 1)
Let a = 191/112 - 9/16. Let r(q) = -q**3 - 12*q**2 - 30*q + 35. Let g be r(-7). Find m, given that -2/7*m**3 - 6/7*m - a*m**2 + g = 0.
-3, -1, 0
Let b(y) be the first derivative of -2*y**3/3 + 5*y**2 - 81. Factor b(n).
-2*n*(n - 5)
Let z = -2 - -10. Suppose 6*v - 8*v = -z. Determine f, given that 2*f**3 - 10*f**4 - f**3 + 9*f**v = 0.
0, 1
Let t(y) = -6*y - 27. Let i be t(-5). Factor 15*j**2 - 2*j**4 - j**4 - 2*j**4 - 10*j**i.
-5*j**2*(j - 1)*(j + 3)
Find i such that 280*i - 223*i**2 + 118*i**2 - 180 + 3*i**3 + 2*i**3 = 0.
1, 2, 18
Let z = 59 + -53. Let u = z - 4. Let 22/5*r**u - 26/5*r**3 + 6*r**5 - 22/5*r**4 - 4/5*r + 0 = 0. Calculate r.
-1, 0, 1/3, 2/5, 1
Let j(h) be the third derivative of -h**6/360 + 2*h**4/9 - 255*h**2. Factor j(p).
-p*(p - 4)*(p + 4)/3
Let v(w) be the second derivative of w**6/165 + w**5/55 + w**4/66 - 572*w. Factor v(j).
2*j**2*(j + 1)**2/11
Let p = 22679 - 22677. Factor -s**p + s + 0 + 1/4*s**3.
s*(s - 2)**2/4
Let y(f) be the second derivative of f**4/12 - 13*f**3/2 - 20*f**2 - 2*f + 2. Determine m so that y(m) = 0.
-1, 40
Suppose j - 3*j - 4*d + 256 = 0, -143 = -j + d. Let 2*a - 2*a**4 - 2*a - 136*a**5 + j*a**5 = 0. Calculate a.
0, 1
Let m(z) be the first derivative of -8 - 9*z**4 - 1/3*z**6 + 6*z + 14/5*z**5 - 13*z**2 + 44/3*z**3. Solve m(c) = 0.
1, 3
Let f be (-6)/15*100/(-18)*(-231)/(-154). Find d such that -2/3*d**2 + f*d - 8/3 = 0.
1, 4
Let c(w) be the first derivative of -w**4/6 + 34*w**3/9 - 40*w**2/3 - 200*w - 182. Factor c(d).
-2*(d - 10)**2*(d + 3)/3
Suppose 14 = -2*d + 4*t, -4*t = -24*d + 20*d - 8. Find p such that -1/4*p**d + p**2 - p + 0 = 0.
0, 2
Let n(c) be the third derivative of 0*c - 44*c**2 - 7/2*c**5 - 4*c**3 + 13/2*c**4 - 49/40*c**6 + 0. Factor n(g).
-3*(g + 2)*(7*g - 2)**2
Find m, given that -18*m**2 + 32*m - 19 + m**3 - 6 + 43*m - 17 - 16*m = 0.
1, 3, 14
Let l be (40/(-180) + 32/63)/(15/105). Determine x so that -4/15 - 14/15*x - 2/5*x**l = 0.
-2, -1/3
Let w(s) be the second derivative of -s**4/84 - 2*s**3/21 - 2*s**2/7 - s + 15. Solve w(r) = 0.
-2
Let s(g) = -24*g**5 - 14*g**4 + 84*g**3 + 60*g**2. Let b(n) = -5*n**5 - 3*n**4 + 17*n**3 + 12*n**2. Let v(w) = -14*b(w) + 3*s(w). Suppose v(x) = 0. Calculate x.
-2, -1, 0, 3
Let x(t) be the second derivative of -t**6/120 + t**5/80 + t**4/16 - t**3/24 - t**2/4 - 4*t - 97. Let x(w) = 0. What is w?
-1, 1, 2
What is v in -25/2*v**2 - 25/2*v + 15 - 5/2*v**4 + 25/2*v**3 = 0?
-1, 1, 2, 3
Let y(w) be the third derivative of -w**8/13440 - 13*w**4/24 + 42*w**2. Let u(l) be the second derivative of y(l). Suppose u(o) = 0. What is o?
0
Let r(k) be the second derivative of k**8/560 - k**6/120 + 4*k**3/3 + 10*k. Let a(v) be the second derivative of r(v). Solve a(p) = 0 for p.
-1, 0, 1
Let x(n) = 7202*n**4 + 1368*n**3 - 528*n**2 + 32*n + 9. Let o(r) = 1801*r**4 + 342*r**3 - 132*r**2 + 8*r + 2. Let t(d) = 9*o(d) - 2*x(d). Solve t(s) = 0 for s.
