/11
Let d = 568851/8 - 71106. Solve d*z**4 - 3/8*z**3 - 9/8*z**2 + 3/4 + 3/8*z = 0 for z.
-1, 1, 2
Suppose -1031 = -16*x + 569. Factor 305*r**2 + 54 + 9*r - 101*r**2 - 2*r**3 - x*r**2 - 63*r - 86*r**2.
-2*(r - 3)**3
Let q(r) be the first derivative of 2*r**6/15 - 2*r**5/5 + 4*r**3/3 - 2*r**2 - 51*r + 1. Let s(b) be the first derivative of q(b). Factor s(y).
4*(y - 1)**3*(y + 1)
Let m(s) = s**3 + 31*s**2 - 31*s + 34. Let w be m(-32). Let -174*o + 166*o - 32 - 4*o**3 + 22*o**2 - 2*o**w = 0. What is o?
-1, 2, 4
Let b(v) = v**2 + 5*v + 7. Suppose 3*c = -5*x + 116, -2*c + 48 = -3*x + 5*x. Let p(t) = -4*t**2 - 21*t - 28. Let l(g) = x*b(g) + 6*p(g). Factor l(o).
-2*(o + 1)*(o + 7)
Let k(y) be the second derivative of -2/15*y**5 + 0 + 1/9*y**4 - 65*y - 2/45*y**6 + 4/9*y**3 + 0*y**2. Determine r, given that k(r) = 0.
-2, -1, 0, 1
Let u(i) = 4*i - 4. Let t be u(1). Let w be 2 + (t - (-3)/(-6))*-2. Factor -8*f**2 - 16*f + 0*f**3 - f**3 + 5*f**w + 32.
4*(f - 2)**2*(f + 2)
Let p(a) be the third derivative of 0*a**3 + 0*a - 2*a**2 + 11/156*a**4 + 28 + 23/390*a**5 + 1/60*a**6 + 1/1365*a**7. Suppose p(z) = 0. Calculate z.
-11, -1, 0
Suppose 15 = 5*x - 5*v, 2*v + 3 = 1. Suppose 10 = -2*m + x, 2*m = y - 10. Factor -5/4*c**3 - 5/8*c - 1/8 - 5/4*c**y - 1/8*c**5 - 5/8*c**4.
-(c + 1)**5/8
Let z(q) = q**4 + 485*q**3 - 1416*q**2 - 14*q + 1880. Let t(k) = 10*k**4 + 5335*k**3 - 15575*k**2 - 155*k + 20680. Let y(a) = -6*t(a) + 65*z(a). Factor y(p).
5*(p - 94)*(p - 2)**2*(p + 1)
Let f(a) be the second derivative of a**5/30 - 17*a**4/24 - 23*a**3/12 - 7*a**2/6 + 872*a. Factor f(p).
(p - 14)*(p + 1)*(4*p + 1)/6
Suppose 1236 = -13*p + 16*p. Let b = 2887/7 - p. Factor 9/7*n**2 + b - 3/7*n**3 - 9/7*n.
-3*(n - 1)**3/7
Let c(p) be the first derivative of -4/35*p**5 - 16/7*p**2 + 52/21*p**3 + 13/14*p**4 - 259 + 0*p. Suppose c(l) = 0. Calculate l.
-2, 0, 1/2, 8
Let z = 12407/124270 - -2/12427. Let j(n) be the second derivative of -8*n + 0*n**2 - 1/27*n**3 + 0 - z*n**5 - 1/9*n**4. Factor j(w).
-2*w*(3*w + 1)**2/9
Factor 22/17*m + 252/17 - 2/17*m**2.
-2*(m - 18)*(m + 7)/17
Let n(r) = 42*r**3 + 220*r**2 - 4106*r + 9724. Let l(w) = 4*w**3 + 21*w**2 - 391*w + 926. Let s(c) = 52*l(c) - 5*n(c). Factor s(y).
-2*(y - 6)*(y - 3)*(y + 13)
Suppose -3*k - 38*k + 82 = 0. Find b, given that -3*b**3 + 12*b**5 + 7*b**k - 13*b**5 + 701*b - 3*b**4 - 707*b + 6*b**3 = 0.
-3, -2, 0, 1
Let v(o) = -o**2 - 9*o + 78. Let r be v(-15). Let p be (-1)/7*r*(-6)/(-8). Suppose p*m**2 + 3/7*m**4 - 12/7*m**3 + 12/7*m - 12/7 = 0. Calculate m.
-1, 1, 2
Suppose 9586 = -4*z + 3974. Let i = 4213/3 + z. Solve -4/3*o - 1/3*o**2 - i = 0.
