By Harley Flanders; Justin J Price
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Extra info for Algebra
This equation looks complicated, but is actually a linear equation as far as y is concerned. With a little rearrangement of terms, it can be written as (x2 + x + 3)y = 4x3 - 5, which is of the form ay = b. It follows that y = 4x3 - 5 · x2 + x + 3 We say that we have solved for y in terms of x, or expressed y in terms of x. 3 The relation between Fahrenheit and centigrade temperatures is F = �C + 32. Express C in terms of F. 2. Linear Equation• SOLUTION 55 The equation is linear in F and also linear in C.
U2 v2 v+u V2 - U2 E.. � 6. x+ I x3 + I (x + y)(x2 - xy + y2) x4 + xy3 · 4 3 _ x +_ I x -_1 + _ -xl - 2x I+ 1 l � x2 - 4 + (x - 2)2 l l I 16. - + - + x xy xy2 18. 1 - x2 y+2 y 2 • 10. 12. 14. --- (:�::)( x2� I ) 22. ( xxz + 3yxy } (x2 2y+ y2 } c� y )(� f) x + 2 x2 - 3xy + 2y2 26. ( x - 2yy } ( (x2 - y2)2 } . 20• 24• Compute the quotient: 27· 29. 3. 28. 30. + - x + Y/( x + Y )2 x + 2y/\ xy (a + wI/a2 ab- b2 . 4 -3 + ' t t2 -9 32. 12+t+3 46 1 . BASIC ALGEBRA 33. (� - �) uz (� u4 35. (xu - yu)2 + (xv + yu)2 x2 + y 2 u2 + I + �) u4 34.
Because of the rules of exponents, the degree of a product of polynomials is the sum of their degrees. For if we multiply amxm + + b0 , we + a0 by bn x n + obtain · · · · · · Thus the degree of the product is m + n since am bn =/: 0, being the product of the non-zero leading coefficients of the factors. The degree of a product of polynomials is the sum of their degrees. EXERCISES Compute: 2. (3x - 2) + (x + 6) 1. (x + 4) + (5x - 3) 4. (x2 + x + 7) - (4x + I) (8x2 + 5x + 6) + (3x - 4) 6.