3/2 + 9/4*a**2 - 3/4*a**4 - 3/4*a**b + 15/4*a.
-3*(a - 2)*(a + 1)**3/4
Let r(j) be the first derivative of -13/14*j**2 + 206 + 5/21*j**3 - 6/7*j. Suppose r(x) = 0. What is x?
-2/5, 3
Let o(l) be the first derivative of 33*l**4/10 - 10*l**3 + 18*l**2/5 + 1171. Find t, given that o(t) = 0.
0, 3/11, 2
What is c in 50/3*c**4 - 940*c**3 + 170 + 4624*c**2 - 5212/3*c = 0?
1/5, 5, 51
Find d such that 83 + 1134*d - 202*d**3 + 408*d**2 + 55 + 151*d**3 + 555*d**2 - 18 = 0.
-1, -2/17, 20
Let d(i) be the third derivative of 32*i**2 + 1/60*i**5 + 0*i + 5/8*i**4 + 0 - 17/3*i**3. Solve d(r) = 0 for r.
-17, 2
Let b(q) be the third derivative of -3*q**2 + 0*q**4 - 1 + 0*q + 1/60*q**5 + 0*q**3 - 1/240*q**6. Let b(k) = 0. Calculate k.
0, 2
Let m = -39 + 45. Factor 15*p - 21*p**3 + 2 - m*p**3 + 11*p**3 + 24*p**2.
-(p - 2)*(4*p + 1)**2
Let j be (-1 + 9/2)*(-2052)/(-2394). Let k = 12 + -8. Factor 17/7*s**j - 20/7*s**2 + 4/7*s - 4/7*s**k + 0.
-s*(s - 2)**2*(4*s - 1)/7
Suppose -m - 2*r = -45, -45 = -5*m + 4*m + r. Determine i, given that 46*i**2 - 65*i + 60 - 86*i**2 + m*i**2 = 0.
1, 12
Let b(d) = -10*d - 58. Let o be b(-6). Suppose 3 = -u, 5*u = -0*t - t - 12. Determine f so that 3*f**2 + 7*f**3 - 9*f**t + 2*f**5 - f**o - f**4 - f**4 = 0.
-1, 0, 1
Suppose 2*v + 2*i + 254 = 48, -1 = i. Let m = 117 + v. What is s in 60*s**4 + 84*s**5 - 102*s**3 + m*s**3 - 13*s**2 - 6 + 33*s - 11*s**2 = 0?
-1, 2/7, 1/2
Let m(q) be the first derivative of -2*q**5/5 + 41*q**4/3 - 3176*q**3/27 - 1142*q**2/9 - 130*q/3 - 1305. Solve m(y) = 0.
-1/3, 13, 15
Let i(c) = -33*c + 1421. Let y be i(43). Let f(o) be the first derivative of -2/15*o**3 + 3/5*o**y - 4/5*o - 7. Suppose f(u) = 0. What is u?
1, 2
Let a(f) = 7*f**4 - 7*f**3 - 11*f. Suppose 2*w = -0*w - 44. Let p(b) = 0*b + 3*b + 4*b**4 - 6*b**4 + 2*b**3. Let h(i) = w*p(i) - 6*a(i). What is v in h(v) = 0?
0, 1
Suppose 23 = 3*r - 4*r - 2*c, 0 = 5*r - 3*c - 54. Factor 480*n + 20*n**r + 2/5*n**4 + 1346/5*n**2 + 1152/5.
2*(n + 1)**2*(n + 24)**2/5
Let b(l) be the third derivative of -l**8/20160 - 11*l**7/5040 + 3*l**5/4 - l**2 + 15*l. Let w(p) be the third derivative of b(p). Factor w(k).
-k*(k + 11)
Suppose -2*i + 0 = -4*p - 4, 0 = -5*p - 15. Let m(c) = -2*c**3 - 8*c**2 - c + 1. Let v be m(i). Factor -2 + 3*d - 17*d + v*d + 13*d - 2*d**2.
-2*(d - 1)**2
Let f(z) be the first derivative of z**6/27 - 34*z**5/15 + 40*z**4 - 3448*z**3/27 - 64*z**2/3 + 512*z - 10840. Find u such that f(u) = 0.
-1, 2, 24
Let d be (-13 - -15)*(-2)/(-80)*-2. Let u = d - -1/2. Factor -2/5 - u*o**4 - 12/5*o**2 + 8/5*o**3 + 8/5*o.
-2*(o - 1)**4/5
Let c(b) be the third derivative of -b**7/420 - 7*b**6/240 - b**5/20 - 69*b**2 + 3. Let c(l) = 0. Calculate l.
-6, -1, 0
Let d = -516 + 520. Let w(q) be the second derivative of -6*q + 0 - 1/3*q**4 - 2*q**3 - d*q**2. Factor w(z).
