(s - 150)/2
Let g(p) be the second derivative of p**5/15 - 17*p**4/9 - 212*p**3/9 - 176*p**2/3 + 3289*p. Solve g(c) = 0.
-4, -1, 22
Let p(r) = -3*r**2 + 51*r - 42. Let v be p(16). Suppose -13*t + 76 = v*t. Solve t*g - 5*g**2 - 4/5 = 0 for g.
2/5
Let x(p) be the third derivative of -11*p + 1/2*p**4 - 1/30*p**5 + 3*p**2 + 0 - 8/3*p**3. Find h such that x(h) = 0.
2, 4
Suppose -11 = -502*h + 493*h + 7. Factor -2/19*v**h - 1352/19 - 104/19*v.
-2*(v + 26)**2/19
Factor 269/4*j + 67 + 1/4*j**2.
(j + 1)*(j + 268)/4
Let c(z) be the second derivative of 2*z**6/15 - 27*z**5/5 - z**4/3 + 18*z**3 + 2*z + 128. Solve c(l) = 0 for l.
-1, 0, 1, 27
Let j(d) = 3*d**3 + d**2 + d - 1. Let n(r) = -13*r**3 + 27*r**2 + 125*r + 105. Let f(s) = 10*j(s) + 2*n(s). Factor f(t).
4*(t + 1)*(t + 5)*(t + 10)
Let q = 143 - 126. Let f be (-15)/(-12) + ((-408)/(-32))/q. Determine h so that 44/5*h**f + 0 - 8/5*h = 0.
0, 2/11
Factor 5 + 55*f + 4 + 799*f**2 - 59 - 804*f**2.
-5*(f - 10)*(f - 1)
Let a(m) be the first derivative of 0*m**3 + 38 + 0*m + 5/2*m**2 - 5/4*m**4. Find d such that a(d) = 0.
-1, 0, 1
Let p = 420 + -413. Factor 0*m**4 - 28*m**3 - 3*m**4 - 4*m**4 + p*m**4 + 28*m - 32 - 4*m**4 + 36*m**2.
-4*(m - 1)**2*(m + 1)*(m + 8)
Suppose -644*v + 650*v - 12 = 0. Let o = -11 + 32. Solve o*p**v + 10*p - 4 - 4 - 23*p**2 = 0.
1, 4
Let n(c) = 145*c**3 - 2395*c**2 + 17645*c - 33530. Let r(s) = -13*s**3 + 218*s**2 - 1604*s + 3048. Let x(j) = -4*n(j) - 45*r(j). Factor x(t).
5*(t - 38)*(t - 4)**2
Let f = 118 + -57. Suppose 13*q - f = -22. Let -4/5*r**q - 4/5*r**2 + 0*r + 0 = 0. Calculate r.
-1, 0
Let w(f) be the first derivative of 2*f**5/5 + 373*f**4/4 + 185*f**3 - f**2/2 - 185*f + 774. Factor w(l).
(l + 1)**2*(l + 185)*(2*l - 1)
Suppose -386/5*o + 388/5 - 2/5*o**2 = 0. What is o?
-194, 1
Let s(x) be the first derivative of -x**4 + 38*x**3/3 + 28*x**2 + 263*x + 242. Let t(b) be the first derivative of s(b). Factor t(k).
-4*(k - 7)*(3*k + 2)
Let f(t) = -4*t**3 + 104*t**2 + 446*t + 448. Let x(s) = -s**3 + 3*s. Let c(l) = f(l) - 2*x(l). What is q in c(q) = 0?
-2, 56
Determine i so that -1024/21*i**3 - 76/7*i**2 + 50/21*i**5 + 98/3*i - 40/7 + 20/7*i**4 = 0.
-5, -1, 1/5, 3/5, 4
Let n be 151 + (-19 - -20)/((-1)/2). Let y = n - 1339/9. Solve -y*i**3 - 250/9 - 10/3*i**2 - 50/3*i = 0.
-5
Let j(f) be the first derivative of 1 + 6*f**2 + 1/60*f**5 + 0*f + 1/8*f**4 - 2/3*f**3. Let w(p) be the second derivative of j(p). Factor w(y).
(y - 1)*(y + 4)
Let -96/5 - 3/5*p**3 - 39*p - 102/5*p**2 = 0. Calculate p.
-32, -1
Find g, given that -1922/7*g**4 + 1044/7*g - 4296/7*g**2 - 54/7 - 7316/7*g**3 = 0.
-3, -1, 3/31
Let r = 156 - 141. Suppose -m + a - r = -20, 3*m = 5*a + 19. Factor -14/5*l - 26/5*l**m + 8/5*l**4 + 2/5 + 6*l**2.