-2/5, 0, 2/19
Let y(l) be the second derivative of -l**7/42 + 11*l**6/10 - 363*l**5/20 + 1331*l**4/12 - l + 2. Factor y(m).
-m**2*(m - 11)**3
Let p = 23 - 19. Let -3*m**5 + 0*m + 0*m - 180*m**3 + 144*m**3 + 24*m**2 + 18*m**p = 0. What is m?
0, 2
Let a(h) be the second derivative of 0 - 1/6*h**3 - 1/12*h**4 + 0*h**2 + h. Determine u, given that a(u) = 0.
-1, 0
Let y = 39 + -49. Let u(g) = -g**3 - 8*g**2 + 19*g - 7. Let j be u(y). Factor -2/7*a**5 + 0 + 0*a**j + 2/7*a - 4/7*a**2 + 4/7*a**4.
-2*a*(a - 1)**3*(a + 1)/7
Let i(a) be the second derivative of a**6/45 + a**5/6 + a**4/2 + 7*a**3/9 + 2*a**2/3 + a + 56. What is c in i(c) = 0?
-2, -1
Let d = -12 + 8. Let g = 7 + d. Factor -z - 2*z**3 - 1 + z**2 + 0*z**3 + 3*z**g.
(z - 1)*(z + 1)**2
Let x(r) be the third derivative of -r**7/210 + 97*r**6/120 - 831*r**5/20 + 6815*r**4/24 - 2209*r**3/3 + 237*r**2. Suppose x(s) = 0. What is s?
1, 2, 47
Let b be ((-8)/2 + 7)*9. Factor -118*i - i**4 - 6 + 97*i - b*i**2 - 15*i**3 - 2*i**4.
-3*(i + 1)**3*(i + 2)
Let o(x) be the third derivative of 2*x**6/15 - 11*x**5/30 - x**4/6 - 26*x**3/3 + 27*x**2. Let h(y) be the first derivative of o(y). Factor h(q).
4*(q - 1)*(12*q + 1)
Let z = 1073957/80547 + 1/26849. Factor z*x**2 - 4/3*x**5 + 20/3*x**4 + 4/3 - 40/3*x**3 - 20/3*x.
-4*(x - 1)**5/3
Let c(w) = w**2 - 3*w - 9. Let t be c(7). Let l = t + -16. Factor -45*r**4 + 10*r**2 - 13*r**2 + 24*r**3 - l*r**4.
-3*r**2*(4*r - 1)**2
Find p such that 24/7*p**4 - 3/7*p**5 - 78/7*p**2 - 39/7*p**3 + 192/7*p - 96/7 = 0.
-2, 1, 4
Let q(p) be the third derivative of -p**2 + 0*p + 1/108*p**5 + 0*p**3 + 0 + 1/54*p**4. Suppose q(i) = 0. What is i?
-4/5, 0
Let l(x) be the first derivative of 0*x**2 - 1/42*x**6 - 1/7*x**4 - 27 - 4/35*x**5 + 0*x**3 + 0*x. Factor l(v).
-v**3*(v + 2)**2/7
Let q(w) = -w**3 - w + 1. Let z(i) = i**4 + 15*i**3 + 33*i**2 + 9*i - 54. Let c(b) = -20*q(b) - 5*z(b). Factor c(u).
-5*(u - 1)*(u + 2)*(u + 5)**2
Let k(d) be the third derivative of -d**8/784 + 4*d**7/245 - d**6/40 - 25*d**2 - 6. What is j in k(j) = 0?
0, 1, 7
Let y = 301 + -178. Factor -v**4 - 5*v**3 - y - 7*v**2 - 124 - 3*v + 247.
-v*(v + 1)**2*(v + 3)
Factor 0 + 12/5*v - 14/5*v**2 + 4/5*v**3.
2*v*(v - 2)*(2*v - 3)/5
Let 25/2*i**4 + 0*i + 0 - 1/2*i**5 - 143/2*i**3 - 169/2*i**2 = 0. What is i?
-1, 0, 13
Factor -20/7*k**2 + 30/7 - 38/7*k.
-2*(2*k + 5)*(5*k - 3)/7
Let q(p) be the third derivative of 10*p**2 + 0 - 7/6*p**4 + 0*p - 1/70*p**7 - 17/120*p**6 - 4/3*p**3 - 17/30*p**5. Solve q(y) = 0 for y.
-2, -1, -2/3
Let q(w) = -2*w**3 + 4*w**2 + w + 3. Let h be q(2). Suppose 10*c - 15 = h. Factor 8/13 - 2/13*s**c - 6/13*s.
