...But a, b, and c are the quotients obtained by dividing each term, ap, bp, and cp, by p. Therefore, to divide a polynomial by a monomial, divide each term of the polynomial by the monomial. 43. Division of Polynomials by Polynomials. If the divisor (one factor) is a + b + c, and the quotient...

...ab3 + abc ; , a?b — ab1 + abc therefore - ! - = a — b + c. ab Hence we have the following rule : To divide a polynomial by a monomial, divide each term of the dividend separately by the divisor. For example (8a* - 6a26 + 2«2c) •*• 2u2 = 4a - 36 + c. (9z...

...XXX 80. To divide a polynomial by a monomial. By the distributive law we have the following rule : Divide each term of the polynomial by the monomial, and add the several quotients. EXAMPLE 1. Divide 12 x3 — 5 ax2 — 2 a2x by 3 x. - 5 oafl 3x 3x 3x EXAMPLE 2....

...is the other number ? 13. ILLUS. 1. а — b + с x To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial, and add the results. ILLUS. 2. 3a^ -2ж +1 3я?.+ 4 ж4 + 6ж3- 4ж2 + 3x То multiply a polynomial by a polynomial, multiply...

...factors: аЧх ax a* o* 1 _i a'bx 4-0*1/= — ¡ — = — ! —, = "', -7 = -í = » aby ya* o' o1 То divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sob — Jaiic) ч- 4a = üb — Se. To divide a polynomial by a polynomial, arrange both dividend...

...polynomial by a monomial. By the distributive law for division, in § 94, we have the following rule : Divide each term of the polynomial by the monomial, and add the resulting quotients. Ex. 1. Divide 12 z3 - 5 яж2 - 2 a?x by 3 x. 12ж»-баха-2а2ж_12ж3 -5...

...a?bx ax a* a3 1 _a a*bx -i-afttf = — r — • = - — > — z = a: —- = —-= a aby y a3 a5 a2 To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (8aft — 12ac) -*- 4a = 2ft — 3c. To divide a polynomial by a polynomial, arrange both dividend...

...me) -*-m = a + b - c, by def . of division. These examples indicate the following method of dividing a polynomial by a monomial : Divide each term of the polynomial by the monomial, and add the quotients (algebraically). 1. Divide 4a2x — 2 aa? by 2 ax. (4 a2a; - 2 ax2) -s- 2 ax = 2 a - x. CHECK....

...a- 6 b Divide 18 a by 3. Next ua-26 divide -6b by 3. Write the quotients. The answer is 6 a - 2 b. To divide a polynomial by a monomial, divide each term of the polynomial by the monomial and write the quotients in succession. EXERCISE 34 Divide : 1. 5 a + 5 by 5. 13. a2 + ab — aс by a....

...them. If the expressions have common factors, remove the common factors: o"bx ax a« os 1 _i , . . To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sab — 12ac) -i- 4a = 36 — 3c. To divide a polynomial by a polynomial, arrange both dividend and...