3*u**4 + 3/130*u**5 + 0 + 0*u. Solve w(m) = 0 for m.
1, 4
Let c(q) be the first derivative of -q**6/15 - 29*q**5/10 - 112*q**4/3 - 196*q**3/3 + 20*q + 83. Let z(k) be the first derivative of c(k). Factor z(w).
-2*w*(w + 1)*(w + 14)**2
Suppose -3*q = 2*u - 47, 0 = -4*q - 52*u + 50*u + 66. Let k(l) be the second derivative of -q*l + 0 + 1/3*l**3 + 1/12*l**4 - 3/2*l**2. Let k(m) = 0. What is m?
-3, 1
Let n = -4724 + 14173/3. Let z(y) be the first derivative of 2/5*y**5 - n*y**3 + 3/2*y**2 - y - 3/4*y**4 - 8. Factor z(a).
(a - 1)**2*(a + 1)*(2*a - 1)
Let c(y) be the second derivative of -2*y**6/15 - 33*y**5/5 - 66*y**4 - 856*y**3/3 - 624*y**2 - 985*y. Suppose c(b) = 0. What is b?
-26, -3, -2
Let g be (2/12*-65)/((-26890)/8067). Find v such that -9 - 1/4*v**2 + 1/4*v**4 - g*v**3 + 1/4*v**5 + 12*v = 0.
-3, 1, 2
Let m(y) be the first derivative of -y**7/84 - y**6/15 - y**5/8 - y**4/12 + 168*y - 126. Let n(p) be the first derivative of m(p). What is b in n(b) = 0?
-2, -1, 0
Let f(y) be the first derivative of 50 - 2*y**4 + 153/2*y**2 - 54*y + 16/5*y**5 - 37*y**3. Determine t, given that f(t) = 0.
-3, 3/4, 2
Let r(a) = -a**3 - 48*a**2 - 88*a + 74. Let j be r(-46). Let s be (-3)/6*40/j. Determine b so that 4/11 - 2/11*b**2 + s*b = 0.
-1, 2
Let i(q) be the third derivative of q**6/120 - 103*q**5/60 + 17*q**4/4 - 2*q**2 - 234*q. Factor i(w).
w*(w - 102)*(w - 1)
Let u = 552017/828030 - -1/276010. What is g in u*g**2 - 10/3*g + 2 + 2/3*g**3 = 0?
-3, 1
Factor -2704*x - 96/5*x**3 - 1716/5*x**2 - 39546/5 - 2/5*x**4.
-2*(x + 9)*(x + 13)**3/5
Let r(q) = 101*q**3 + 323*q**2 - 670*q - 870. Let d(l) = 34*l**3 + 107*l**2 - 225*l - 290. Let n(m) = -11*d(m) + 4*r(m). Determine a, given that n(a) = 0.
-29/6, -1, 2
Factor -155*q**2 + 70*q**3 + 8*q**3 - 18*q**3 + 78*q + 16*q**3 + q**4.
q*(q - 1)**2*(q + 78)
Let y(b) = -4*b + 121. Let v be y(30). Factor 44*h**3 + 9 - 308*h**2 - v + 8 - 80*h + 256*h**2.
4*(h - 2)*(h + 1)*(11*h - 2)
Let j(u) be the second derivative of -2*u**6/15 - 2*u**5 - 17*u**4/3 + 80*u**3/3 + 168*u**2 - 30*u + 42. Suppose j(k) = 0. What is k?
-7, -3, -2, 2
Let b = -1524 - -1523. Let c be 6/b - (-29)/(203/56). Find g, given that -3/4*g**4 - 3/8*g**5 + 3/4*g**c + 0*g + 0 + 3/8*g**3 = 0.
-2, -1, 0, 1
Suppose -4*r - 27*r = 163*r + 252*r. Factor -5/6*c**4 + 0*c**2 + r*c + 2/3*c**3 + 0.
-c**3*(5*c - 4)/6
Solve -2100 + 2*h + 35*h**2 - 50*h + 19*h - 30*h**2 - 51*h = 0.
-14, 30
Let i(f) be the third derivative of f**6/40 - 7*f**5/10 + 41*f**4/8 + 28*f**3 + 51*f**2 - 2*f - 10. Find g, given that i(g) = 0.
-1, 7, 8
Let j(t) = -5*t**2 - 82*t - 84. Let u(g) = g**3 + 4*g**2 + 4. Let f(r) = -5*j(r) - 5*u(r). Factor f(a).
-5*(a - 10)*(a + 1)*(a + 8)
Suppose 5*q = 4*w - 18, q = w + 4*w - 12. Suppose -2*t - w*n = 4, 0 = -t - 0*t - 2*n - 6. Suppose -14*p**2 + p**2 - p**3 + 4*p**t + 7*p**2 - p = 0. What is p?
