/12 - 4*i**3/3 + 2*i**2 + 123*i + 18. Let s(t) be the first derivative of m(t). What is w in s(w) = 0?
-2, 2/3, 1
Find l, given that 1/7*l**5 + 0*l**4 - 40/7 + 12/7*l + 34/7*l**2 - 19/7*l**3 = 0.
-5, -1, 2
Determine o, given that 0 - 93/2*o**2 - 220*o - 1/2*o**3 = 0.
-88, -5, 0
Let p(g) = 2*g + 4. Let l be p(0). Factor -23*v**3 + 0*v**2 + l*v - 2*v + 12*v**2 + 33*v**3.
2*v*(v + 1)*(5*v + 1)
Let h(m) = 4*m**2 + 8*m + 33. Let u be h(-5). Suppose -55*v - 53*v - u*v + v - 40*v - 5*v**2 - 2880 = 0. Calculate v.
-24
Determine y, given that -3000*y**3 - 256*y**4 - 45161*y + 20316*y**2 + 15482*y**3 + 13695*y**3 + 48977*y + 767*y**3 = 0.
-3/8, 0, 106
Factor -5*m**4 + 5*m**2 + 188*m - 154*m - 184*m + 150*m**3.
-5*m*(m - 30)*(m - 1)*(m + 1)
Factor 200 + 836*n + 255 + 13*n - 40*n**3 + 192*n**2 - 5*n**4 + 31*n + 198*n**2.
-5*(n - 7)*(n + 1)**2*(n + 13)
Let s be 3/(-15) - (-116)/(-420). Let y = 209/42 + s. Find p, given that -5/2*p**2 - 2 + y*p**4 - 6*p**3 + 6*p = 0.
-1, 2/3, 1
Let m(p) = -8*p + 227. Let a be m(28). Let f(w) be the second derivative of 3/35*w**5 + 0*w**3 + 0 - a*w + 0*w**2 + 3/28*w**4. What is q in f(q) = 0?
-3/4, 0
Let v(l) be the second derivative of -l**9/3024 + l**8/840 - l**7/840 - l**3/6 - 5*l**2/2 - 29*l. Let k(b) be the second derivative of v(b). Factor k(a).
-a**3*(a - 1)**2
Let d = -36 - -39. Factor 31 + 4*u**2 - 2*u**2 - 30 - d*u**2.
-(u - 1)*(u + 1)
Let a(d) = 4*d - 8 + 18 - 36. Let z be a(7). Factor -49 - 7*o**3 + o**z + 6*o**3 - 35*o + 12*o**2.
-(o - 7)**2*(o + 1)
Factor 74*s**2 - 3644*s**4 + 39*s**3 - 3647*s**4 + 7292*s**4.
s**2*(s + 2)*(s + 37)
Let k be 80/320*(-4)/(-3). Let u(r) be the first derivative of 3*r - k*r**3 - r**2 - 48. Let u(p) = 0. Calculate p.
-3, 1
Let g(x) be the first derivative of -x**6/5 + 2*x**5/5 - x**4/6 - 69*x - 19. Let m(n) be the first derivative of g(n). Factor m(v).
-2*v**2*(v - 1)*(3*v - 1)
Let d(m) be the second derivative of -3*m**7/112 + 47*m**6/80 + 3*m**5/10 + 251*m. Solve d(r) = 0.
-1/3, 0, 16
Let p be ((-9)/(-5))/(-98 - 497/(-5)). Factor 39/7*v + 48/7*v**2 - p*v**3 - 18/7.
-3*(v - 6)*(v + 1)*(3*v - 1)/7
Determine u, given that 173 - 1/4*u**2 + 169/4*u = 0.
-4, 173
Let f = 1565 + -1563. Let i = -2 - -5. Let 9*z**2 + 3*z**f - z**2 + 15 + 27*z - i*z**3 - 2*z**2 = 0. Calculate z.
-1, 5
Let n(w) be the second derivative of w**6/105 + 38*w**5/35 + 683*w**4/21 - 988*w**3/7 + 1521*w**2/7 - 1825*w - 2. Let n(t) = 0. Calculate t.
-39, 1
Let o = -20/31 - -133/62. Let i(b) be the second derivative of -3*b**2 - 1/4*b**4 + 0 - 5*b + o*b**3. Factor i(w).
-3*(w - 2)*(w - 1)
Let u be 14336/(-96768)*(-42)/2. Factor -10/3*f + u + 2/9*f**2.
2*(f - 14)*(f - 1)/9
Solve -67*k**2 + 578 - 578 + 54*k**3 - 53*k**3 = 0.
