In continuation of part - 8, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

### Factorization (Continued):

### b) Factorization of Polynomial (Continued):

### 3) Synthetic Division:

Example-4: Divide 4x

^{4}+(13/3)x^{3}-(23/3)x^{2}+11x-(18/3) by (x-2/3) using the synthetic division method.Solution:

1) Write all the terms in descending order:

4x

^{4}+(13/3)x

^{3}-(23/3)x

^{2}+11x-(18/3)

2) Write this polynomial in the coefficient form:

[4, 13/3, -23/3, 11, -18/3]

3) Now we will see the division using the synthetic division method.

a) Here the divisor is (x-2/3) so we have x-2/3=0, x=2/3.

^{3}+7x

^{2}-3x+9 and the remainder is 0.

c) So we have 4x

^{4}+(13/3)x

^{3}-(23/3)x

^{2}+11x-(18/3) = (x-2/3) (4x

^{3}+7x

^{2}-3x+9)+0.

Example-5: Divide 3x

^{5}+(9/5)x

^{4}-2x-(6/5) by (x+3/) using synthetic division method.

Solution:

1) Write all the terms in descending order:

3x

2) Write this polynomial in the coefficient form:

[3, 9/5, 0, 0, -2, 6/5]

3) Now we will see the division using the synthetic division method.

a) Here the divisor is (x+(3/5)) so we have x+3/5=0, x=-3/5.

1) Write all the terms in descending order:

3x

^{5}+(9/5)x^{4}+0x^{3}+0x^{2}-2x-(6/5)2) Write this polynomial in the coefficient form:

[3, 9/5, 0, 0, -2, 6/5]

3) Now we will see the division using the synthetic division method.

a) Here the divisor is (x+(3/5)) so we have x+3/5=0, x=-3/5.

b) Here the quotient is 3x

^{4}-2 and the remainder is 0.
c) So we have 3x

^{5}+(9/5)x^{4}-2x-(6/5) = (x+3/5) (3x^{4}-2)+0.In the next part, we will see a few examples and some essential formulae.