-1, 0
Let b = 934 - 934. Let c(q) be the second derivative of b + 3*q + 4*q**2 - 22/3*q**3 - 13/3*q**4. Factor c(w).
-4*(w + 1)*(13*w - 2)
Let r = 392 + 194. Suppose -r + 646 = 6*l. What is t in -10 - 5/2*t**2 + l*t = 0?
2
Let g(b) be the first derivative of b**4/3 - 22*b**3/3 + 57*b + 74. Let v(r) be the first derivative of g(r). Determine u, given that v(u) = 0.
0, 11
Let o be (915/30 - 17)/((-207)/(-46)). Factor 0 - 27/5*g**2 + 6/5*g - 12/5*g**4 + 36/5*g**o.
-3*g*(g - 2)*(2*g - 1)**2/5
Let j(i) be the first derivative of -i**4/18 + 200*i**3/27 - 2773*i**2/9 + 8836*i/3 + 8020. Let j(w) = 0. What is w?
6, 47
Solve 1280*k - 1048 + 7*k**2 + 331*k - 566 + 0*k**2 - 4*k**2 = 0 for k.
-538, 1
Suppose -2 = -3*m - 4*f + 3*f, 4 = -3*m + 2*f. Suppose -4*q = 16, 13*l - 5*q = 10*l + 20. Let l*p - 1/4*p**3 + m - 7/4*p**2 = 0. Calculate p.
-7, 0
Let p(l) be the third derivative of l**7/147 + l**6/35 - 101*l**5/210 + 4*l**4/7 + 12*l**3/7 + 3*l**2 - 300*l. Determine b so that p(b) = 0.
-6, -2/5, 1, 3
Let g(h) = -62*h - 8*h**2 + 5*h**3 - 12*h**3 + 45 + 10*h**3. Let k(l) = l**3 - 3*l**2 - 21*l + 15. Let s(t) = 4*g(t) - 11*k(t). Factor s(d).
(d - 3)*(d - 1)*(d + 5)
Find z such that -1845*z - 144*z**3 - 924*z**2 - 152*z**3 - 152*z**3 - 922 + 447*z**3 = 0.
-922, -1
Let l be 47064/1908 - (24 + 0). Factor 0*a**2 - 4/5*a**4 - 2/15*a**5 + 0*a - l*a**3 + 0.
-2*a**3*(a + 1)*(a + 5)/15
Let k(p) = p**2 + 8*p - 4. Let m(o) = -o**2 - 8*o + 4. Let v(y) = 5*k(y) + 4*m(y). Let d be v(-10). Factor -21*n**2 + 48*n**2 - 23*n**2 - d*n**3.
-4*n**2*(4*n - 1)
Let d(o) be the second derivative of -18*o**5 - 217*o**4/6 + 155*o**3/6 - 3*o**2 + 139*o - 3. What is g in d(g) = 0?
-3/2, 2/45, 1/4
Suppose -12*v = -16 - 32. Suppose -68 = k - 71. Factor 1/3*d**2 + 0 - 1/6*d + 1/6*d**k - 1/3*d**v.
-d*(d - 1)*(d + 1)*(2*d - 1)/6
Solve 3/4*i**4 + 129/4*i**3 + 111/4*i**2 + 189/2 - 621/4*i = 0.
-42, -3, 1
Let z(m) be the third derivative of m**7/840 + m**6/40 - 7*m**5/40 - 4*m**4/3 - m**3/6 + 43*m**2. Let g(q) be the second derivative of z(q). Factor g(p).
3*(p - 1)*(p + 7)
Determine s so that 24/5*s + 2/5*s**2 + 22/5 = 0.
-11, -1
Let m = -1726 + 1726. Let a(l) be the third derivative of m - 1/18*l**4 + 1/144*l**6 + 0*l + 16*l**2 + 1/9*l**3 - 1/120*l**5 + 1/630*l**7. Factor a(r).
(r - 1)*(r + 2)**2*(2*r - 1)/6
Let c = -7 + 9. Let a = -44 - -77. Factor -20*v - 17 - 5*v**c + a + 9.
-5*(v - 1)*(v + 5)
Factor -5094/5*i**2 - 134/5*i**3 - 2/5*i**5 - 4320 - 3888*i + 62/5*i**4.
-2*(i - 20)**2*(i + 3)**3/5
Let k(h) = 4*h**2 - 184*h + 2472. Let r(z) = -2*z - 4. Let c(l) = k(l) + 10*r(l). Factor c(t).
4*(t - 32)*(t - 19)
Factor 170/13*g**2 - 2/13*g**4 + 82/13*g**3 + 86/13*g + 0.
