tive of 121*j**9/20160 + 11*j**8/2240 + j**7/840 + 41*j**4/12 + 63*j. Let l(z) be the third derivative of q(z). Factor l(v).
3*v**2*(11*v + 2)**2/4
Let b be ((-15)/(-6))/(1/2) - (-114609)/(-24311). What is k in b*k**2 + 8/7 - 16/7*k + 2/7*k**5 - 10/7*k**4 + 2*k**3 = 0?
-1, 1, 2
Let q(l) be the third derivative of l**8/112 - 31*l**7/10 + 207*l**6/40 + 1933*l**5/20 + 593*l**4/2 + 432*l**3 + 14162*l**2. Let q(r) = 0. Calculate r.
-1, 4, 216
Suppose -19*a + 18 = -65 + 7. Let r(d) be the third derivative of -3/4*d**a + 6*d**2 + 0 - 5/2*d**3 - 1/20*d**5 + 0*d. Factor r(s).
-3*(s + 1)*(s + 5)
Let l(g) be the third derivative of -124/21*g**3 + 0 + 10/7*g**4 - 9/70*g**5 - 1/420*g**6 + 4*g - 5*g**2. Let l(t) = 0. Calculate t.
-31, 2
Suppose -7*t + 20 = -36. Let -x**4 + t*x**5 + 3*x**2 + 12*x**5 - 22*x**3 + 640*x - 2*x**4 - 638*x = 0. What is x?
-1, -1/4, 0, 2/5, 1
Let p(y) be the third derivative of 180*y**2 - 13/12*y**4 + 0 + 169/2*y**3 + 0*y + 1/180*y**5. Factor p(h).
(h - 39)**2/3
Let c(s) be the second derivative of -s**7/42 + 8*s**6/15 + 9*s**5/10 - 4*s**4/3 - 17*s**3/6 - 5*s + 30. Factor c(q).
-q*(q - 17)*(q - 1)*(q + 1)**2
Let v be (-67)/(1876/784) - -30. Determine u so that v + 1/2*u**2 - 2*u = 0.
2
Let c = -85 + 87. Suppose -c*q - l + 24 = 3*q, -5 = 5*l. Factor 20*s - 5*s**2 - q + 21 + 4 - 5*s**3.
-5*(s - 2)*(s + 1)*(s + 2)
Suppose 3*x + 28*x + 0*x = 0. Let o(k) = 47*k. Let w be o(x). Factor -6/7*y**4 + 0*y**2 - 3/7*y**3 + w*y - 3/7*y**5 + 0.
-3*y**3*(y + 1)**2/7
Let l = 344 + -341. Let c be (4/(-8))/((-5)/10)*l. Solve 2/5*g**c + 0 - 4/5*g**2 + 2/5*g = 0 for g.
0, 1
Let n = 267/1285 - 2/257. Suppose -17*q = 2*q + 8*q. Solve q*i**2 - n*i**3 + 1/5*i + 0 = 0.
-1, 0, 1
Let q be 29 + 363/(-12) - 10/(-6). Let t(h) be the second derivative of 15/2*h**2 - 13*h - q*h**4 + 0 - 5/3*h**3. Find x, given that t(x) = 0.
-3, 1
Let o be 97/3686 + 4*(-525)/(-1064). Suppose -12/7*c**3 + 12/7*c - 4/7*c**4 - 4/7*c**o + 8/7 = 0. Calculate c.
-2, -1, 1
Let l(r) = -21*r**3 - 74*r**2 + 251*r - 236. Let q(y) = -2*y**3 - y**2 + y. Let m(b) = 2*l(b) - 22*q(b). Factor m(s).
2*(s - 59)*(s - 2)**2
Find o, given that 2184 + 726*o + 47*o**2 - 44*o**2 + 43686 - 1947 = 0.
-121
Let z(l) = 20*l**2 + 80*l + 80. Let p(w) be the second derivative of -1/3*w**4 - 8/3*w**3 - 12*w + 0 - 8*w**2. Let x(k) = -24*p(k) - 5*z(k). Factor x(a).
-4*(a + 2)**2
Suppose -5*l - 6220 = -8*x + 2*x, 5*l + x + 6255 = 0. Let f = 1252 + l. Factor 3*a**f - 3/4*a**3 + 3/2 - 15/4*a.
-3*(a - 2)*(a - 1)**2/4
Factor -698/3*k + 284 + 2/3*k**3 + 44*k**2.
2*(k - 3)*(k - 2)*(k + 71)/3
Let q(s) be the first derivative of -s**8/5040 + s**7/840 - s**6/540 + 208*s**3/3 + 189. Let j(a) be the third derivative of q(a). Solve j(p) = 0 for p.
0, 1, 2
Let g be (-55594)/(-2660) - (-20)/(-8). Let -2116/5 - 1/5*k**2 - g*k = 0. Calculate k.
