First Course in Algebra

Cover First Course in Algebra
First Course in Algebra
Herbert E Herbert Edwin Hawkes
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Solve for y, i/m — 2/ = m^ — 4 m + 3.
26. Solve for ^, r^ + r = r^ + 5 « — 20.
27. Solve for r, ar -j- Sac — a^ = 2cr -{- 2 c^.
28. Solve for 6-, 2 as -{- a^ -^ a'^ = 6 a^ -\- ah.
64. The general quadratic trinomial. The type form is For many trinomials of this type, two binomial factors of the form (hx + ^) (mx + ri) may be found. The method of factoring such trinomials is illustrated in the following: EXAMPLES 1. Factor 2x^ -{-5x-^S.
Solution. 2 a;2 + 5 a: + 3 = (?:r + ?) (?x + ?). T^^>>^ ^2)
... To get the proper factors we must supply 2 ^r^ + ? x such numbers for the interrogation points in _j_ ? a; + 3 (1) and in (2) as will give (3). 2x^ +bx + 3 (3) 2 x^ for the product of the first two terms of the binomials, + 3 for the product of the last two terms of the binomials, and + 5 a; for the sum of the cross products. Now 2 x'^ = 2 X ' Xy and +3 = 1. 3.
FACTORING 131 The factors 1 and 3 may be substituted for the interrogation points in (1) and (2) in either of the following ways: 3, 4.


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