2*(l - 1)**3*(4*l - 1)/5
Let d(m) be the third derivative of 0 + 15/4*m**3 + 65/72*m**4 + 6*m**2 + 20*m - 1/72*m**5. Factor d(l).
-5*(l - 27)*(l + 1)/6
Let f(s) be the third derivative of 16*s**2 - 2/15*s**7 + 4/3*s**4 + 3 + 0*s**3 + 0*s + 1/84*s**8 + 7/15*s**5 - 3/10*s**6. Solve f(q) = 0 for q.
-1, 0, 1, 8
What is c in -4*c**2 + 12862 - 24*c + 1020*c - 11862 = 0?
-1, 250
Let g = 355522 + -1422075/4. Factor -12*y - 1/4*y**3 - 9 - g*y**2.
-(y + 1)*(y + 6)**2/4
Let h(v) = -65*v + 41. Let c be h(4). Let f = c - -222. Factor 0*i + 0 - 12/5*i**f - 8/5*i**2 - 4/5*i**4.
-4*i**2*(i + 1)*(i + 2)/5
Let l(w) = -2*w**2 + 38*w + 61. Let v be l(20). Let j be (v + -17)/((-2)/(-1)). Factor -5/6*n**j - 4/3*n - 1/6*n**3 - 2/3.
-(n + 1)*(n + 2)**2/6
Let 165/7*v + 3/7*v**5 + 0 + 72*v**3 + 498/7*v**2 + 174/7*v**4 = 0. What is v?
-55, -1, 0
Let j(z) be the second derivative of z**7/112 - 23*z**6/80 - 117*z**5/80 - z**4/8 + 13*z**3/2 - 3*z + 440. Suppose j(q) = 0. Calculate q.
-2, 0, 1, 26
Determine b so that -4*b**4 - 51*b**3 + 1203*b**3 + 1236*b**3 - 240100*b**2 - 428*b**3 = 0.
0, 245
Let b(o) be the third derivative of o**7/315 - 13*o**5/30 + 35*o**4/18 - 1282*o**2. Factor b(z).
2*z*(z - 5)*(z - 2)*(z + 7)/3
Let f(t) be the second derivative of -225*t**2 + 2 - 3*t - 10*t**3 - 1/6*t**4. Find p, given that f(p) = 0.
-15
Let i(y) be the first derivative of -y**6/18 + 8*y**5/5 - 33*y**4/2 + 652*y**3/9 - 267*y**2/2 + 108*y - 1186. Suppose i(k) = 0. Calculate k.
1, 4, 9
Let n(x) = 2*x**4 + 150*x**3 - 8253*x**2 + 131217*x + 472395. Let o(f) = -f**4 + 3*f**3 - 3*f**2 + f - 1. Let y(b) = -2*n(b) - 6*o(b). What is g in y(g) = 0?
-3, 54
Let i = 40207/6 - 6701. Let b(l) be the first derivative of -13 - 1/6*l**2 + 0*l - 1/30*l**5 - i*l**4 - 5/18*l**3. Suppose b(c) = 0. What is c?
-2, -1, 0
Let k(f) be the first derivative of -1/2*f**4 + 0*f + 0*f**2 - 13/18*f**3 + 1/30*f**5 - 34. Factor k(g).
g**2*(g - 13)*(g + 1)/6
Let q(b) be the third derivative of -b**6/24 + 65*b**4/24 + 10*b**3 + 4*b**2 + 622. Find c such that q(c) = 0.
-3, -1, 4
Let g = -245509 - -744187/3. Let s = -2552 + g. Factor -s*c**4 + 0 + 4/3*c**3 + 0*c - 4/3*c**5 + 4/3*c**2.
-4*c**2*(c - 1)*(c + 1)**2/3
Let v(y) be the third derivative of -y**6/36 - y**5/10 - y**4/12 - 7*y**3 + 2*y**2 - 27*y. Let t(p) be the first derivative of v(p). What is j in t(j) = 0?
-1, -1/5
Let v(r) be the first derivative of -r**5/45 + 8*r**4/27 - 32*r**3/27 + 85*r + 3. Let i(g) be the first derivative of v(g). Factor i(t).
-4*t*(t - 4)**2/9
Let k = -121381/5 + 24277. Determine n, given that 4/5*n**2 + k*n**4 + 12/5*n - 8/5 - 12/5*n**3 = 0.
-1, 1, 2
Let f be ((-156)/(-24) - 6)/((-21)/(-175)). Let g(i) be the second derivative of -5*i**2 + f*i**3 + 17*i + 0 - 5/4*i**4. Factor g(t).
-5*(t - 1)*(3*t - 2)
Suppose 2*b = -10, 4*x = -5*b + 124 - 21. Let s = x + -29. Factor 20/3*d**2 + 16/3 - 4/3*d**s - 32/3*d.
