Q5) Divide (synthetic division) the polynomial by the monomial factor x ?2, is x = 2 a root? f(x) = x^4 - 7.5x^3 + 14.5x^2 + 3x - 20 Solution To factor given polynomial by a factor x - 2, Use \'2\' as a factor for synthetic division. For (x + a) to be a factor we use -a as a factor for synthetic division. Write all coefficients of \'x\' terms in descending order. First coefficient \'1\' will be carried as it is. multiply 2 by 1. 2*1 = 2, so 2 would be carried in second row below -7.5. Add -7.5 and 2. i.e. -7.5+2 = -5.5 Hence -5.5 would be carried in last row below -7.5 Now we repeat the same procedure untill we get remainder of last column. Since last remainder is \'0\' (x - 2) is a factor of a polynomial. Since (x - 2) is a factor of given polynomial x = 2 is root of a polynomial.21-7.514.53-20-2- 117201-5.53.5100.

1. Q5) Divide (synthetic division) the polynomial by the monomial factor x ?2, is x = 2 a root? f(x)
= x^4 - 7.5x^3 + 14.5x^2 + 3x - 20
Solution
To factor given polynomial by a factor x - 2, Use '2' as a factor for synthetic division.
For (x + a) to be a factor we use -a as a factor for synthetic division.
Write all coefficients of 'x' terms in descending order.
First coefficient '1' will be carried as it is.
multiply 2 by 1. 2*1 = 2, so 2 would be carried in second row below -7.5.
Add -7.5 and 2. i.e. -7.5+2 = -5.5
Hence -5.5 would be carried in last row below -7.5
Now we repeat the same procedure untill we get remainder of last column.
Since last remainder is '0' (x - 2) is a factor of a polynomial.
Since (x - 2) is a factor of given polynomial x = 2 is root of a polynomial.21-7.514.53-20-2-
117201-5.53.5100