 that 540*p - 52*p + 353 + 496*p - 3*p**3 - 1057*p**2 - 277*p = 0.
-353, -1/3, 1
Let w(n) be the first derivative of 2*n**3/15 - 3*n**2/5 - 2108*n/5 - 6636. Determine j, given that w(j) = 0.
-31, 34
Let u be 3*((-57)/(-45) - (-75)/(-125)). Factor -13/3*t - 1/3*t**u + 1/3 + 13/3*t**3.
(t - 1)*(t + 1)*(13*t - 1)/3
Let m(q) be the second derivative of -2*q**7/21 + 236*q**6/15 - 936*q**5 + 21294*q**4 - 39546*q**3 + 983*q + 1. Factor m(t).
-4*t*(t - 39)**3*(t - 1)
Suppose -p + 5*z = -5, -5*p + 45*z - 49*z = -112. Let r(i) be the first derivative of 1/16*i**4 + 1/3*i**3 + 1/2*i**2 + 0*i + p. Find v such that r(v) = 0.
-2, 0
Let b(p) be the first derivative of -p**3/3 + 12*p**2 + 297*p + 4560. Factor b(l).
-(l - 33)*(l + 9)
Suppose -69 = -3*d + 5*u, -4*d = -d + 4*u - 42. Suppose -d*l + 15*l + 9 = 0. Let 2*w**3 + 0*w**2 + 4*w**2 + 12*w**4 + 4*w**5 + 10*w**l = 0. Calculate w.
-1, 0
Let y = 2198/3 + -732. Let h = -2359/435 - -165/29. Solve -h - y*g + 2/5*g**2 = 0.
-1/3, 2
Let t(n) = -5*n**3 + 2. Let a(o) = 21*o**3 - 2811*o**2 + 2633907*o - 822656961. Let m(l) = a(l) + 4*t(l). Factor m(i).
(i - 937)**3
Let l(o) = -9*o**2 + 12*o. Let b(i) = -25*i**2 + 81*i + 37*i + 41*i - 124*i. Let v(q) = 6*b(q) - 17*l(q). Let v(u) = 0. What is u?
-2, 0
Let 0 + 4374/7*s - 729/7*s**2 - 81*s**3 - 3/7*s**5 - 75/7*s**4 = 0. What is s?
-9, 0, 2
Let s(h) = -h**5 - h**4 - 9*h**3 - 5*h**2 + 22*h - 6. Let d(n) = -3*n**5 - 3*n**4 - 17*n**3 - 9*n**2 + 46*n - 14. Let t(v) = -3*d(v) + 7*s(v). Factor t(x).
2*x*(x - 2)*(x - 1)*(x + 2)**2
Let x = 1019 + -324. Let j = -695 + x. Factor 0*a + j - 1/2*a**2 + 1/2*a**3.
a**2*(a - 1)/2
Let v(l) be the third derivative of -l**8/112 + 63*l**6/40 + 31*l**5/2 + 141*l**4/2 + 180*l**3 + 154*l**2. Let v(q) = 0. Calculate q.
-3, -2, 10
Let a(z) = -4*z**3 + 2*z**2 - z. Let m(x) = -9*x**3 - 8*x**2 + 59*x - 48. Let t(q) = -4*a(q) + 2*m(q). Suppose t(o) = 0. What is o?
-16, 1, 3
Let g(m) be the first derivative of 4*m**2 + 8*m - 1/2*m**4 + 0*m**3 + 187 - 1/10*m**5. What is a in g(a) = 0?
-2, 2
Let f(z) = 4*z**2 + 828*z - 410. Let a(j) = -6*j + 2. Let d(h) = 5*a(h) + f(h). Factor d(q).
2*(q + 200)*(2*q - 1)
Let y be 175/(-21)*468/(-420). Let z = y - 188/21. Find v, given that -v**3 - v**2 - 1/3*v**4 - z*v + 0 = 0.
-1, 0
Find t, given that 0 - 20/7*t**4 - 120/7*t - 134/7*t**3 + 2/7*t**5 - 232/7*t**2 = 0.
-2, -1, 0, 15
Let j(h) = -17*h**3 - 80*h**2 + 97*h + 42. Let m(b) = b**3 + b**2 - 2*b - 3. Let x(s) = -j(s) - 14*m(s). Factor x(i).
3*i*(i - 1)*(i + 23)
Let v be ((-4)/(-6))/((3200/(-225))/(-8)). Let f(c) be the first derivative of -8 + 2*c + 1/6*c**3 + 2*c**2 - v*c**4. Determine t so that f(t) = 0.
