High School Algebra

Cover High School Algebra
High School Algebra
J H John Henry Tanner
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3. 5 m''' — 2 m — 3 and 15 m^ — 6 m^ — 4 m -f- 3.
4. C3_2c2-2c-3 andc^-c3-3c2^4c-2.
5. 12x'-Sa^-55a^-2x-^5and6a^-x'-29x-15.
6. LSx^-\-75a^-{-17x'-2Sx-lSand6a^-}-2Sx^-3x-10.
7. S0y' + 16y* + 16f-Sy^-3y-2a, nd20f + 4:y'-y-3.
8. 4. K'-\-201(^-10k'-^SJc-\-S5sind21i^ + llk'-25, 9. 5n*-10n3 + lln2-67i-hl and 10 5n*-7n^ + ldn'-Un-{'2.
102 HIGH SCHOOL ALGEBHA [Ch. VII 11* Proof of principle involved in § 76 (see footnote, p. 100). The success of the method employed in § 70 is due to the follow- ing con
...siderations : Let A and B represent any two polynomials in ic, the degree of A being at least as high as that of B, and let q and R represent the quotient and remainder respectively, when A is divided by B\ then A = qB^R. [Ex. 20, p. 50 This equation shows that: (1) every divisor common to B and II is a divisor of A also (why ?), and (2) every divisor common to A and ^ is a divisor of H also (why?); hence the H. C. F. Of B and R is the same as that of A and B.
If now B is divided by R, giving p and M as quotient and remainder respectively, then, by reasoning as above, we see that the H.


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