-4*(z + 1)*(z + 2)
Suppose -5*q = -3*n + 98, n - 57 = -3*q - 15. Let w(l) be the first derivative of -n - 1/8*l**4 - 1/6*l**3 + 0*l + 3/2*l**2. Factor w(i).
-i*(i - 2)*(i + 3)/2
Suppose q = 4*h - 2 - 7, -24 = -4*q + h. Factor q*k + 3204*k**2 - 8 - 2*k**4 - 12*k**3 - 3230*k**2 - 31*k.
-2*(k + 1)**2*(k + 2)**2
Let x(p) be the second derivative of p**6/10 + 27*p**5/20 + 23*p**4/4 + 15*p**3/2 + 2294*p. Solve x(w) = 0.
-5, -3, -1, 0
Let y = -1101571 - -1101573. Find q such that 133/4*q**3 + 21296 + 1/4*q**4 + 22748*q + 1485*q**y = 0.
-44, -1
Let f(u) be the second derivative of -u**4/54 + u**3/27 + 2*u**2/9 - 9*u + 40. Factor f(d).
-2*(d - 2)*(d + 1)/9
Let x(n) be the first derivative of -n**3 + 114*n**2 - 1260*n + 8755. Factor x(a).
-3*(a - 70)*(a - 6)
Let r(d) be the first derivative of 148*d**3/9 + 89*d**2/3 + 10*d + 6993. Factor r(s).
2*(s + 1)*(74*s + 15)/3
Let h(v) = -5*v**2 + 8*v - 3. Let k(r) = 4 - 5*r + 4*r**2 - 13*r - 11*r + 21*r. Let s(j) = -2*h(j) - 3*k(j). Factor s(u).
-2*(u - 3)*(u - 1)
Suppose -14 - 393*v + v**3 + 65*v**2 - 99*v + 146*v + 294 = 0. Calculate v.
-70, 1, 4
Let 13/5*w**5 - 18/5*w**4 - 29/5*w**3 + 18/5*w**2 + 0 + 16/5*w = 0. What is w?
-1, -8/13, 0, 1, 2
Suppose -8*q + 12*q + 976 = 0. Let c be (q/(-56) + -3)*6. Suppose c*d**3 + 0 + 0*d - 180/7*d**4 - 6/7*d**2 + 27*d**5 = 0. What is d?
0, 2/7, 1/3
Let p(n) be the first derivative of 8*n**3 - 46*n**2 + 60*n + 669. Find z, given that p(z) = 0.
5/6, 3
Let c be (-183)/4 - (-1)/(-4). Let f = c + 49. Factor 39*z**f + 10*z**2 + 5*z**4 - 48*z**3 - 61*z**3 + 235*z**2.
5*z**2*(z - 7)**2
Let r(q) be the first derivative of -5*q**6/6 + 97*q**5 - 12875*q**4/4 + 52415*q**3/3 + 6440*q**2 - 52900*q - 8549. Let r(f) = 0. Calculate f.
-1, 1, 5, 46
Let p(n) be the first derivative of -2*n**5/55 + 21*n**4/11 - 304*n**3/33 - 1175. Factor p(v).
-2*v**2*(v - 38)*(v - 4)/11
Let g be 15968/6487*13/7. Determine m, given that 22*m**2 + 0 + g*m**3 + 28*m + 2/7*m**4 = 0.
-7, -2, 0
Let r(z) = -20*z + 350. Let x be r(16). Let a be -3 - 4/(-28)*(3 + x). Factor 8/7*t**2 + 0*t + 0 + 4/7*t**4 + a*t**3.
4*t**2*(t + 1)*(t + 2)/7
Let u(b) be the second derivative of -b**4/24 + 235*b**3/6 - 469*b**2/4 - 3407*b. Solve u(w) = 0.
1, 469
Let p(d) be the first derivative of d**5/20 + 5*d**4/16 - 19*d**3/12 - 29*d**2/8 + 21*d/2 + 8001. Determine f, given that p(f) = 0.
-7, -2, 1, 3
Let x(h) be the second derivative of h**7/42 - 14*h**6/15 + 13*h**5/10 + 7*h**4/3 - 9*h**3/2 - 334*h + 2. Factor x(j).
j*(j - 27)*(j - 1)**2*(j + 1)
Let z(s) = -s**3 - 9*s**2 - 7*s + 14. Let w be z(-8). Let v be w/(-2)*(-3 - 4). Solve 7*c**3 + 3 - 15*c**2 - 5 + 11*c + v*c**2 - 22*c**2 = 0 for c.