-1, -2/3, 2
Let s = 626 + -890. Let i be s/(-143) - (-12)/78. Suppose -1/6*z + 1/6*z**3 + 0*z**i + 1/12*z**4 - 1/12 = 0. Calculate z.
-1, 1
Let y(i) be the second derivative of 49/2*i**2 + 106*i - 7/3*i**3 + 1/12*i**4 + 0. Let y(k) = 0. Calculate k.
7
Let b(x) be the second derivative of 92/27*x**4 + 400/9*x**2 + 4/15*x**5 + 160/9*x**3 + 1/135*x**6 - 106*x + 0. Factor b(i).
2*(i + 2)**2*(i + 10)**2/9
Let k(p) be the third derivative of p**6/10 - 39*p**5/20 - 447*p**2. Factor k(u).
3*u**2*(4*u - 39)
Suppose 2 = 4*l + 2*d, 22*d = 2*l + 17*d - 19. Suppose 4*o = 8 - 0. Factor -11*a + l*a**2 + 3*a**o - 5*a**4 + 6*a + 5*a**3.
-5*a*(a - 1)**2*(a + 1)
Let w(m) be the first derivative of 3*m**5/25 + 3*m**4/10 - m**3/5 - 3*m**2/5 + 7940. Determine b so that w(b) = 0.
-2, -1, 0, 1
Let m(n) = 4*n**3 - 372*n**2 + 1339*n - 1063. Let f(b) = b**3 - 94*b**2 + 335*b - 266. Let x(s) = -23*f(s) + 6*m(s). Solve x(p) = 0 for p.
1, 4, 65
Suppose 45*h - 84 = 24*h. Factor -12 - 3*o - 3*o**4 - 31*o - 30*o**2 - 6*o**3 + 6*o**h + o**4 - 2*o**4.
2*(o - 6)*(o + 1)**3
Let r = -23315/4 - -5829. Let t(h) be the third derivative of 0*h**3 + 0 - r*h**4 - 9*h**2 - 1/20*h**5 + 0*h. Solve t(q) = 0.
-2, 0
Let w(j) be the second derivative of -j**4/42 + 54*j**3/7 + 163*j**2/7 - 64*j. Find p such that w(p) = 0.
-1, 163
Let m(k) be the third derivative of -232*k**2 - 1/60*k**5 - 5/6*k**4 + 0*k - 50/3*k**3 + 0. Factor m(b).
-(b + 10)**2
Let x(d) be the second derivative of -d**7/441 - d**6/315 + d**5/10 + 41*d**4/126 + 20*d**3/63 - 19*d - 29. Solve x(p) = 0.
-4, -1, 0, 5
Let f(c) be the first derivative of 5*c**4/48 - 5*c**3/24 - 5*c**2/4 + c - 90. Let o(y) be the first derivative of f(y). Solve o(q) = 0 for q.
-1, 2
Let k = -419026 - -419040. Factor -22/3*u - k*u**2 - 4/3 - 10/3*u**4 - 34/3*u**3.
-2*(u + 1)**3*(5*u + 2)/3
Let d(w) be the second derivative of 2*w**6/45 + 16*w**5/15 - 22*w**4 + 144*w**3 - 450*w**2 - 239*w. Factor d(h).
4*(h - 3)**3*(h + 25)/3
Let f(q) be the second derivative of q**6/165 + q**5/10 + q**4/33 - 92*q**3/33 - 120*q**2/11 + 5507*q. Let f(l) = 0. Calculate l.
-10, -2, 3
Let u(j) be the second derivative of 31*j**4/9 - 1055*j**3/9 + 17*j**2/3 + 5*j - 342. Solve u(o) = 0 for o.
1/62, 17
Let -3208*u**3 + 340*u**4 + 808 + 563*u**4 - 111*u**4 - 1419*u + 4832*u**2 + 4*u**5 - 1809*u = 0. Calculate u.
-202, 1
Let f(y) be the third derivative of 0*y - 1/300*y**6 - 2/5*y**3 + 0 - 1/60*y**4 + 2/75*y**5 + 33*y**2. Factor f(n).
-2*(n - 3)*(n - 2)*(n + 1)/5
Let b = -123 + 198. What is f in b*f**2 - 92*f**4 + 480*f**2 + 280*f**3 + 220*f - 127 + 152 + 12*f**4 = 0?
-1, -1/4, 5
Suppose -10 = 5*o, -4*q - 4*o + 100 = -2*o. Suppose -6*n = -5*n - q. Solve 20*j**3 - 20*j - n*j**2 + 25 - 4*j**2 + j**4 + 4*j**4 = 0.
