2*h*(27*h + 2)**3
Let v(a) be the second derivative of -a**5/54 + a**4/108 + 75*a**2/2 + 44*a + 2. Let d(g) be the first derivative of v(g). Factor d(o).
-2*o*(5*o - 1)/9
Let i(n) = 330*n**2 + 36*n - 46. Let z(f) = -66*f**2 - 7*f + 9. Let g = -287 + 303. Let u(q) = g*z(q) + 3*i(q). Factor u(p).
-2*(3*p + 1)*(11*p - 3)
Let w(u) be the second derivative of -5*u**7/42 + 83*u**6/60 - 183*u**5/40 - 35*u**4/24 + 301*u**3/12 + 15*u**2 - 4223*u. Determine g so that w(g) = 0.
-1, -1/5, 5/2, 3, 4
Let n(b) = 3*b**3 + 1. Let d(l) be the first derivative of -39*l**4/4 + 16*l**3 + 54*l**2 - 12*l + 55. Let u(z) = -d(z) - 12*n(z). Factor u(p).
3*p*(p - 18)*(p + 2)
Determine v so that -24*v**2 + 141*v - 33*v + 131*v**3 + 152*v**3 - 287*v**3 = 0.
-9, 0, 3
Let -475/2*z**2 - 269/2*z**3 - 57/2*z**4 - 1/2*z**5 - 52 - 183*z = 0. Calculate z.
-52, -2, -1
Let o be (-1197)/(-28) + ((-52)/(-16) - 2). Suppose -s - 5*x = -17, 43 - o = -2*s + x. Determine v so that 12/7 - 2*v - 6/7*v**s = 0.
-3, 2/3
Let c(q) be the third derivative of -3/20*q**4 - 1 - 14*q**2 + 0*q - 27/10*q**3 - 1/300*q**5. Factor c(t).
-(t + 9)**2/5
Let d(v) be the second derivative of v**4/3 + 144*v**3 + 23328*v**2 + 21*v + 15. Let d(r) = 0. What is r?
-108
Let l be -12 + (20/18)/((-68)/(-765)). Factor 0*t**2 - 1/2*t - 1/4*t**4 + 1/4 + l*t**3.
-(t - 1)**3*(t + 1)/4
Let t(v) be the third derivative of -v**6/10 + 136*v**5/15 + 31*v**4/2 - 92*v**3/3 + 2*v**2 + 426*v. Factor t(y).
-4*(y - 46)*(y + 1)*(3*y - 1)
Let q(m) = -35*m**2 - 20*m + 195. Let o(g) = -5*g**2 - 3*g + 28. Suppose -17 = -2*w - 5. Let t = 21 - w. Let x(h) = t*o(h) - 2*q(h). Factor x(d).
-5*(d - 2)*(d + 3)
Suppose 0 = 4*s - 2*l - 224, 32 = s + 5*l - 2. Determine z so that -3040*z - 2*z**3 + 2888 + 9*z**2 + s*z**2 + 91*z**2 = 0.
1, 38
Find l such that 33*l**4 - 23170*l**5 - 192*l**2 + 23176*l**5 - 18*l**3 - 173*l + 269*l = 0.
-4, 0, 1/2, 2
Find j such that -278*j**4 + 0*j**3 + 2/5*j**5 + 0*j + 0*j**2 + 0 = 0.
0, 695
Let y(c) = c**3 + 8*c**2 + 4*c + 33. Let i be y(-8). Let f(b) = 2*b**2 - 23*b + 34. Let x(k) = k + 2. Let t(m) = i*x(m) + f(m). Find o, given that t(o) = 0.
2, 9
Let p = 169737/7 + -24248. Suppose -8 = -7*z + 6. Let p*x**z - 6/7*x + 0 = 0. Calculate x.
0, 6
Solve 4765/2*v**3 + 12045/2*v**2 - 13310 - 16940*v + 475/2*v**4 + 15/2*v**5 = 0.
-11, -2/3, 2
Let g(j) be the first derivative of -j**8/2520 - j**7/1260 + j**6/540 + j**5/180 + 98*j**3/3 - 58. Let y(b) be the third derivative of g(b). Factor y(o).
-2*o*(o - 1)*(o + 1)**2/3
Find f such that 75076/9*f**2 + 2/9*f**5 - 544/9*f**4 + 0*f + 36442/9*f**3 + 0 = 0.
-2, 0, 137
Factor -894*c - 1049*c - 1154*c + 812*c + 85*c**2 - 270.
5*(c - 27)*(17*c + 2)
Let k(u) be the third derivative of u**5/180 + 47*u**4/18 + 62*u**3/3 - 3454*u**2. Determine l, given that k(l) = 0.
