Write the polynomial x45x32x220x24 as a product of first deg

Write the polynomial x^45x^3+2x^2+20x24 as a product of first degree factors given that 2 is a zero of multiplicity 2?

Solution

Solution:

hi that an easy problem
becaz it required tooo much space to do i\'ll do it in a short one

factor of 24\'s are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12,...

|1 5 10 20 24
-3 | -3 -6 -12 -24
--------------------------
1 2 4 8 0

-3 is one of the zeros

after that there are 3 possible methods to do rest of sum.
1. Factorization
2. quadratic formula
3. i don\'t know the name the same i did for first zero\'s.
note: for the sum having a square in that case only you can use quadratic formula.
for this sum u need to use either first method or factorize
i used factorize to get another two zeros.
x³+2x²+4x+8

X²(x+2)+4(x+2)
(x^2+4) (x+2)
both sets equals to zero
x²+4=0 & x+2=0
x=-2 and x²=-4

becaz for this type of sum if it is like square roots leave it as i did.
this sum is difficult to write in algebric terms
hope you understand the sum

Thus the four roots are -2, -4, 2i, -2i