-46
Let t be (-28)/(-4) + -2 + (-1 - 2). Find f, given that 5*f - 1470 + 10*f**t + 3*f**3 + 2*f**3 + 1470 = 0.
-1, 0
Let z be (2/10)/(189/15 - 3). Let w(k) be the third derivative of 0 + 1/480*k**6 + z*k**5 - 32*k**2 + 0*k - 5/24*k**3 - 1/96*k**4. Solve w(g) = 0 for g.
-5, -1, 1
Let p be (-939)/2191 + ((-5)/21 - 1) + (-125)/(-30). Let -4/5 - 13/5*l + p*l**4 + 19/10*l**3 - 17/10*l**2 + 7/10*l**5 = 0. What is l?
-2, -1, -4/7, 1
Find a such that 9/5*a**4 - 378/5*a**2 + 48*a + 0 + 21/5*a**3 = 0.
-8, 0, 2/3, 5
Let i(b) be the first derivative of -1/6*b**2 + 6 + 0*b + 1/3*b**3. Factor i(j).
j*(3*j - 1)/3
Let o(f) = 13*f**3 - 61*f**2 - 692*f - 2366. Let q(n) = -5*n**3 + 31*n**2 + 347*n + 1183. Let c(d) = -2*o(d) - 5*q(d). Let c(y) = 0. Calculate y.
-13, -7
Let k = -191 + 243. Solve 338 - 22*l**2 - k*l + 7*l**2 + 17*l**2 = 0.
13
Suppose -6*m = z - 29, -5*m + 41 = -m + 5*z. Let g(l) be the second derivative of -m*l**2 + 1/3*l**4 + 2/3*l**3 + 23*l + 0. Factor g(d).
4*(d - 1)*(d + 2)
Let r(s) = -47*s**2 + 183*s + 598. Let p(j) = -209*j**2 + 731*j + 2391. Let t(c) = 2*p(c) - 9*r(c). Solve t(a) = 0.
-3, 40
Let y(o) be the second derivative of -o**6/30 + 49*o**5/20 - 575*o**4/12 - 625*o**3/6 - 715*o. Factor y(a).
-a*(a - 25)**2*(a + 1)
Let q(g) be the first derivative of 7*g**6 - 173*g**5/5 + 93*g**4/2 - 4*g**3 - 4*g**2 + 2714. Find d, given that q(d) = 0.
-1/6, 0, 2/7, 2
Let s = 111101 - 111096. Find c, given that -26/3*c**3 + 40/3*c**4 - 32/3*c**2 + 34/3*c - 8/3*c**s - 8/3 = 0.
-1, 1/2, 1, 4
Let g = 112547 - 112545. Solve 0 + 375/4*f + 150*f**g + 3/4*f**5 + 135/2*f**3 + 12*f**4 = 0.
-5, -1, 0
Factor 2*n**2 + 99*n + 6392 + 15866 + 18070 - 667*n.
2*(n - 142)**2
Factor 614*y**4 + 89*y**2 - 140*y - 619*y**4 + 186*y**2 - 130*y**3.
-5*y*(y - 1)**2*(y + 28)
Determine m, given that 2 - 82/3*m**2 - 7*m**3 - 55/3*m = 0.
-3, -1, 2/21
Let g(n) = n**3 + 20*n**2 + 3. Suppose 4*c + 80 = -5*w, -6*w + c = -3*w + 65. Let m be g(w). Factor -4*f**5 + 13*f**m - 9*f**3 + 4*f**4 - 8*f**2 + 4*f**2.
-4*f**2*(f - 1)**2*(f + 1)
Let y be (-4 + 27/6)*10. Suppose 119*b**2 + 25*b**3 - 25*b**4 + 0*b**5 - 4*b**5 + 106*b**2 - 540 - b**y = 0. Calculate b.
-3, 2
Let f(n) be the first derivative of -5*n**3/12 - 35*n**2/8 + 10*n - 7805. Let f(s) = 0. Calculate s.
-8, 1
Let a(s) = -5*s**4 + 27*s**2 + 40*s + 15. Let y be 14/6 - (-148)/222. Let c(k) = k**2. Let u(p) = y*c(p) + a(p). Let u(h) = 0. What is h?
-1, 3
Suppose 0 = -20*n + 4*n - 1168. Let k = n - -76. Factor 24*b**3 - 20*b**3 + k*b**5 + 6*b**4 - b**5.
2*b**3*(b + 1)*(b + 2)
Let r be (-8600)/83850*(-26)/4. Factor -r*l**3 + 16/9 + 28/9*l**2 - 38/9*l.
-2*(l - 1)**2*(3*l - 8)/9
Let x(c) be the third derivative of c**6/105 - 11*c**5/30 + 13*c**4/12 - 6*c**3/7 - 2369*c**2. Let x(p) = 0. What is p?