0, 67
Let y be ((-8)/(-44))/((-342)/(-418)). Let v(f) be the first derivative of -14/3*f**2 + 98/3*f + y*f**3 - 19. Factor v(p).
2*(p - 7)**2/3
Suppose 4*q + 13*o - 12*o - 13 = 0, -2*o = 4*q - 18. Determine s so that -4 + 1/3*s**q + 4/3*s = 0.
-6, 2
Let x(v) = 28*v**2 + 260*v + 10. Let o(c) = -29*c**2 - 261*c - 25. Let t(z) = -2*o(z) - 3*x(z). Find m, given that t(m) = 0.
-10, 1/13
Let q = 180/187 - 8/11. Let i be (-16632)/(-1904) + (-68)/8. Solve 0 - i*z**3 + 2/17*z**4 + q*z - 2/17*z**2 = 0 for z.
-1, 0, 1, 2
Let x(f) be the first derivative of f**8/630 - f**7/180 - f**6/270 + 2*f**3/3 + 5*f**2/2 - 82. Let g(b) be the third derivative of x(b). Factor g(w).
2*w**2*(w - 2)*(4*w + 1)/3
What is o in 1/4*o**3 + 19/4*o**2 + 0 - 5*o = 0?
-20, 0, 1
Let -407*z - 120*z**5 - 1104*z**3 + 1497*z + 232*z**5 + 300 - 136*z**4 - 164*z**2 - 98*z**5 = 0. Calculate z.
-5, -1, -2/7, 1, 15
Let y(p) be the third derivative of -p**7/210 + p**4/24 - p**3/6 + 3*p**2 - 7. Let i(l) = -48*l**3 - 144*l**2 - 4*l + 4. Let d(t) = -i(t) - 4*y(t). Factor d(m).
4*m**2*(m + 6)**2
Let u(d) be the first derivative of d**5/16 + 5*d**4/6 + 65*d**3/24 + 15*d**2/4 + 14*d + 154. Let a(y) be the first derivative of u(y). Factor a(w).
5*(w + 1)**2*(w + 6)/4
Let t be (816/32 + -24)/10. Let k(u) be the second derivative of -t*u**5 + 15*u + 0*u**2 + 0 + 0*u**4 + 1/2*u**3. What is n in k(n) = 0?
-1, 0, 1
Let d(p) be the second derivative of p**7/42 - 9*p**5/20 + p**4/3 + 2*p**3 - 560*p. Solve d(q) = 0.
-3, -1, 0, 2
Factor 51/7*q**2 - 3/7*q**3 - 288/7*q + 540/7.
-3*(q - 6)**2*(q - 5)/7
Let j(f) be the second derivative of -f**5 + 10*f**4 - 4*f**2 - 168*f. Let q(u) = -7*u**3 + 41*u**2 - 3. Let b(z) = -3*j(z) + 8*q(z). Solve b(l) = 0.
0, 8
Suppose -106*p + 302 = 90. Let k(t) be the first derivative of -25/18*t**4 + 20/27*t**3 - 1/9*t**p + 0*t + 2. Factor k(o).
-2*o*(5*o - 1)**2/9
Let j(x) = -6*x**4 + 219*x**3 - 612*x**2 - 42*x. Let g(n) = n**4 - 44*n**3 + 119*n**2 + 8*n. Let u(t) = 21*g(t) + 4*j(t). Factor u(d).
-3*d**2*(d - 1)*(d + 17)
Let c(w) be the first derivative of -1/72*w**4 + 1/360*w**5 + 0*w + 0*w**3 - 1/2*w**2 + 1. Let f(v) be the second derivative of c(v). Factor f(l).
l*(l - 2)/6
Suppose -t - 12*t = -156. Suppose 13 - 13 = -t*a. Find w, given that -4/9*w**2 + a*w + 0 = 0.
0
Suppose 6*t - 5*h + 28 = -h, 0 = -2*t - 4*h + 44. Factor -8/3*o + 8/3*o**3 - t + 2*o**2.
2*(o - 1)*(o + 1)*(4*o + 3)/3
Let j = -97/45 - -2209/990. Let b(k) be the second derivative of 0 + 2/55*k**5 + 1/33*k**3 + 11*k + 0*k**2 + j*k**4. Suppose b(o) = 0. What is o?
-1, -1/4, 0
Suppose -278*f**4 - 369*f + 275*f**4 - 183*f**2 - 270 + 0*f**3 - 39*f**3 = 0. What is f?
-5, -3, -2
Suppose 3*c + 2*v - 43 + 17 = 0, 4 = v. Let -2*h**2 + 29*h - h - 27 - 4*h + c*h - h**2 = 0. What is h?
1, 9
Find z such that -6*z**3 + 81/2 + 201/2*z**2 + 9/4*z**5 - 21*z**4 + 495/4*z = 0.
