25
| -1 5 5 -25
-----------------------
1 -5 -5 25 0

5  1 -5 -5 25.

0   5   0 -25

----------------------

1 0  -5     0

so( x-5)  is a factor

x^2-5=0

the lenior eqution isx^4-4x^3-10x^2+20x+25=(x+1)(x-5)(x^-5)
reshown Dec 28, 2012
Let f(x) =x^4-4x^3-10x^2+20x+25

Let us check for x = -1 then

f(-1) = (-1)^4-4(-1)^3-10(-1)^2+20(-1)+25

= 1-4(-1)-10(1)-20+25

= 1+4-10-20+25

= 30-30

= 0

So x+1 is a factor

by using synthetic division

-1| 1 -4 -10 20 25
| -1 5 5 -25
-----------------------
1 -5 -5 25 0

5  1 -5 -5 25.

0   5   0 -25

----------------------

1 0  -5     0

so( x-5)  is a factor

x^2-5=0

the lenior eqution isx^4-4x^3-10x^2+20x+25=(x+1)(x-5)(x^2-5)