By Denes Petz

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**Additional info for An Invitation to the Algebra of Canonical Commutation Relations**

**Example text**

Each term has a factor of x 2, so we factor it out first: x 4 - 6x 3 + 8x 2 = x 21x 2 - 6x + 82. Now we consider the trinomial x 2 - 6x + 8. We look for two numbers whose product is 8 and whose sum is - 6. Since the constant term, 8, is positive and the coefficient of the middle term, - 6, is negative, we look for a factorization of 8 in which both factors are negative. Solution Pairs of Factors Sums of Factors - 1, - 8 - 2, - 4 -9 -6 The numbers we need are - 2 and - 4. The factorization of x 2 - 6x + 8 is 1x - 221x - 42.

2w + 2h + l = p, for h 74. 3x + 4y = 12, for y 75. 2x - 3y = 6, for y 76. T = 3 10 1I - 12,0002, for I 77. a = b + bcd, for b 78. q = p - np, for p 79. z = xy - xy2, for x 80. st = t - 4, for t Synthesis h Solve. 81. 335 - 314 - t24 - 2 = 53315t - 42 + 84 - 26 82. 63418 - y2 - 519 + 3y24 - 21 = - 73317 + 4y2 - 44 b 62. A = pr , for p (Area of a circle) 2 83. x - 53x - 32x - 15x - 17x - 12246 = x + 7 r 84. 23 - 234 + 31x - 124 + 53x - 21x + 324 = 75x - 235 - 12x + 3246 85. 15x 2 + 6x2112x 2 - 5x - 22 = 0 63.

Synthesis Savings Plan. The formula a1 + S = PE # r 12 t b - 1 12 U r 12 gives the amount S accumulated in a savings plan when a deposit of P dollars is made each month for t years in an account with interest rate r, compounded monthly. Use this formula for Exercises 97–100. 97. James deposits $250 in a retirement account each month beginning at age 40. If the investment earns 5% interest, compounded monthly, how much will have accumulated in the account when he retires 27 years later? 98. Kayla deposits $100 in a retirement account each month beginning at age 25.