Algebra by Harley Flanders; Justin J Price

By Harley Flanders; Justin J Price

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7. 9. 11. 13. 15. 17. 19. 21. /29 = 23 efV: = Vx VX2+T = x + l 2a(a2 + 4a + I ) = 2a3 + 8a2 + 1 a3 + b3 = (a + b)3 a-2a-2 = a4 Vx3 + 2x2 + x = x(x + 1 ) (25x)(4x) = 100x x+y = t +L x+z z ( - x)4 = -x4 x4 6. = x2 + 1 xz + x4 8. (x - y)(x + y) = x2 + y2 I 10. YY x +y 12. v'3X+5 + v'2X+T = vsx + 14. W = a-213 16. (x/y2)2 = x/y4 18. x + x + x + x = x4 20. Vx + v'2X = v'3X -2 22. x-2 = x 4. ( r - 6 48 1 . BASIC ALOEBRA 23. 25. 27. 29. 31. (x + l )(y + l)(z + I ) 1 = xyz + x + y + z + 3 4x - x7x2 + I = 4x2 - 7x + I (x + y)3 = x3 + 3xy + y3 x2 + 4x + 8 = I + 2 + 4 = 7 x2 + 2x + 2 24.

I + x3)(1 + x4 )(1 + x5)(1 + x6) 54. (I + 2x)(I + 3x2 )(1 + 4x3 )(1 + 5x4) SS. x(2x + 1)(3x + l ) - (x2 + 2)(3x - I ) S6. ( I + x + xz + x3 )3. 9. POLYNOMIALS IN SEVERAL VARIABLES A polynomial in several variables is a sum of terms of the form I, x, y, x2, xy, y2, x3, x2y, xyz, x3y2z, with various coefficients. A term such as axkymzn is called a monomial. Its degree is the sum k + m + n of its exponents. Thus the degree of 5x2y4 is 6; the degree of -8xyz is 3 . The degree of a polynomial is the highest degree of the monomials it contains.

For if it did, we would be forced to the false conclusion that I = 3. A system with no solution is called inconsistent. Remark 2: A system of two equations may really be a single equation in disguise. For example, in the system {3x x + 6y = 12 + 2y = 4, 3. Quadratic Equation• 57 the first equation is three times the second. Any attempt to eliminate one unknown from the system will simultaneously eliminate the other, so the result will be Such a system, called underdetermined, is inadequate to determine a single answer.

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