/2
Let z(v) be the first derivative of -5*v**4/4 - 45*v**3 - 675*v**2/2 + 3375*v + 8286. Factor z(n).
-5*(n - 3)*(n + 15)**2
Let l = 6446727/5 - 1289345. Find d such that -8/5*d - l*d**2 + 0 = 0.
-4, 0
Determine m, given that -m**2 + 4*m**2 - 344 + 360*m - 249 + 230 = 0.
-121, 1
Find d such that 75*d - 5625 - 1/4*d**2 = 0.
150
Let y(p) be the second derivative of -5/18*p**3 + 1/18*p**4 - 1/2*p**2 + 2*p + 14. Find w, given that y(w) = 0.
-1/2, 3
Let q(g) = 25*g**2 - 695*g - 185. Let s(i) = -26*i**2 + 695*i + 187. Let v be (-2)/(-5 + (-1)/(25/(-115))). Let u(t) = v*s(t) + 6*q(t). Factor u(a).
5*(a - 35)*(4*a + 1)
Let b be 40/60*((-150)/4)/(-5). Suppose -7*l + 4*l = j - 2, b*j = 2*l - 24. Factor 2/5*q**l + 128/5 - 32/5*q.
2*(q - 8)**2/5
Find j such that -4/3*j**3 + 40204/3 + 260/3*j**2 - 5612/3*j = 0.
19, 23
Let b(v) be the first derivative of v**8/2016 - v**7/315 - 59*v**2/2 + 91. Let c(l) be the second derivative of b(l). Solve c(w) = 0.
0, 4
Let b be 1/(7542/(-3774) - -2). Let i be b/11 - 4*(-3)/(-66). Factor -10*v**3 - 25*v**4 + i*v**4 + 10*v - 20*v**2 + 15 - 27*v**4.
5*(v - 3)*(v - 1)*(v + 1)**2
Let w be ((-28)/(-40) + -1)/((-20)/525). Let m = w + -409/56. Factor 0 + 10/7*c**4 - 2/7*c**2 - 2/7*c + 6/7*c**3 + m*c**5.
2*c*(c + 1)**3*(2*c - 1)/7
Let l = 171207 + -171205. What is k in 5/2*k**3 + 0 - 5/4*k**4 - 5/2*k + 5/4*k**l = 0?
-1, 0, 1, 2
Let g(m) be the first derivative of m**4/4 - 61*m**3/3 + 600*m**2 - 7488*m + 4884. Factor g(v).
(v - 24)**2*(v - 13)
Factor -81*o + 5*o**2 - 1711*o - 1587*o + 877*o - 1088*o + 644405.
5*(o - 359)**2
Suppose -18*q - 18596 + 18632 = 0. Let v(g) be the second derivative of 3/8*g**4 + 0*g**q + g**3 - 3/40*g**5 + 0 + 11*g. Solve v(i) = 0.
-1, 0, 4
Factor -7576580 + 11160*b - 2031723 + 39423 - 809920 - 3*b**2.
-3*(b - 1860)**2
Let x(l) be the third derivative of -116*l**2 + 0*l**5 - 1/280*l**6 + 0*l**3 + 0*l**4 + 0*l + 0. Factor x(d).
-3*d**3/7
Let h(m) = -56*m**3 + 3026*m**2 + 17*m - 2974. Let s(d) = -9*d**3 + 504*d**2 + 3*d - 496. Let c(n) = -2*h(n) + 13*s(n). What is l in c(l) = 0?
-1, 1, 100
Let r = -850 - -866. Suppose 0 = 5*h - 5 - 15. Factor 3*m**3 + 0*m**3 + 4*m**h + 16*m**4 + r*m**5 + m**3.
4*m**3*(m + 1)*(4*m + 1)
Let k = -12599/10 - -1781/2. Let w = k - -17743/45. Factor -196/9 - 64/9*x**2 + w*x.
-4*(4*x - 7)**2/9
Factor -3*k**2 + 823*k - 235*k - 209*k + 707*k - 14782 - 83501.
-3*(k - 181)**2
Find o, given that 385/3*o + 0 + 5/6*o**2 = 0.
-154, 0
Suppose -17*g + 144*g**2 + 17*g**3 - 289/2 + 1/2*g**4 = 0. What is g?
-17, -1, 1
Suppose 6177 = -6*o + 6891. Let p be ((-17)/(o/10))/((-3)/21). Let -50 + p*x - 1/2*x**2 = 0. What is x?
10
Let v(d) = -192*d + 2145. Let w be v(11). Let g(y) be the first derivative of 0*y**2 + 4/51*y**3 - w - 1/34*y**4 + 0*y. Determine m so that g(m) = 0.
