Friday, July 6, 2018

105-GRE Math Test - Important Key points and formulas Part - 8

BLOG-105


In continuation of Blog-104we 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 4x6-20x5+7x2-46x+55 by (x-5) using synthetic division method.

Solution:
1) Write all the terms in descending order:
     4x6-20x5+0x4+0x3+7x2-46x+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.


   b) Here the quotient is 4x6-20x5+0x4+0x3+7x2-46x+55 which can also be written as 4x6-205+7x2-46x+55. Here the remainder is 0.

    c) So we have 4x6-205+7x2-46x+55 = (x-5) (4x5+7x-11)+0.

Example-3: Divide 5x5+20x4-2x3-8x2+3x+15 by (x+4) using synthetic division method.


Solution:
1) Write all the terms in descending order:
     5x5+20x4-2x3-8x2+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 5x5+20x4-2x3-8x2+3x+15. Here the remainder is 3.

   c) So we have 5x5+20x4-2x3-8x2+3x+15 = (x+4) (5x4-2x2+3)+3.

Next part of GRE Math Test - Important Key points and formulas will be published in the next blog.


ANIL SATPUTE