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Additional resources for Higher Algebra
The is even and when n is odd. + C 2n _2c 2n ~ cn+l x and multiply by x m for 2 3 n (l+# + a; + ;r ) :=c (ii) -l) P~l2* (vi) C C 2 [In ... , and , , (v)c n ,. - In ""-- or zero, according as n . that , t ci -nc 1 + + ac + a d + bc + bd + cd)*. +c 2nx 2n prove z In . j, C 2 =c 8n _ 2 etc. -f . . : . . v (iii) 21. , , In the expansion of (i) (ii) What is the term containing the highest power of x Find the sum of the ? coefficients. that the sum of the coefficients of the even terms that of the odd terms.
Coefficients. that the sum of the coefficients of the even terms that of the odd terms. (iii) Show (iv) Show is equal to that the coefficients of the terms equidistant from the beginning and end are equal. 22. In the expansion of w n (l+z) (l+ y) (l+ z) n , show that the sum of the 371 == | coefficients of the terms of degree r is -. |r 23. By . 3n-r expanding the two sides of the identity and equating the coefficients of xn show that , Also write down the last term of the series on the is odd.
2 quotient 4# + 1 Ix + 10. compared with ordinary division. form . . The remainder is -12rc-31 and the 4 Divide 4z 2 is 19a; + 1 Ix + 10 by x 2 - 2x + 3. - 2 and the quotient 4. The remainder + 11 + 10 -12 Hence 8 ~ 2 - 12* -31. 4. Applications of Synthetic Division. formations are often required. Let/(x) be a polynomial in (I) first ; Express f(x)= 4x* 3. + 10 and (c) 4; 4 (2 -3) = 8 -12; put 8 in line (6) and -12 ll(2-3) = 22-33 put 22 in (6) and -33 in (a); + 3 = 11; and so on. The reckoning Ex.