0, 2
Factor 1112*m**3 - 4717853*m**2 - 132277719656 - 65708641142 - 4*m**4 - 8680*m**3 - 651643*m**2 - 1693181072*m - 2232300966.
-4*(m + 473)**4
Suppose -48/5*r**5 + 9656/5*r**4 + 8069/5*r**3 + 2221/5*r**2 + 0 + 202/5*r = 0. Calculate r.
-1/3, -1/4, 0, 202
Let p(h) be the second derivative of -h**7/210 + 32*h**6/15 + 483*h**5/50 + 242*h**4/15 + 323*h**3/30 - 2624*h. Determine l so that p(l) = 0.
-1, 0, 323
Let q(v) = 2*v**2 - 1. Let s(z) = 3*z**2 + 1620*z + 131221. Let b(g) = q(g) + s(g). Factor b(n).
5*(n + 162)**2
Let i = 175560 - 175556. Determine p, given that 1/4*p**5 + 1 - 2*p + 7/4*p**3 + 1/4*p**2 - 5/4*p**i = 0.
-1, 1, 2
Suppose -14 + 2/3*n**2 + 17/3*n = 0. What is n?
-21/2, 2
Let q(h) be the first derivative of h**4/12 + 5*h**3/3 + 8*h**2 + 13*h - 41. Let y(i) be the first derivative of q(i). Let y(v) = 0. What is v?
-8, -2
Let o(y) = -346*y**2 + 2153*y + 5. Let z(v) = 831*v**2 - 5382*v - 12. Let p(q) = -12*o(q) - 5*z(q). Factor p(r).
-3*r*(r - 358)
Suppose 20 = r + 2*t, -10*r + 128 = -5*r - 4*t. Factor 0*d**3 - 6*d**3 + 6*d**3 - 2*d**3 - 2*d**3 + r*d**2.
-4*d**2*(d - 6)
Suppose 1480*a - 1481*a = -3, 4*a + 8 = 4*b. Factor 0*o + 0*o**3 - 3/2*o**b + 0*o**2 + 0 - 9/2*o**4.
-3*o**4*(o + 3)/2
Determine k, given that -2162/7*k + 60/7 + 19512/7*k**2 - 648/7*k**3 = 0.
1/18, 30
Let z(q) be the first derivative of -4*q**5/5 - q**4 + 8*q**3/3 - 325. Factor z(h).
-4*h**2*(h - 1)*(h + 2)
Let t(d) = d**2 + 3*d - 1. Let b be t(-4). Let o(u) = u**3 - 4*u**2 + 4*u. Let i be o(b). Solve -9*m**2 + 3*m**2 + 2*m - 2*m**2 + 9 - i = 0.
-3/4, 1
Let f(t) be the first derivative of -6/7*t + 10/21*t**3 + 2/7*t**2 + 11. Find r, given that f(r) = 0.
-1, 3/5
Factor 191*q**5 - 35*q**3 - 187*q**5 + q**2 + 23*q**2 + 7*q**3.
4*q**2*(q - 2)*(q - 1)*(q + 3)
Determine n so that 54/7*n**3 - 2/7*n**4 + 234/7*n - 386/7*n**2 + 676/7 = 0.
-1, 2, 13
Let a = -26201/540 + 6854/135. Let -3 + 3/4*n**2 - 6*n**3 + a*n**4 + 6*n = 0. What is n?
-1, 2/3, 1, 2
Factor 156/7*q**2 + 0 - 8*q**3 + 216/7*q + 4/7*q**4.
4*q*(q - 9)*(q - 6)*(q + 1)/7
Let k(p) = 3*p**3 - p**2 + 4*p - 3. Let g be k(2). Suppose 0 = 27*j - g*j - 68. Factor 30 - j - h + 2*h**3 - 5*h.
2*(h - 2)*(h + 1)**2
Suppose -3*v - 14 = -4*b, -10 = 2*b - 4*b. Determine s, given that -42*s**2 - 43*s**2 + 82*s**v - 9*s = 0.
-3, 0
Let l(a) = 60*a**2 - 294*a + 148. Let y(x) = -46*x**2 + 293*x - 147. Let j(w) = -3*l(w) - 4*y(w). Factor j(n).
2*(n - 72)*(2*n - 1)
Let b = -400 + 408. Suppose -2*m + 26 = 2*o, -2*m = -o - o + 22. Suppose -16*t - 1/2*t**4 - b - o*t**2 - 4*t**3 = 0. Calculate t.
-2
Determine n so that -20/3*n**3 + 22*n**2 + 660*n - 1/3*n**4 - 675 = 0.
-15, 1, 9
Factor 0*q**3 - 140*q - 4*q**3 + 5515 - 2*q**4 - 5515 + 146*q**2.
