## BLOG-105

In continuation of

**Blog-104**, we will see all the important formulas and useful statements which are to be used in Math test of GRE.### Factorization (Continued):

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

#### 3) Synthetic Division:

Example-2: Divide 4x

^{6}-20x^{5}+7x^{2}-46x+55 by (x-5) using synthetic division method.Solution:

1) Write all the terms in descending order:

4x

^{6}-20x

^{5}+0x

^{4}+0x

^{3}+7x

^{2}-46x+55

2) Write this polynomial in the coefficient form:

[4, -20, 0, 0, 7, -46, 55]

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

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

^{6}-20x

^{5}+0x

^{4}+0x

^{3}+7x

^{2}-46x+55 which can also be written as 4x

^{6}-20

^{5}+7x

^{2}-46x+55. Here the remainder is 0.

c) So we have 4x

^{6}-20

^{5}+7x

^{2}-46x+55 = (x-5) (4x

^{5}+7x-11)+0.

Example-3: Divide 5x

^{5}+20x

^{4}-2x

^{3}-8x

^{2}+3x+15 by (x+4) using synthetic division method.

Solution:

1) Write all the terms in descending order:

5x

^{5}+20x

^{4}-2x

^{3}-8x

^{2}+3x+15

2) Write this polynomial in the coefficient form:

[5, 20, -2, -8, 3, 15]

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

a) Here the divisor is (x+4) so we have x+4=0, x=-4.

b) Here the quotient is 5x

^{5}+20x

^{4}-2x

^{3}-8x

^{2}+3x+15. Here the remainder is 3.

c) So we have 5x

^{5}+20x

^{4}-2x

^{3}-8x

^{2}+3x+15 = (x+4) (5x

^{4}-2x

^{2}+3)+3.

ANIL SATPUTE