138)/4
Suppose 45*t - 11 = 79. Solve 3*n**2 - 71 - 3*n**t + 36*n - 2*n**2 + 14 - 33 = 0 for n.
3, 15
Let g(y) be the third derivative of y**5/150 + 17*y**4/60 - 22*y**3/3 - 3652*y**2. Let g(q) = 0. Calculate q.
-22, 5
Factor 25*p**4 + 2*p + 4*p**3 - 14106 + 5*p**2 - 24*p**4 + 14106.
p*(p + 1)**2*(p + 2)
Let m(k) be the second derivative of -19*k**5/30 + 7*k**4/6 - 2*k**3/9 - 1010*k. Factor m(u).
-2*u*(u - 1)*(19*u - 2)/3
Let p = 14/2461 - -2419/7383. Solve 0 + 1/3*f**3 - 1/3*f + 1/3*f**2 - p*f**4 = 0 for f.
-1, 0, 1
Let a = -13356/11 + 93503/77. Let 6/7*z**3 + 0 + a*z**5 + 4/7*z**4 + 1/7*z + 4/7*z**2 = 0. What is z?
-1, 0
Let b(q) be the first derivative of q**4/2 - 16*q**3 + 144*q**2 + 608. Factor b(v).
2*v*(v - 12)**2
Let o(s) be the second derivative of -s**5/5 + 571*s**4/3 - 162448*s**3/3 - 163592*s**2 - 21*s - 11. Factor o(y).
-4*(y - 286)**2*(y + 1)
Factor -120*b**2 + 2376*b + 35*b**3 - 69*b**3 - 15488 + 13*b**3 + 11*b**3 + 12*b**3.
2*(b - 22)**2*(b - 16)
Suppose 5*p + 35 = b + 33, -5*b + 50 = -5*p. Determine s so that 0*s - 2/3 + 2/3*s**p = 0.
-1, 1
Factor 230/3 - 2/3*h**3 - 286/3*h + 58/3*h**2.
-2*(h - 23)*(h - 5)*(h - 1)/3
Determine u so that 0 - 1/2*u**4 - 25/2*u**3 + 24*u - 11*u**2 = 0.
-24, -2, 0, 1
Let a(j) be the third derivative of -j**6/600 + 259*j**5/300 + 521*j**4/120 + 87*j**3/10 + 3*j**2 + 2*j - 218. Factor a(l).
-(l - 261)*(l + 1)**2/5
Let t(f) be the first derivative of -f**4/12 + 131*f**3/27 + 164*f**2/9 - 92*f/3 + 1458. Let t(z) = 0. Calculate z.
-3, 2/3, 46
Let k(y) be the first derivative of -2/45*y**5 - 1/18*y**4 + 0*y + 2/27*y**3 + 1/9*y**2 - 76. Factor k(h).
-2*h*(h - 1)*(h + 1)**2/9
Let j(x) = 6*x - 21. Let p be j(4). What is b in -5*b**2 + p - 78 - 25*b - 55*b = 0?
-15, -1
Let v(w) = -96*w + 13156. Let t be v(137). Factor -1346/17*j**2 + 1472/17*j + 326/17*j**3 + 2/17*j**5 - 512/17 + 58/17*j**t.
2*(j - 1)**3*(j + 16)**2/17
Let f(g) be the first derivative of -212 + 39/2*g**4 - 507*g**3 + 0*g**2 - 1/5*g**5 + 0*g. Suppose f(z) = 0. Calculate z.
0, 39
Let s(y) be the second derivative of y**5/180 + 1193*y**4/36 + 1423249*y**3/18 + 1697936057*y**2/18 + 17*y - 27. Factor s(l).
(l + 1193)**3/9
Let p be ((-99372)/17199)/((-4)/234). Factor 26*n + p + 1/2*n**2.
(n + 26)**2/2
Let n(c) be the first derivative of 3*c**4/8 - 106*c**3 + 8427*c**2 + 1112. Let n(u) = 0. Calculate u.
0, 106
Let m be (-8 - 200/(-28))*-140. Let t be 9/(-36) + 894/m. Solve 1/5*d**2 + t - 12/5*d = 0 for d.
6
Suppose 3*u - 12 = 4*i, 0 = -8344*i + 8348*i + 2*u - 8. Factor -8/19*d**2 - 6/19*d**3 + 30/19*d + i.
-2*d*(d + 3)*(3*d - 5)/19
Let n(t) be the first derivative of 3*t**4/20 - 303*t**3 + 459045*t**2/2 - 77272575*t + 2464. Solve n(k) = 0.
505
Suppose -1350*b + 2294 - 162*b - 860*b + 34*b**2 - 30*b**2 + 74 = 0. Calculate b.
