Saturday, December 1, 2018

107-GRE Math Test - Important Key points and formulas Part - 9

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Factorization (Continued):

b) Factorization of Polynomial (Continued):

3) Synthetic Division: 

Example-4: Divide 4x4+(13/3)x3-(23/3)x2+11x-(18/3) by (x-2/3) using synthetic division method.

Solution:

1) Write all the terms in descending order:
     4x4+(13/3)x3-(23/3)x2+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.








b) Here the quotient is 4x3+7x2-3x+9 and the remainder is 0.
c) So we have 4x4+(13/3)x3-(23/3)x2+11x-(18/3) = (x-2/3) (4x3+7x2-3x+9)+0.

Example-5: Divide 3x5+(9/5)x4-2x-(6/5) by (x+3/) using synthetic division method.



Solution:
1) Write all the terms in descending order:
     3x5+(9/5)x4+0x3+0x2-2x-(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 3x4-2 and the remainder is 0.
c) So we have 3x5+(9/5)x4-2x-(6/5) = (x+3/5) (3x4-2)+0.
Next part of GRE Math Test - Important Key points and formulas will be published in the next blog.

ANIL SATPUTE