-2*g*(g - 43)*(g + 1)**2/13
Let x be (-100)/(-18)*(-72)/(-360). Suppose -25/9 + x*o - 1/9*o**2 = 0. Calculate o.
5
Let y = 3570 - 3565. Let g(f) be the third derivative of 0 - 43*f**2 - 1/15*f**y - 1/420*f**7 + 0*f**4 + 3/80*f**6 + 0*f + 0*f**3. Factor g(c).
-c**2*(c - 8)*(c - 1)/2
Let o(d) = 23*d**2 + 194*d - 6. Let v(z) = 65*z**2 + 581*z - 17. Let g(x) = -17*o(x) + 6*v(x). Factor g(s).
-s*(s - 188)
Suppose 497 + 726*u - 54*u**2 + 53*u**2 - 1222 = 0. Calculate u.
1, 725
Let g be ((-2)/(-4 - -2))/((-2)/(-4)). Let -96*i**g + 5064*i - 37*i**3 - 5082*i - 50*i**5 - 151*i**3 - 160*i**4 = 0. Calculate i.
-1, -3/5, 0
Let y(u) be the second derivative of u**6/60 - 2*u**5/5 - 25*u**4/8 - 49*u**3/6 - 10*u**2 - 651*u + 2. Let y(w) = 0. What is w?
-2, -1, 20
Determine j, given that 1/8*j**2 - 1/8 + 1/8*j - 1/8*j**3 = 0.
-1, 1
Let r = 1363/8 - 6799/40. Let u = 155/2 + -2321/30. Factor -r*z - u*z**2 - 4/15.
-2*(z + 1)*(z + 2)/15
Let b(g) = 44*g**4 + 278*g**3 + 550*g**2 + 428*g + 98. Let w(i) = -30*i**4 - 185*i**3 - 365*i**2 - 285*i - 65. Let o(u) = 5*b(u) + 7*w(u). Factor o(p).
5*(p + 1)**2*(p + 7)*(2*p + 1)
Let l(x) be the first derivative of x**4/24 + 11*x**3/18 + 5*x**2/6 + 3965. Factor l(a).
a*(a + 1)*(a + 10)/6
Find w such that 0*w**3 - w**4 - 84579*w**2 + 84585*w**2 - 3*w**3 + 8*w**3 = 0.
-1, 0, 6
Let d(f) be the first derivative of -7*f**6/27 - 38*f**5/45 + f**4/3 + 56*f**3/27 - 8*f**2/9 - 105. Find p, given that d(p) = 0.
-2, 0, 2/7, 1
Factor -b**3 + 0*b**3 - 48*b**2 + 163*b**2 + 168 - 214*b - 68*b**2.
-(b - 42)*(b - 4)*(b - 1)
Let t(y) be the second derivative of -16*y**7/63 - 22*y**6/15 + 26*y**5/15 + 56*y**4/3 - 4*y**3 - 90*y**2 - 17*y + 26. Let t(s) = 0. Calculate s.
-3, -1, 1, 15/8
Let v = -3/539 - -67/3234. Let i(l) be the third derivative of 0 - 3*l**2 - 1/660*l**6 + 0*l**3 + 0*l - v*l**4 - 1/110*l**5. Factor i(y).
-2*y*(y + 1)*(y + 2)/11
Let a be 8832/28 - 5 - 6/14. Let d = a + -310. Suppose 0 - 9/7*h**2 - h**4 + 1/7*h**5 + d*h + 15/7*h**3 = 0. What is h?
0, 1, 3
Let b(y) be the second derivative of 13*y**5/60 - 7*y**4/9 - 191*y**3/18 + 5*y**2 - 1949*y. Let b(s) = 0. Calculate s.
-3, 2/13, 5
Let f(o) be the third derivative of o**5/330 + 1247*o**4/132 - 416*o**3/11 + 12*o**2 - 6*o - 12. Find h such that f(h) = 0.
-1248, 1
Let y(q) = -2*q + 19. Let n be y(10). Let h(b) = b**3 - b**2 + b - 2. Let j(t) = -30*t**3 - 5*t**2 - 85*t + 10. Let k(c) = n*j(c) - 25*h(c). Factor k(a).
5*(a + 2)**3
Let c(i) be the first derivative of -i**3/3 - 545*i**2 - 297025*i + 264. What is v in c(v) = 0?
-545
Determine j so that 57/5*j**3 + 179/5*j - 1/5*j**4 + 177/5*j**2 + 12 = 0.
-1, 60
Let o be -4 - -5 - (-278)/120*-2. Let a = o + 62/15. Suppose -a*k**2 - 1/2*k**3 + 1/2*k