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.
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.
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.
