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

Click here for the previous basics.

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 4x⁴+(13/3)x³-(23/3)x²+11x-(18/3) by (x-2/3) using the 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.

In the next part, we will see a few examples and some essential formulae.

ANIL SATPUTE