1, 592
Suppose -2*p**3 + 1588/7*p**2 + 0*p + 0 = 0. What is p?
0, 794/7
Suppose 36 = 18*z - 6*z. Determine t, given that 4478 + 2400*t + 75*t**2 + 2*t**z + 11522 + 45*t**2 = 0.
-20
Let k be (-5)/(-3) - (-32 + 1104/36). Suppose 0 - 2/5*t**2 + 2/5*t**4 + 6/5*t - 6/5*t**k = 0. Calculate t.
-1, 0, 1, 3
Let t(h) = 27*h**3 + h**2 + 7*h - 9. Let x be t(2). Factor -37 + x*g + g**2 - 17 - 169*g**2 - 147*g**3.
-3*(g + 2)*(7*g - 3)**2
Let y(a) = -6*a**4 + 20*a**3 + 13*a**2 - 69*a + 40. Let k(u) = -u**4 - 2*u**2 + u. Let o = 251 - 252. Let h(b) = o*k(b) + y(b). Factor h(i).
-5*(i - 4)*(i - 1)**2*(i + 2)
Factor -9/2*j**2 + 34 + 59/2*j.
-(j + 1)*(9*j - 68)/2
Let w(l) be the first derivative of -150*l**2 + 65/6*l**3 + 29 - 1000/3*l - 5/24*l**4. What is o in w(o) = 0?
-1, 20
Let c(i) be the second derivative of i**4/12 + 121*i**3/2 + 181*i**2 - 138*i. Determine n so that c(n) = 0.
-362, -1
Let a = 593 + -623. Let z be (-3 + 10)*(a/147)/(-5). What is d in 1/7*d**5 - 1/7 - 3/7*d - z*d**2 + 3/7*d**4 + 2/7*d**3 = 0?
-1, 1
Let r be (-25 - -9)/240 + 111/45. Factor -r*l**3 + 12/5*l + 2/5*l**4 - 16/5*l**2 + 14/5.
2*(l - 7)*(l - 1)*(l + 1)**2/5
Let p = -85136 - -85140. Let 0 + 2/7*v**3 - 1/7*v**p - 1/7*v**2 + 0*v = 0. Calculate v.
0, 1
Suppose -4*a = -52, 2*a = -103*f + 108*f - 954. Factor -f - 1/4*q**2 + 14*q.
-(q - 28)**2/4
Suppose -5263 = -18*a + 8453. Let b = a + -5332/7. Let -2/7 + 2/7*k**2 + b*k**3 - 2/7*k = 0. What is k?
-1, 1
Suppose 9*q - 16 = q. Let 27*s - 3 - 106*s**2 + 136*s**q + 9 = 0. What is s?
-1/2, -2/5
Let g(p) be the first derivative of p**5/4 + 65*p**4/6 + 845*p**3/6 - 15*p + 1. Let k(x) be the first derivative of g(x). Suppose k(w) = 0. Calculate w.
-13, 0
Suppose 0 = 342*s - 257*s. Let u(k) be the third derivative of 3/20*k**5 + s*k**3 - 1/4*k**4 - 18*k**2 + 0*k + 0 + 1/8*k**6. Factor u(t).
3*t*(t + 1)*(5*t - 2)
Find q such that q - 41*q**2 + 2*q - 15*q + 81*q - 17*q + 7*q**3 = 0.
0, 13/7, 4
Let g(p) = -6*p**4 + 129*p**3 + 123*p**2 - 225*p. Let z(c) = 23*c**4 - 510*c**3 - 491*c**2 + 901*c. Let f(w) = 11*g(w) + 3*z(w). Factor f(k).
3*k*(k - 38)*(k - 1)*(k + 2)
Let c(r) = -31*r + 1. Let z be c(-1). Suppose 5*y + z = 4*x, 4*y - 3*y = 0. Find o such that -12*o + 98*o**3 - 24*o - 12*o - 42*o**2 - x = 0.
-2/7, 1
Let k(d) be the second derivative of 2*d**7/21 - 6*d**6/5 - 36*d**5/5 - 4*d**4/3 + 32*d**3 - 656*d. Let k(y) = 0. Calculate y.
-2, 0, 1, 12
Let t(s) be the second derivative of -s**6/20 + s**5/4 - 3*s**4/8 - 3*s**2 - 328*s. Let k(z) be the first derivative of t(z). Solve k(x) = 0.
0, 1, 3/2
Let p = 14530/7 - 2074. Let o be 0 + -10*(-6)/15. Find k such that p*k - 12/7 - 3/7*k**o - 6/7*k**3 + 9/7*k**2 = 0.