-186, -2
Let p = -923 + 905. Let h be (1 - 1)*1 + (-54)/p. Let -1/3 + 3/2*v - 11/6*v**2 + 2/3*v**4 + 0*v**h = 0. What is v?
-2, 1/2, 1
Find b such that -2/5*b**5 - 2508/5*b**3 - 20216/5*b**2 - 41154/5*b - 24*b**4 + 0 = 0.
-19, -3, 0
Let y be (2 + (-98)/35)*5/(-6). Let s(u) be the first derivative of -2/9*u**3 - y*u + 2/3*u**2 - 6. What is n in s(n) = 0?
1
Let h = -44 + 47. Find u, given that 13 + 1 - 1 + h - u**2 = 0.
-4, 4
Let p(i) = 2*i**2 - 48*i + 51. Let y(u) = 24*u - 26. Suppose -35 = -4*h + 3*q, -4*q + 9*q = -5*h. Let c(a) = h*y(a) + 2*p(a). Suppose c(t) = 0. What is t?
-7, 1
Suppose -7*q - 3*s - 7 = -3*q, 5*q + 5*s + 15 = 0. Factor -8 + 10*n**q - 8 + 9*n**2 - 27*n**2 + 36*n.
-4*(n - 4)*(2*n - 1)
Let r(j) be the second derivative of 3*j**5/50 + 161*j**4/60 + 43*j**3/10 - 13*j**2/5 - 2466*j. Suppose r(w) = 0. Calculate w.
-26, -1, 1/6
Suppose 141 = 7*z + 40*z. Let k = 121 + -119. Factor 1/3*h**z + 5/3*h - 4/3*h**k - 2/3.
(h - 2)*(h - 1)**2/3
Let u be -30 + 2769/195 + 18. Determine k so that -9/5*k**2 + 21/5 - u*k - 1/5*k**3 = 0.
-7, -3, 1
Let i be (-1850)/3885*(-3)/15*7. Factor i*q**3 - 8/3 + 2*q**2 + 0*q.
2*(q - 1)*(q + 2)**2/3
Let j be (-3)/((3/36)/(-17 - 1064/(-63))). Factor -3*y**3 - 12/5*y**j + 0 - 6/5*y**2 + 0*y - 3/5*y**5.
-3*y**2*(y + 1)**2*(y + 2)/5
Let r = 664077 + -664075. Factor 8/7*z + 4/7*z**r + 0.
4*z*(z + 2)/7
Let f(n) be the first derivative of n**4/6 - 20*n**3/9 - n**2/3 + 20*n/3 - 528. Solve f(t) = 0.
-1, 1, 10
Let t(z) be the second derivative of -51*z**4 - 920*z**3/3 - 6*z**2 - 3*z + 838. Factor t(k).
-4*(k + 3)*(153*k + 1)
Let k = 919/86 - 438/43. Let x(c) be the first derivative of 17 - 3/5*c**3 + 0*c + 1/25*c**5 + k*c**2 + 3/20*c**4. Factor x(w).
w*(w - 1)**2*(w + 5)/5
Let s(l) = -4*l**2 + 13*l + 10. Let y be s(6). Let o be 4/14 + 4/y*-1060. Factor -20 + 104*d - o*d**2 + 60*d**2 - 4 - 4*d.
-4*(d - 6)*(4*d - 1)
Let s(f) = -f**2 + f. Let t(q) be the first derivative of q**3/3 + 59*q**2/2 - 256*q + 97. Let h(x) = -5*s(x) - t(x). Suppose h(m) = 0. Calculate m.
8
Let v(o) be the first derivative of -16 - 10/3*o**3 + 5/2*o**4 + 5/2*o**2 - o**5 + 1/6*o**6 - 35*o. Let c(l) be the first derivative of v(l). Factor c(x).
5*(x - 1)**4
Let c(p) = -p**2 + 31*p + 10. Let q be c(-7). Let z be (-2)/((-4)/14) - (-1408)/q. Factor -4*t + z*t**2 - 3/2.
(t - 3)*(3*t + 1)/2
Let l(k) be the second derivative of k**6/24 + 99*k**5/160 + 5*k**4/3 + 21*k**3/16 - k**2/2 - 3252*k. Determine r so that l(r) = 0.
-8, -1, 1/10
Let f be (-252)/(-30) - 1593/270. Solve 5/2*o - 5*o**2 + f = 0.
-1/2, 1
Let y(a) = a**2 + a - 2. Let v = 107 - 63. Let p(r) = -10*r**2 + 23*r + 311. Let l(j) = v*y(j) + 4*p(j). Factor l(z).