2/7, 1
Let j(b) = -40*b**3 - 1286*b**2 - 1449*b - 173. Let t(y) = -39*y**3 - 1281*y**2 - 1452*y - 174. Let u(g) = -6*j(g) + 5*t(g). Factor u(k).
3*(k + 1)*(k + 28)*(15*k + 2)
Suppose 57*y = 33*y - 5736. Let r = y + 1197/5. Solve 4*o**2 - r*o**5 + 2/5 - 4*o**3 - 2*o + 2*o**4 = 0.
1
Suppose 10*q = 217 - 167. Suppose -2*s + 22 = 2*d, 0 = d + 17*s - 20*s + q. Let 1/2*p**2 + d*p + 49/2 = 0. Calculate p.
-7
Let i = 1043760 - 19807106/19. Factor i + 138/19*b**2 + 3174/19*b + 2/19*b**3.
2*(b + 23)**3/19
Let z(q) be the third derivative of -q**6/480 - 147*q**5/20 - 21609*q**4/2 - 8470728*q**3 + 88*q**2 - 3. Let z(m) = 0. Calculate m.
-588
Let x(s) = -10*s**2 + 14*s + 6. Let k(z) = -2*z**2 + 70*z - 12. Let j be k(35). Let t(w) = 2*w**2 - 2*w - 1. Let l(u) = j*t(u) - 2*x(u). Factor l(o).
-4*o*(o + 1)
Find o such that -1/6*o**3 - 8/3*o**2 + 8/3*o**4 + 1/6*o**5 + 0 + 0*o = 0.
-16, -1, 0, 1
Let f be ((-20)/40)/(-3*2/153). Suppose -3/4*v**3 + f*v**2 - 12*v + 0 = 0. What is v?
0, 1, 16
Let k(f) be the first derivative of -f**6/20 + 2*f**5/15 + f**4/3 + 9*f**2 - f - 173. Let j(t) be the second derivative of k(t). Let j(i) = 0. Calculate i.
-2/3, 0, 2
Solve -191/2 - 478/5*x - 1/10*x**2 = 0 for x.
-955, -1
Let r(b) be the second derivative of -2*b**6/3 + 13*b**5/4 + 65*b**4/12 - 10*b**3/3 - 17*b + 8. Factor r(h).
-5*h*(h - 4)*(h + 1)*(4*h - 1)
Let r be 300/(-360) + (-5238)/(-5508). Factor 128/17 + 60/17*t - r*t**2.
-2*(t - 32)*(t + 2)/17
Factor -980/17*x**3 + 0*x + 2/17*x**4 + 0 + 0*x**2.
2*x**3*(x - 490)/17
Let v(p) be the third derivative of p**5/60 + 7*p**4/6 - 671*p**3/2 + 89*p**2 - 3*p - 2. Determine l, given that v(l) = 0.
-61, 33
Suppose 33*r - z - 13 = 34*r, -2*z = 5*r + 71. Let l be 8/6*r/(-30). Factor 1/9*c - l + 1/9*c**2.
(c - 2)*(c + 3)/9
Let s(l) be the third derivative of -1/36*l**6 - 1/15*l**5 + 0*l - 1/315*l**7 + 0*l**4 + 0*l**3 + 29 - 2*l**2. Solve s(p) = 0 for p.
-3, -2, 0
Let c(p) = -4*p**2 + 644*p - 24961. Let q(w) = -36*w**2 + 5800*w - 224648. Let z(x) = 28*c(x) - 3*q(x). What is t in z(t) = 0?
79
Let u = -56243 - -56243. Factor 0 + 12/7*s**2 + u*s - 17/7*s**3 - s**4.
-s**2*(s + 3)*(7*s - 4)/7
Suppose 6*m + 0*m = 4*m. Suppose 3*v - 2*s - 1 = m, -2*s - 27 = -5*v - 5*s. Let d**3 - 80 - 7*d**3 - 12*d**v + 5*d**4 + 80*d - 2*d**3 = 0. What is d?
-2, 2
Let l(m) = -42*m**2 - 2262*m - 4680. Let x(j) = 3*j**2 + 174*j + 360. Let v(b) = 2*l(b) + 27*x(b). Factor v(r).
-3*(r - 60)*(r + 2)
Let z(y) be the second derivative of 0*y**2 + 1 - 1/4*y**4 - y**3 + 3/10*y**5 + 1/10*y**6 - 22*y. Factor z(l).
3*l*(l - 1)*(l + 1)*(l + 2)
Let m = -196929 + 590789/3. Factor m*z**2 + 20/3 - 22/3*z.
2*(z - 10)*(z - 1)/3
Let p(w) = -12*w - 115. Let v be p(-10). Factor -9*q + 5*q - 16 - 21*q + v*q + 12*q**2 + 20*q**3 + 4*q**4.
4*(q - 1