-2, 1
Factor -23*a**2 + 69668*a + 17*a**2 - 10 - 69700*a.
-2*(a + 5)*(3*a + 1)
Suppose t = -4*r + 7 + 10, 3*t - 7 = -r. Let i be (-2)/(-9)*t*(-12)/(-8). Factor 2/3 + i*x**3 - 2/3*x - 1/2*x**2 + 1/6*x**4.
(x - 1)**2*(x + 2)**2/6
Let w(h) be the first derivative of 293 + 0*h**4 + 2/95*h**5 + 0*h**2 + 18/19*h - 20/57*h**3. Find o such that w(o) = 0.
-3, -1, 1, 3
Let t be (-2709)/(-30) + (-3)/(-15). Let x = t - 89. Suppose 2*i**2 + 13/4*i + x + 1/4*i**3 = 0. Calculate i.
-6, -1
Let t = 340839 + -340837. Suppose -4/3 - 8/9*z**4 - 50/9*z**3 - 70/9*z - 100/9*z**t = 0. Calculate z.
-3, -2, -1, -1/4
Let p be 0*3*3/(-18)*-1. Let a(t) be the second derivative of 0*t**2 + 1/140*t**5 + 0 + 13*t + p*t**3 + 1/42*t**4. Find j such that a(j) = 0.
-2, 0
Let h(u) be the first derivative of 1/10*u**5 + 1/24*u**6 + 124 + 0*u**2 + 0*u - 1/16*u**4 - 1/6*u**3. Factor h(q).
q**2*(q - 1)*(q + 1)*(q + 2)/4
Factor 1/3*m**2 + 114*m + 9747.
(m + 171)**2/3
Let g(h) be the third derivative of -h**5/60 + 31*h**4/24 - 14*h**3 - 1013*h**2. Factor g(j).
-(j - 28)*(j - 3)
Let b(d) = -d**2 + 4*d + 9. Let v be b(5). Suppose 4*f - 265 = -y, -v*f + 202 = -3*y - 43. Find n, given that 12*n**2 - f*n**3 - 8*n + 26*n + 67*n**3 = 0.
-3, 0
Let i = -117387/2 - -58695. Factor -1/2*l**3 - i*l - 9/2 + 5/2*l**2.
-(l - 3)**2*(l + 1)/2
Let u(t) be the third derivative of t**5/60 - 193*t**4/12 + 385*t**3/6 - 100*t**2 + 2*t + 7. Factor u(z).
(z - 385)*(z - 1)
Let j = -2625/11 - -23647/99. Determine c so that -40/9*c - 4/9*c**2 - 16/3 + j*c**3 = 0.
-2, 6
Let b(f) = -117*f**2 - 119*f - 38. Let p(s) = -118*s**2 - 118*s - 32. Let v(m) = 8*b(m) - 9*p(m). Let v(y) = 0. What is y?
-1, 8/63
Suppose -12*s + 2350 = 13*s. Solve -s*b**2 + 2*b + 95*b**2 + 4*b = 0.
-6, 0
Let i = 2/812733 - 9695091973/6501864. Let k = i - -1493. What is p in -k*p**4 + 0*p + 0*p**2 + 3/4*p**3 + 0 - 9/8*p**5 = 0?
-2, 0, 1/3
Let k(o) be the second derivative of -2/21*o**7 + 0 + 10/3*o**4 - 5*o - 250*o**2 + 350/3*o**3 - 26/15*o**6 - 46/5*o**5. What is t in k(t) = 0?
-5, 1
Let 0 + 2/7*t**3 - 240/7*t**2 - 488/7*t = 0. Calculate t.
-2, 0, 122
Let t(x) be the first derivative of x**8/2100 + x**7/210 + 7*x**6/450 + x**5/50 - 3*x**3 + 70. Let k(f) be the third derivative of t(f). Solve k(i) = 0 for i.
-3, -1, 0
Suppose -66*p - 241 + 237 = -202. Let -9/4*l**p - 6*l - 29/4*l**2 - 1 = 0. What is l?
-2, -1, -2/9
Let 2/3*z**2 - 24*z + 136/3 = 0. What is z?
2, 34
Suppose 37*w + 700 = 212*w. Let g(h) be the third derivative of -24*h**2 + 1/6*h**3 + 7/96*h**w + 0 + 0*h - 1/480*h**6 + 1/120*h**5. Factor g(b).
-(b - 4)*(b + 1)**2/4
Let x(r) be the second derivative of -r**4/42 - 121*r**3/21 - 120*r**2/7 - 215*r. Determine u so that x(u) = 0.
-120, -1
Let o be -2*(-16 - -19)/(-1 + -1). Factor -26*d + d**3 + d**o + 162 - 148 - 13*d**