4*(z + 17)**2
Factor q**3 - 485*q**2 - 215704 + 215704.
q**2*(q - 485)
Let j(t) be the second derivative of 3362*t**2 + 1/3*t**4 - 164/3*t**3 - 1 + 53*t. Factor j(r).
4*(r - 41)**2
Let b = -1446 + 1450. Let j(m) be the second derivative of -36*m + 0*m**2 + 1/2*m**3 + 1/24*m**b + 0. Solve j(y) = 0.
-6, 0
Suppose 221*h - 120*h - 202 = 0. Factor 0 + 3/4*t**3 + 3*t + 15/4*t**h.
3*t*(t + 1)*(t + 4)/4
Solve -68/19*m - 48/19 - 22/19*m**2 - 2/19*m**3 = 0.
-6, -4, -1
Let x(p) = 7*p**2 + 141*p - 234. Let b(s) = 48*s**2 + 969*s - 1638. Let v(i) = 4*b(i) - 27*x(i). Factor v(u).
3*(u - 3)*(u + 26)
Let l = 1443 - 14429/10. Let o(s) be the first derivative of 2/5*s**2 - 21 + 0*s - l*s**4 + 2/15*s**3. Determine d, given that o(d) = 0.
-1, 0, 2
Let n(p) be the second derivative of 13 - 9*p + 1/48*p**4 + 47/12*p**3 + 2209/8*p**2. Solve n(k) = 0.
-47
Let d(h) be the first derivative of -h**6/3 - 16*h**5/15 + 29*h**4/2 - 56*h**3/9 - 2638. Solve d(k) = 0 for k.
-7, 0, 1/3, 4
Let m(v) be the third derivative of -v**6/30 + v**5/3 - 7*v**4/6 + 2*v**3 + 4*v**2 + 2*v + 578. Suppose m(l) = 0. What is l?
1, 3
Determine w, given that -768/7*w**2 - 528/7*w**3 + 192/7 - 12/7*w**5 - 256/7*w - 20*w**4 = 0.
-6, -2, 1/3
Let k = 101 + -90. Suppose 2*y + 2 = -4*t, 5*y - t + k = 39. Factor 4*q**y - 84*q**4 - 4*q**3 + 0*q**5 + 88*q**4 - 4*q**2.
4*q**2*(q - 1)*(q + 1)**2
Let y(n) be the first derivative of 85*n**6/6 - 70*n**5 + 95*n**4 - 40*n**3/3 + 5599. Factor y(u).
5*u**2*(u - 2)**2*(17*u - 2)
Find n, given that -1/4*n**3 + 9/4*n**2 - 5*n + 3 = 0.
1, 2, 6
Let q(u) be the second derivative of -u**5/4 + 245*u**4/12 - 475*u**3/6 + 235*u**2/2 + 652*u. Factor q(z).
-5*(z - 47)*(z - 1)**2
Suppose 40/9 + 2/9*f**3 + 64/9*f + 26/9*f**2 = 0. What is f?
-10, -2, -1
Let y(i) be the first derivative of i**6/18 - 2*i**5/5 - 17*i**4/12 + 2*i**3/3 + 8*i**2/3 + 1020. Solve y(c) = 0 for c.
-2, -1, 0, 1, 8
Factor -50*s**2 - 3*s**3 + 8738 - 26*s**2 + 1887*s - 32147 + 97*s**2.
-3*(s - 17)**2*(s + 27)
Let z(s) be the first derivative of 750*s**5/7 - 23775*s**4/28 + 2458*s**3/7 + 822*s**2/7 + 72*s/7 + 1058. Determine v so that z(v) = 0.
-2/25, 1/2, 6
Let m = -261818 + 261821. Suppose 4 - 2/7*i**m - 12/7*i**2 + 18/7*i = 0. What is i?
-7, -1, 2
Let l(i) = i**3 + i**2 - i. Let r be (-2)/(-4 - 35/(-9)). Let c(s) = -14*s**2 - 10 + 29*s**3 - r*s**3 - 51*s + 70*s**3. Let a(x) = c(x) - 6*l(x). Factor a(v).
5*(v - 1)*(3*v + 1)*(5*v + 2)
Let i(c) = 7*c**2 + 34*c - 93. Let l be i(3). Find r, given that -15*r**4 + 3*r**5 - 30*r**2 + 162*r - 3 + 0 - l*r + 30*r**3 - 75*r = 0.
1
Let n(a) be the second derivative of a**6/80 + 3*a**5/40 - 3*a**4/2 - 20*a**3 + 81*a**2 + 147*a. Let q(o) be the first derivative of n(o). Solve q(j) = 0.
-4, 5
Let y = -2576911/280 + 65040/7. Let z = y + -439/5. 