-4*(d - 2)**2*(d - 1)/3
Factor -17*h + 2/7*h**2 - 121/7.
(h + 1)*(2*h - 121)/7
Let v(n) be the second derivative of -4/35*n**5 - 11/42*n**4 + 4/105*n**6 + 0*n**2 - 1 - 1/7*n**3 - 121*n. Factor v(s).
2*s*(s - 3)*(2*s + 1)**2/7
Let r(k) be the third derivative of 125*k**8/448 + 75*k**7/7 + 4157*k**6/32 + 16901*k**5/40 + 627*k**4 + 484*k**3 + 2*k**2 - 332*k. Let r(m) = 0. Calculate m.
-11, -4/5, -2/5
Let u be (-11)/(33/18)*23130/(-81). Let o = u - 1712. Determine b, given that o*b**3 - 2/3*b**4 - 4/3*b + 0*b**2 + 2/3 = 0.
-1, 1
Suppose 10*x + 2363 - 9963 = 0. Let o be (x/(-57))/(-20)*3/8. What is l in 0*l**2 + 0*l + o*l**4 + 1/2*l**3 + 0 - 1/4*l**5 = 0?
-1, 0, 2
Factor -187/7 + 1/7*x**2 - 186/7*x.
(x - 187)*(x + 1)/7
Let i = 6937 + -90176/13. Let s(h) be the first derivative of -i*h**2 - 4 - 4/13*h - 2/13*h**3. Factor s(j).
-2*(j + 1)*(3*j + 2)/13
Let x(g) = -17*g + 83. Let o(w) = 15*w - 83. Let p(c) = -7*o(c) - 6*x(c). Let k be p(27). Solve -3/4*b**4 + 0*b**k + 0 + 0*b - 9/4*b**3 = 0.
-3, 0
Let p = 429 - 411. Factor 2*j**4 - 4*j**2 + 2*j**4 + p*j**3 + 5*j - 22*j**3 - j.
4*j*(j - 1)**2*(j + 1)
Let o = 835673 + -2506996/3. Suppose 10*t = 5*t + 20. Factor -o*q**3 - 9*q**2 - 13/3*q - 7/3*q**t - 2/3.
-(q + 1)**3*(7*q + 2)/3
Suppose -37 = -2*f + a, 7*f = 2*f - 2*a + 88. Let u be 4/24*f - (1 - 2). Solve 0 - 4*x**3 + 12/7*x**u - 4/7*x + 20/7*x**2 = 0 for x.
0, 1/3, 1
Let c(f) be the third derivative of f**6/30 - f**5/3 + f**4 + 1650*f**2. Solve c(v) = 0 for v.
0, 2, 3
Solve -195/2 + 141/2*s + 51/2*s**2 + 3/2*s**3 = 0.
-13, -5, 1
Suppose 0 = 18*y - 7*y - 22. Find n, given that -619*n**3 - 1882384*n - 165*n**3 - 9480*n**2 - 22804*n**2 - 25340*n**y - 4*n**4 - 23059204 = 0.
-49
Let r(u) = -u**3 + 624*u**2 + 10901*u + 70. Let q be r(-17). Factor -81/4*l + 39/4 + 45/4*l**q - 3/4*l**3.
-3*(l - 13)*(l - 1)**2/4
Let l = -712 + 720. Let y(k) be the third derivative of -4/5*k**5 - 14*k**2 + 0*k + l*k**4 - 128/3*k**3 + 1/30*k**6 + 0. Determine u, given that y(u) = 0.
4
Let m(r) be the first derivative of 2*r**6/3 + 24*r**5/5 + 4*r**4 - 8*r**3 - 10*r**2 + 839. What is h in m(h) = 0?
-5, -1, 0, 1
Let n(j) = -j**3 + 6*j**2 - 8*j + 2. Let c be n(4). Let d = -1360 - -6808/5. Factor -8/5*a + 2/5*a**c + d.
2*(a - 2)**2/5
Let t be (10/(-15))/((-2)/8). Let i = -10353 - -10353. Let t*o - 22/3*o**2 + 5/3*o**3 + i = 0. What is o?
0, 2/5, 4
Factor -24*c**3 - 3/8*c**4 - 12000 - 4800*c - 540*c**2.
-3*(c + 4)*(c + 20)**3/8
Let d = 675143 + -23633857/35. Let s = d - -556/5. Solve 6/7 + 2/7*h - s*h**2 = 0 for h.
-3/4, 1
Let u(l) be the first derivative of l**3/6 + 3*l**2 - 13*l/2 - 932. Factor u(v).
(v - 1)*(