1/4, 1, 18
Let y = -4212 + 4216. Let k(h) be the third derivative of -1/12*h**3 - 1/360*h**5 + 0*h + 0 - 10*h**2 + 1/36*h**y. What is s in k(s) = 0?
1, 3
Suppose 5*f = -0*w + 2*w - 6, w - 3 = -3*f. What is r in -380*r**2 - 451*r + 15*r**3 + 576 + r**w + 2659*r = 0?
-1/4, 12
Suppose -22 = -3*m - 2*c, 4*m + 2*c - 7*c - 37 = 0. Let q = 1 + m. Factor q*w**2 - 10*w - 5 + 7*w**2 - 21*w**2.
-5*(w + 1)**2
Let n = -14149 - -14151. Let b(q) be the first derivative of -30 + q**n + 1/3*q**6 + 4/3*q**3 - 2/5*q**5 - 2*q - q**4. Factor b(w).
2*(w - 1)**3*(w + 1)**2
Let c(a) be the third derivative of 25*a**8/672 + 11*a**7/28 - 59*a**6/48 - 17*a**5/24 + 45*a**4/8 - 20*a**3/3 - 4015*a**2. What is n in c(n) = 0?
-8, -1, 2/5, 1
Let j(t) = -3*t**2 - 43*t + 32. Let f be j(-15). Suppose z - 2*z = -5*c + 7, c - f = 0. Factor 0*k + 3/5*k**4 + 0 + 0*k**2 + 0*k**z + 6/5*k**5.
3*k**4*(2*k + 1)/5
Let j(w) = -2*w + 21. Suppose 6 = 2*q - 12. Let s be j(q). Factor 0*g**2 + 6 + 6*g**s - 3*g - 3*g**3 - 8*g**2 + 2*g**2.
3*(g - 2)*(g - 1)*(g + 1)
Let b(x) = 7*x**3 + 17*x**2 - 144*x + 288. Let k(n) = -6*n**3 - 18*n**2 + 145*n - 286. Let o(i) = -7*b(i) - 8*k(i). Determine p, given that o(p) = 0.
4, 17
Let a(f) be the second derivative of f**5/25 + 2*f**4/15 - 6*f**3/5 - 36*f**2/5 + 704*f. Find p such that a(p) = 0.
-3, -2, 3
Let g(c) = -14*c - 1. Let o(m) = 5*m. Let t(l) = 6*g(l) + 17*o(l). Let d be t(9). Factor -7*a**d - a**3 - a**3 - 2*a**2 + 8*a + 7*a**3 + 8.
-2*(a - 2)*(a + 1)*(a + 2)
Let o = -231655 + 231660. Factor 18/17*y**o + 32/17*y**3 - 42/17*y**4 + 0*y + 0 - 8/17*y**2.
2*y**2*(y - 1)*(3*y - 2)**2/17
Let c = 19/18 + 4/9. Suppose 24*u + 198 = 347 + 211. Factor c*g**2 - u*g + 75/2.
3*(g - 5)**2/2
Let k(d) be the first derivative of -2*d**5/55 + 36*d**4/11 - 138*d**3/11 - 8532. Find q such that k(q) = 0.
0, 3, 69
Suppose 144*c + 144 - 216 + 692 + 4*c**2 = 0. What is c?
-31, -5
Let s = -499 + 728. Factor 80*z**2 + 2*z**4 + 1361*z**3 + 13*z**4 - 1535*z**3 - s*z**2 - 78*z - 118*z**2.
3*z*(z - 13)*(z + 1)*(5*z + 2)
Let h(y) = 10*y**3 - 24*y**2 + 6*y - 6. Let v(m) = -8*m**3 + 24*m**2 - 5*m + 5. Let j(f) = -5*h(f) - 6*v(f). Suppose j(c) = 0. What is c?
-12, 0
Let i = -1968 - -1962. Let k be (-16)/i*(-342)/(-72). Solve 4*n + 0 + 16/3*n**3 - k*n**2 + 10/3*n**4 = 0 for n.
-3, 0, 2/5, 1
Suppose -6748/3*g - 3376/3 + 4/3*g**3 - 3368/3*g**2 = 0. What is g?
-1, 844
Let x(t) = -3*t + 6. Let o be x(6). Let u be 2/9 - 3/((-162)/o). Let 3*m**4 - 3*m**2 + 2*m**3 + m**5 - m**3 - 2*m + u*m**5 = 0. Calculate m.
-2, -1, 0, 1
Suppose -5*b + 2*d - 19 = 0, -1407*b - d = -1408*b - 14. Solve -2/7*a**b + 40/7*a + 16/7*a**2 + 0 = 0 for a.
-2, 0, 10
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