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

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In continuation of part - 7, 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 2: Divide 4x⁶-20x⁵+7x²-46x+55 by (x-5) using the 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 the 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.

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

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ANIL SATPUTE