-5, -1, 1
Suppose 0 = 4*t + 4*s - 8, 11*t - 4*s = 6*t + 19. Suppose -t*d = 2*h + 8, h + d = -3*h + 4. Suppose 74*p + 4*p**3 + 24*p**h - 26*p - 12*p = 0. What is p?
-3, 0
Let o(h) be the first derivative of 100*h + 57 - 95/2*h**2 - 5/3*h**3. Find f such that o(f) = 0.
-20, 1
Let k(l) be the second derivative of l**6/180 - 2*l**5/45 - 5*l**4/36 - 6*l**2 + 114*l. Let j(i) be the first derivative of k(i). Solve j(w) = 0 for w.
-1, 0, 5
Suppose -19*j + 13*j = -180. Factor -16 - q**2 - 25 - 21*q + j + 9*q.
-(q + 1)*(q + 11)
Let d(h) be the third derivative of h**6/480 - 517*h**5/120 + 267289*h**4/96 + 356*h**2. Determine o, given that d(o) = 0.
0, 517
Determine j, given that 169*j**2 - 170*j**3 - 304*j - 7*j**3 + 4*j**4 + 121*j**2 + 174*j**2 + 13*j**3 = 0.
0, 1, 2, 38
Let f = -4 - -8. Suppose 1 = -4*j + 5*i - 3, f*i - 36 = -5*j. Factor -19*u**4 + 24*u**4 - 5*u**2 - 6*u + 10*u**3 - j*u.
5*u*(u - 1)*(u + 1)*(u + 2)
Let t = 57 - 281/5. Let d(c) = -3*c**2 - 20*c - 7. Let w be d(-6). Let -2/5*b**3 + 0 + 2/5*b**w - 4/5*b**2 + 0*b + t*b**4 = 0. Calculate b.
-2, -1, 0, 1
Let s(r) = 4*r**3 - 4*r**2 - 3. Let z be (-3 + 3 - 1)/1. Let b(j) = j**3 - 2*j**2 + j - 1. Let u(n) = z*s(n) + 3*b(n). Determine v, given that u(v) = 0.
-3, 0, 1
Let i(y) be the second derivative of -1/27*y**3 - 4/9*y**2 + 1/108*y**4 + 0 - 47*y. Solve i(d) = 0 for d.
-2, 4
Suppose -3*d - d - 20 = 0, 4*d = -2*n - 664. Let t = 326 + n. Factor o**3 + 0*o - 1/2*o**t + 0*o**2 + 0.
-o**3*(o - 2)/2
Let w(u) = -3*u**3 + 326*u**2 - 206*u + 18. Let y(r) = -r**3 + 82*r**2 - 52*r + 4. Let j(z) = -4*w(z) + 18*y(z). Factor j(x).
-2*x*(x - 28)*(3*x - 2)
Suppose y = -2*a + 17, 0 = 2*a - 29 + 15. Let x(b) be the first derivative of 3125/3*b**y - 250*b**2 + 16 + 20*b. Factor x(n).
5*(25*n - 2)**2
Let o be (-3*(-25)/(-15))/((-14)/4 + 1). Let z(j) be the first derivative of -2/57*j**3 + 0*j - 2/95*j**5 + 0*j**o + 12 - 1/19*j**4. Find v such that z(v) = 0.
-1, 0
Let v be -3*8/182 - 2912/(-10192). Solve -6/13*n + 6/13*n**3 - 2/13*n**4 + 4/13 - v*n**2 = 0 for n.
-1, 1, 2
Let g(c) be the second derivative of -c**6/180 + c**5/24 + 7*c**4/24 - 85*c**3/36 - 25*c**2/3 - 3575*c. Solve g(u) = 0 for u.
-4, -1, 5
Determine x, given that 0*x**4 + 704*x + 30*x**4 - 3*x**5 + 118*x**2 + 275*x**2 + 111*x**2 + 5*x**5 + 384 + 176*x**3 = 0.
-4, -3, -2
Let o(v) be the first derivative of -11/10*v**2 + 0*v - 3/20*v**4 + 34/15*v**3 - 65. Factor o(g).
-g*(g - 11)*(3*g - 1)/5
Let b(k) be the third derivative of -k**6/120 + k**4/24 + k**3/6 - 75*k**2. Let n(x) = -4*x**3 - x**2 + 4*x + 6. Let g(y) = -20*b(y) + 4*n(y). Factor g(m).
4*(m - 1)**2*(m + 1)
Let r(w) be the first derivative of -2/45*w**3 + 6 - 32/15*w - 8/15*w**2. Factor r(j).
-2*(j + 4)**2/15
Let y be 1 + (-11)/9 + 3978/(-1053). Let m(i) = -i**2 - 23*i - 49. Let b be m(y). Determine u so that -6*u + b + 1/3*u**2 = 0.