-2
Let g(j) be the second derivative of 1/45*j**6 + 0*j**2 - 1/18*j**4 + 1/378*j**7 + 7*j + 1/45*j**5 - 5/54*j**3 + 3. Find c, given that g(c) = 0.
-5, -1, 0, 1
Let v be (39/(-3) + -12)*(-2)/10. Suppose 4*l = -v*p - 20, 4*l + 2*p + 17 = 9. Determine d, given that l + 1/2*d**2 - 5/2*d = 0.
0, 5
Let k(h) = 3*h - 198. Let f be k(-9). Let c be f/(-540)*(-2 - -4). Let 25/6*v + 5/3 + 5/3*v**5 - 35/6*v**3 - 5/6*v**2 - c*v**4 = 0. Calculate v.
-1, -1/2, 1, 2
Let o = 1729892/7 - 247127. Determine j so that -3/7*j**2 + 6/7 - o*j = 0.
-2, 1
Let y be -2 + (6/(-4))/(105/(-140)). Let x(p) be the first derivative of -p**3 - 1/4*p**4 - 10 + 0*p + y*p**2. Factor x(m).
-m**2*(m + 3)
Factor 99/2*f**2 - 31/2*f**3 - 1/2*f**4 + 17 - 101/2*f.
-(f - 1)**3*(f + 34)/2
Let a(m) = 1. Let p(c) = 16*c - 2. Let r(q) = -4*a(q) + p(q). Let b be r(2). Suppose -33*x - x**2 - b*x - 30*x + 80*x = 0. What is x?
-9, 0
Suppose 2*r + 2*w = 16, -251*r + 253*r + 5*w - 34 = 0. Let k(u) be the first derivative of 1 - 1/15*u**5 + 1/3*u**4 + 0*u + 0*u**r - 4/9*u**3. Factor k(a).
-a**2*(a - 2)**2/3
Let v(x) be the first derivative of x**6/90 + 2*x**5/45 - x**4/6 - x**2/2 + 3*x - 25. Let z(g) be the second derivative of v(g). Factor z(q).
4*q*(q - 1)*(q + 3)/3
Let t(m) = -81190*m + 81200. Let l be t(1). What is y in l + 3/4*y - 1/4*y**2 = 0?
-5, 8
Let h(z) = -3*z + 10. Let v(w) = 1. Let y(p) = -h(p) + 5*v(p). Let g be y(3). Factor 6*u - 4*u - 4*u + 2*u**3 - 2*u**g - 454*u**2 + 456*u**2.
-2*u*(u - 1)**2*(u + 1)
Let m(r) be the first derivative of r**4/12 + 5*r**3/6 - 3*r**2 - 123*r + 266. Let k(j) be the first derivative of m(j). Factor k(n).
(n - 1)*(n + 6)
Let a(b) be the third derivative of 0 - 17/63*b**7 + 0*b - 23/90*b**5 + 25/504*b**8 + 9/20*b**6 + 1/18*b**4 - 185*b**2 + 0*b**3. Solve a(o) = 0 for o.
0, 1/5, 1, 2
Let r(c) be the third derivative of c**6/80 + 5*c**5/4 - 943*c**4/16 - 13448*c**3 - c**2 + 8383. Factor r(j).
3*(j - 32)*(j + 41)**2/2
Suppose 3*n + 8*y - 4 = 6*y, -5*n = 2*y. Let o(r) = r**3 - 2*r + 4. Let h be o(n). Solve h*j + 1/4*j**4 + 1/4*j**3 - 1/4*j**5 - 1/4*j**2 + 0 = 0 for j.
-1, 0, 1
Let m be (-248)/(-1116) - (-22)/63. Let h be 66/(-44)*10/(-21). Suppose m + 12/7*u + h*u**2 = 0. What is u?
-2, -2/5
Let z = 76 - 18. Let n = -53 + z. Factor -t + n*t**5 - 5*t**2 - 18*t**4 + t + 15*t**3 + 3*t**4.
5*t**2*(t - 1)**3
Factor 67/2*g**3 - 578*g - 544*g**2 - 1/2*g**4 + 0.
-g*(g - 34)**2*(g + 1)/2
Let v(w) be the first derivative of w**7/280 - 29*w**6/120 - 61*w**5/40 - 31*w**4/8 + 29*w**3 + 99. Let l(r) be the third derivative of v(r). Factor l(u).
3*(u - 31)*(u + 1)**2
Factor -4*f**4 + 0 + 0*f - 1952/5*f**2 + 4888/5*f**3.
-4*f**2*(f - 244)*(5*f - 2)/5
Let x(v) be the third derivative of -14/9*v**5 + 0*v + 10/9*v**4 + 0*v**3 - 2/63*v**7 + 10*v**2 - 31/72*v**6 + 0. Factor x(d).