-2*q*(q - 7)*(q - 1)*(q + 10)
Let m be ((-42)/(-24) - (-1)/(-4))*2. Let q = -9 + 13. Factor 8*h**3 - 5*h**5 - 12*h**m - 16*h**3 - 20*h**q.
-5*h**3*(h + 2)**2
Let m(l) be the third derivative of -l**5/75 + 143*l**4/15 - 38*l**3 + 2387*l**2. Solve m(p) = 0 for p.
1, 285
Let n(q) = 8*q**3 - q**2 + q + 2. Let j(b) = 42*b**3 - 2*b**2 - 18*b + 28. Let c(a) = j(a) - 5*n(a). Factor c(i).
(i - 2)*(i - 1)*(2*i + 9)
Let m(r) be the third derivative of r**5/60 + 25*r**4/24 + 50*r**3/3 - r**2 - 32*r. Let a be m(-20). Factor -12/5*v + a + 2*v**2 - 2/5*v**3.
-2*v*(v - 3)*(v - 2)/5
Let n(d) be the third derivative of d**7/1155 + d**6/330 - 3*d**5/110 - 3*d**4/22 - 1497*d**2. Factor n(r).
2*r*(r - 3)*(r + 2)*(r + 3)/11
Let n be 903/(-28) + 3/(10 + 2). Let j be 2/((-160)/(-78)) - (-12)/n. Determine k, given that -k + 1/5*k**3 + j + 1/5*k**2 = 0.
-3, 1
Factor -8018/9*n**3 - 2/9*n**5 + 106032 + 11140*n**2 + 224/9*n**4 - 57528*n.
-2*(n - 47)**2*(n - 6)**3/9
Let r(n) be the first derivative of 0*n - 214 + 1/8*n**4 - 1/10*n**5 + 0*n**2 + 0*n**3. Factor r(x).
-x**3*(x - 1)/2
Let k(t) = -t**2 + 43*t - 188. Let m be k(5). Let q(y) = y**2 - 10*y - 20. Let z be q(12). Factor 0 - z*s + 1/3*s**m.
s*(s - 12)/3
Let d(z) = -36*z + 22 + 32*z**2 - 7 - 14*z**2. Let a(g) = g**3 - g - 1. Let w(s) = -3*a(s) + d(s). Factor w(r).
-3*(r - 3)*(r - 2)*(r - 1)
Suppose -5*v + 9*r - 24*r = 10, 5*v - 26 = 3*r. Let c(z) be the first derivative of 0*z**2 + 2*z**5 + 0*z**v + 0*z + 5/6*z**6 + 0*z**3 + 41. Factor c(f).
5*f**4*(f + 2)
Let k = 66 - 64. Determine t, given that -4*t**2 + 1 + 7*t**k + 4*t + 5*t + 0 - 31 = 0.
-5, 2
Let o(s) be the third derivative of -s**8/60480 + s**7/2520 + s**6/135 + s**5/5 - s**4/24 + 199*s**2. Let i(b) be the third derivative of o(b). Factor i(j).
-(j - 8)*(j + 2)/3
Let z(j) be the first derivative of 4*j**5/45 + 4*j**4/9 + 20*j**3/27 + 4*j**2/9 + 929. Factor z(k).
4*k*(k + 1)**2*(k + 2)/9
Let o(p) be the second derivative of -p**5/48 - p**4/8 - p**3/6 - 21*p**2/2 - 26*p + 1. Let j(a) be the first derivative of o(a). Find q such that j(q) = 0.
-2, -2/5
Let s be (-2)/3*(-36)/8. Suppose s*i = -2*b - 4, -i + 3*b + 12 = b. Factor -i*l**5 - 13*l**4 + 0*l - 4*l**2 + 17*l**4 + 2*l.
-2*l*(l - 1)**3*(l + 1)
Solve -29401032/5 - 3/5*f**3 - 1926/5*f**2 - 412164/5*f = 0.
-214
Factor 3201618*z**4 - z**5 - 3600*z - 2*z**5 + 29*z**3 + 4*z**5 - 1830*z**2 - 3201594*z**4.
z*(z - 8)*(z + 2)*(z + 15)**2
Let z(w) be the first derivative of -58/9*w - 20 - 10/3*w**2 - 2/27*w**3. Let z(u) = 0. What is u?
-29, -1
Let h(f) be the second derivative of f**6/70 + 339*f**5/35 + 12993*f**4/7 + 14464*f**3 + 43008*f**2 + f + 386. Factor h(g).
3*(g + 2)**2*(g + 224)**2/7
Let w = -504 + 72. Let h = 2168/5 + w. Determine t so that -1/5*