-2*(s - 1)*(s + 4)/13
Factor 6 + 63/2*b**2 + 5/2*b**4 - 33/2*b**3 - 47/2*b.
(b - 4)*(b - 1)**2*(5*b - 3)/2
Let d(m) = 17*m**2 - 4553*m + 519833. Let b(q) = -8*q**2 + 2277*q - 259917. Let i(t) = 7*b(t) + 3*d(t). Factor i(g).
-5*(g - 228)**2
Let u(q) = 5*q**4 - 20*q**3 - 50*q**2 + 70*q. Let l(x) = 2*x**3 - x**2. Let f(s) = 5*l(s) - u(s). What is g in f(g) = 0?
-2, 0, 1, 7
Let n(b) = 3133*b**2 - 1151*b - 47. Let l(t) = 1044*t**2 - 383*t - 16. Let g(o) = 17*l(o) - 6*n(o). Factor g(a).
-5*(5*a - 2)*(42*a + 1)
Let n = -33 - -29. Let f be n - (9/(-5) - 3). Let -f*y - 14/5*y**4 + 6/5*y**5 + 6/5*y**2 + 0 + 6/5*y**3 = 0. Calculate y.
-2/3, 0, 1
Let 84*d**3 + 2*d**4 - 1255*d**2 + 1495*d**2 + 22 + 56 + 236*d = 0. Calculate d.
-39, -1
Let z be 17/(612/24) - 0. Suppose -8/9 - z*j**3 + 8/9*j + 10/9*j**2 = 0. What is j?
-1, 2/3, 2
Let i(o) = -25*o**2 - 135*o - 145. Let b(m) = -2*m**2 - 11*m - 12. Let j(c) = -35*b(c) + 3*i(c). Factor j(t).
-5*(t + 1)*(t + 3)
Suppose 4/9*g**2 - 8/9*g + 2/9*g**4 - 2/3 + 8/9*g**3 = 0. Calculate g.
-3, -1, 1
Suppose 4 = 3*q - g, 3*g + g = 5*q - 9. Let x = q - -6. Determine h so that -h**4 - 7*h**4 - x*h**4 - 21*h**2 + h + 5*h + 27*h**3 + 3*h**5 = 0.
0, 1, 2
Let j = 87 - 83. Let c(f) be the third derivative of 1/120*f**5 + 0 + 0*f**3 + 4*f**2 - 1/96*f**j - 1/480*f**6 + 0*f. Find d, given that c(d) = 0.
0, 1
Suppose n - 2*y = 124 - 20, -4*n + 466 = 2*y. Let v = n + -1252/11. Find h such that -2/11*h**2 - 4/11*h - v = 0.
-1
Let k(d) be the second derivative of -d**8/2240 - d**7/840 + d**6/240 + d**5/40 - d**4/4 - d. Let o(u) be the third derivative of k(u). Factor o(f).
-3*(f - 1)*(f + 1)**2
Let p(q) be the second derivative of q**4/12 + 7*q**3/3 + 51*q**2/2 - 24*q. Let k(u) = -2*u**2 - 28*u - 103. Let w(v) = -2*k(v) - 5*p(v). Factor w(f).
-(f + 7)**2
Let b(f) be the first derivative of f**5/25 - f**4/20 - f**3/5 + f**2/10 + 2*f/5 - 151. Factor b(k).
(k - 2)*(k - 1)*(k + 1)**2/5
Let g(r) be the third derivative of -r**6/160 + 3*r**5/40 - 30*r**2. Factor g(i).
-3*i**2*(i - 6)/4
Factor -9/2*k**4 - 16*k - 97/4*k**3 - 1/4*k**5 - 36*k**2 + 0.
-k*(k + 1)**2*(k + 8)**2/4
Let z(t) be the second derivative of -t**6/120 - 3*t**5/20 - 9*t**4/8 - 8*t**3/3 + 17*t. Let k(w) be the second derivative of z(w). Find h such that k(h) = 0.
-3
Let r(u) be the third derivative of 1 - 4/15*u**5 + 0*u**3 + 1/6*u**4 + 0*u - 3*u**2. Factor r(z).
-4*z*(4*z - 1)
Let v(j) be the third derivative of j**6/300 + j**5/150 - 2*j**4/15 - 4*j**3/5 + 2*j**2 - 10. Factor v(q).
2*(q - 3)*(q + 2)**2/5
Let x(a) = -a**4 + a**3 - a - 1. Let j(v) = 2 + 3*v + 0*v - 9*v**3 + 19*v**2 - 21*v**2 - 2*v**4. Let b(y) = j(y) + 2*x(y). Factor b(d).
-d*(d + 1)**2*(4*d - 1)
Let i(p) be the first derivative of 2*p