Question

Obtain all other zeroes of $x^{4}+9 x^{3}+28 x^{2} +36 x+16$, if two of its zeroes are -1 and -2

Answer 1

first of all take x=-1 , x=-2
then we get  x + 1 = o and x + 2 = o
then multiply these two, (x+1)(x+2)=x square +3x +2
now divide the given polynomial by this product
that will give you this quotient > x square + 6x + 8
now split the middle term and factorise the obtained quotient
that will give you these factors> (x + 4)(x + 2)
take x + 4 = o , x + 2= o
then you get the other zeroes of the polynomial,that are -4 and -2
this tells us that the polynomial has total three zeroes -1 -2 -4