-1, -2/3, 3, 9
Let r(t) be the first derivative of -5*t**6/8 + 12*t**5/5 - 21*t**4/8 - t**3 - 87*t**2/2 + 244. Let k(x) be the second derivative of r(x). Factor k(c).
-3*(c - 1)**2*(25*c + 2)
Let x(r) = 28*r**3 - 109*r**2 - 115*r - 23. Let y(n) = -32*n**3 + 110*n**2 + 116*n + 22. Let o(h) = 6*x(h) + 5*y(h). Factor o(l).
2*(l - 14)*(2*l + 1)**2
Let z = 287984 + -1439912/5. Let 154/5*j**3 + 8/5*j + z - 34*j**2 = 0. Calculate j.
-2/11, 2/7, 1
Let d(c) be the third derivative of -3*c**7/70 + 2023*c**6/120 - 1191*c**5/20 + 371*c**4/8 + 223*c**3/3 + 32*c**2 + 8*c. Let d(g) = 0. Calculate g.
-2/9, 1, 223
Let f(z) be the second derivative of 1 + 4/15*z**3 - 9/5*z**2 + 115*z - 1/90*z**4. Determine v, given that f(v) = 0.
3, 9
Let u(m) = m**2 + 12*m + 8. Let z be u(-12). Let s(c) = -20*c + 103. Let p be s(5). Solve -32*t - 3*t**4 - z*t**p - t**4 + 4 + 40*t = 0 for t.
-1, 1
Let j(h) = h**2 - 11*h + 6. Let x be j(12). Find q such that 14*q**2 - 98*q**2 + x*q**3 + 69*q**4 - 24*q + 61*q**5 - 40*q**5 = 0.
-2, -2/7, 0, 1
Let c(o) be the first derivative of -4/21*o**3 - 189 + 0*o - 1/14*o**4 + 15/7*o**2. Suppose c(d) = 0. Calculate d.
-5, 0, 3
Let z(d) be the third derivative of -39*d**2 + 5/336*d**8 - 19/3*d**5 - 1/6*d**7 + 25/3*d**4 + 80*d**3 + 0 - 9/4*d**6 + 0*d. Factor z(k).
5*(k - 12)*(k - 1)*(k + 2)**3
Let g(p) = p**2 + 10*p + 58. Let m(y) = y**2 + 7*y + 58. Let t(x) = 8*g(x) - 7*m(x). Factor t(c).
(c + 2)*(c + 29)
Let j(b) be the third derivative of b**5/210 - 207*b**4/28 + 620*b**3/21 - 2014*b**2 - 2*b. Factor j(i).
2*(i - 620)*(i - 1)/7
Let k(w) be the third derivative of w**6/240 + 97*w**5/120 - w**4/12 - 97*w**3/3 - 1072*w**2. Factor k(z).
(z - 2)*(z + 2)*(z + 97)/2
Let u(v) be the third derivative of -v**8/168 - 2*v**7/21 - 11*v**6/60 + 41*v**5/15 + v**4 - 24*v**3 + 647*v**2. Let u(n) = 0. Calculate n.
-6, -1, 1, 2
Factor -2/3*f**4 + 2/3*f**2 + 2*f - 2*f**3 + 0.
-2*f*(f - 1)*(f + 1)*(f + 3)/3
Factor 13632/5*d**2 - 19360 + 1/5*d**4 - 227/5*d**3 - 16588*d.
(d - 110)**2*(d - 8)*(d + 1)/5
Let c be 5/(-9) - (-19832)/21312. Factor 9 + 15/4*v - c*v**2.
-3*(v - 12)*(v + 2)/8
Let i = 175/107 - 7243/4494. Let o(y) be the second derivative of i*y**4 + 0*y**2 + 0 - 1/7*y**3 - 23*y. Factor o(m).
2*m*(m - 3)/7
Let g be (455/2002)/((-50)/(-110)). Factor 13/2*o**2 + g*o**3 + 18 + 24*o.
(o + 1)*(o + 6)**2/2
Let k = 454 - 498. Let g(h) = 58*h**4 + 36*h**3 + 8*h**2 - 14*h + 44. Let f(i) = -8*i**4 - 5*i**3 - i**2 + 2*i - 6. Let b(u) = k*f(u) - 6*g(u). Factor b(r).
4*r*(r - 1)*(r + 1)**2
Suppose 49*w + 10 = 54*w. Factor -15*u**w - 3*u**4 + 15*u**3 + 5*u**2 - 2*u**4.
-5*u**2*(u - 2)*(u - 1)
Let y = 5550/97 + -16553/291. Factor 4/3 + y*w