-5*d*(d + 4)**2*(4*d - 1)/3
Suppose -6*p + 81 = -75. Let d = 31 - p. Factor -16*v**2 + 19*v**2 + 3*v**3 - 3*v**4 + 10*v**5 - 13*v**d.
-3*v**2*(v - 1)*(v + 1)**2
Let y(s) be the second derivative of -s**4/6 - 149*s**3/3 + 302*s**2 + 14*s - 37. Determine k, given that y(k) = 0.
-151, 2
Let b(d) = 31*d**2 - 15*d - 38. Let p(g) = -138*g**2 + 60*g + 150. Let u(n) = 9*b(n) + 2*p(n). Suppose u(y) = 0. Calculate y.
-2, 7
Let k(t) be the first derivative of -t**6/540 - 23*t**5/30 - 529*t**4/4 + t**3/3 + 100. Let g(n) be the third derivative of k(n). Suppose g(s) = 0. Calculate s.
-69
Let p be 6 - 11 - (-20 + 13). Let j(v) be the first derivative of 4/9*v**3 + 2/3*v**p + 0*v + 14 - 2/3*v**4. Factor j(r).
-4*r*(r - 1)*(2*r + 1)/3
Let r = 3076942/4314345 - 156/12085. Let c = r + -4/119. Find z such that 0 + 1/3*z**3 + c*z**2 + 1/3*z = 0.
-1, 0
Let x(v) be the second derivative of 0*v**3 - 1/4*v**4 + 1/40*v**6 + 0 - 1/20*v**5 - 21*v - 6*v**2. Let b(j) be the first derivative of x(j). Factor b(g).
3*g*(g - 2)*(g + 1)
Let o(k) be the second derivative of 0 + 3/2*k**2 + 1/20*k**5 + 5/12*k**4 + 7/6*k**3 + 11*k. Determine q so that o(q) = 0.
-3, -1
Let d be (-4104214)/(-530) + 1/5 + 0. Factor -146*a - 153*a + 72*a + 4*a**2 - 125*a + d.
4*(a - 44)**2
Let w(z) = 59*z**2 + z - 1. Let c(l) = 58*l**2 + 2999*l - 2247002. Let p(h) = -2*c(h) + 2*w(h). Solve p(k) = 0 for k.
1499
Factor -59*j + 10443/2 + 1/6*j**2.
(j - 177)**2/6
Suppose -25*t + 181*t + 4*t**3 + 103 + 88*t**2 - 1471 = 0. What is t?
-19, -6, 3
Let h = 30 - 26. Suppose 3 = 5*a - h*a. Determine m so that 2*m**3 + m + 5*m**5 - 12*m**a + 8*m - 4*m = 0.
-1, 0, 1
Let r be 156/5 + 100/125. Factor -43*p**5 - 580*p**3 - 20*p**5 + 152*p**2 + r - p**5 + 352*p**4 + 208*p.
-4*(p - 2)**3*(4*p + 1)**2
Let n(u) = -u - 1. Let v(g) be the third derivative of g**5/30 + 3*g**4/8 + 7*g**3/6 - 80*g**2. Let y(o) = 6*n(o) + 2*v(o). Factor y(s).
4*(s + 1)*(s + 2)
Suppose -1128*k = -1121*k + 42. Let b(h) = 18*h**2 - 152*h - 376. Let d(i) = 2*i**2 - 17*i - 42. Let c(a) = k*b(a) + 52*d(a). Factor c(l).
-4*(l - 9)*(l + 2)
Let d = 6 - 1. Suppose -2*k - d + 9 = 0. Determine h so that h + 10*h - 3*h + 8 + k*h**2 = 0.
-2
Suppose -18*q + 21/5*q**4 - 11/5*q**5 - 13/5*q**2 - 8/5 + 101/5*q**3 = 0. What is q?
-2, -1, -1/11, 1, 4
Let q(d) be the third derivative of -2*d**7/315 + 82*d**6/45 - 6557*d**5/45 - 6889*d**4/9 - 4*d**2 + 8*d + 1. Factor q(m).
-4*m*(m - 83)**2*(m + 2)/3
Let f = -637801/2 + 318902. Let m = 2 - 2. Factor -243/8*a**4 + 0*a - f*a**2 - 27/2*a**3 + m.
-3*a**2*(9*a + 2)**2/8
Find g, given that 693464 + 157464*g + 6*g**3 + 5283575 + 6*g**3 + 972*g**2 + 2526017 - 10*g**3 = 0.
-162
Suppose 127*z = 130*z + 63. Let a = z + 23. Solve -120*u**a - 2*u + 4 + 12*u + 8 + 118*u**2 = 0.
-1, 6
Factor 0 - 1/5*m**3 + 0*m + 6/5*m**2.
-m**2*(m - 6