0. Let m(i) be the third derivative of -48/7*i**3 - 2*i**2 + 2/7*i**4 - 2*i - 1/210*i**d + 0. Find k, given that m(k) = 0.
12
Let y(k) be the first derivative of 5*k**4/3 - 104*k**3/3 + 40*k**2 - 57*k + 51. Let b(g) be the first derivative of y(g). What is x in b(x) = 0?
2/5, 10
Let u = 117 - 124. Let s(g) = -g**3 - 34*g**2 + 37*g + 307. Let b(v) = -v**3 - 16*v**2 + 19*v + 154. Let r(z) = u*b(z) + 4*s(z). Factor r(w).
3*(w - 5)**2*(w + 2)
Let p(d) be the third derivative of -5/12*d**4 + 1/12*d**5 + 0*d + 1/6*d**6 - 74*d**2 + 0*d**3 - 1/14*d**7 + 0. Factor p(m).
-5*m*(m - 1)**2*(3*m + 2)
Let -484*i**3 - 3776/3*i - 512/3 - 4466/3*i**2 = 0. Calculate i.
-16/11, -1/6
Let s(p) be the second derivative of p**7/1680 - p**6/72 + 7*p**5/60 - p**4/2 - p**3/3 + p + 66. Let x(h) be the second derivative of s(h). Factor x(v).
(v - 6)*(v - 2)**2/2
Let 0 - 700*p + 1390/3*p**2 + 22/3*p**4 - 304/3*p**3 = 0. What is p?
0, 42/11, 5
Suppose 4*u = -4*c + 21 + 7, -2*u = -2*c + 2. Suppose -2*s + a = -2 + 1, 3 = -3*s + u*a. Factor -22/9*o + 14/3*o**s - 34/9*o**3 + 4/9 + 10/9*o**4.
2*(o - 1)**3*(5*o - 2)/9
Determine s so that 386*s - 2183*s**5 - 442*s**2 + 4340*s**5 - 2175*s**5 + 658*s**2 + 688*s**3 + 52 + 612*s**2 + 176*s**4 = 0.
-1, -2/9, 13
Factor 996*l - 6978/7 + 6/7*l**2.
6*(l - 1)*(l + 1163)/7
Factor 69/2*m**2 - 369/2 + 597/4*m + 3/4*m**3.
3*(m - 1)*(m + 6)*(m + 41)/4
Let i(f) = 5*f**2 + 313*f + 210. Let z(k) = 21*k**2 + 1250*k + 840. Let o(u) = -18*i(u) + 4*z(u). Factor o(d).
-2*(d + 105)*(3*d + 2)
Let s(t) be the second derivative of t**5/570 + t**4/76 - 14*t**2 + 133*t. Let p(r) be the first derivative of s(r). What is y in p(y) = 0?
-3, 0
Let f(j) = -5*j**3 - 20*j**2 - 211*j - 840. Let r be f(-4). Solve 0 + 48/7*u**3 + 33/7*u**5 + 0*u - 93/7*u**r + 12/7*u**2 = 0.
-2/11, 0, 1, 2
Let y be 10*(2 + 1 + -2) - -2. Let d(j) = j**3 - 16*j**2 + 47*j + 14. Let k be d(y). Factor 0*i - 2/15*i**k + 0 + 4/15*i**3 + 16/15*i**4.
2*i**2*(2*i + 1)*(4*i - 1)/15
Factor -112*j**2 + 38 + 62 + 80 + 49*j - 25*j + 40*j**3 - 4*j**4.
-4*(j - 5)*(j - 3)**2*(j + 1)
Let a(h) be the second derivative of -h**5/110 + 41*h**4/66 - 340*h**3/33 + 300*h**2/11 + 344*h - 3. Let a(d) = 0. Calculate d.
1, 10, 30
Let v = 165128 + -165125. Factor 4*o + 0 + 1/2*o**3 + v*o**2.
o*(o + 2)*(o + 4)/2
Let u = 2061 + -2057. Let v(s) be the second derivative of 0 + 7*s + 1/6*s**u + 0*s**2 + 2/9*s**3. What is i in v(i) = 0?
-2/3, 0
Let m(u) be the third derivative of -u**5/60 + 1003*u**4/12 - 1006009*u**3/6 + 2394*u**2. Factor m(z).
-(z - 1003)**2
Let g(a) = a**4 - 2*a**3 + a**2 - 1. Let o(i) = i**5 + 20*i**4 - 417*i**3 - 444*i**2 + 2. Let u(m) = -2*g(m) - o(m). Let u(r) = 0. What is r?
-34, -1, 0, 13
Let z(i) be the first derivative of i**4/4 + 5*i**3/3 - 13*i**2/2 + 7*i + 5213. Factor z(a).
(a - 1)**2*(a + 7)
Suppose 468 + 0*g**2 + 233*g + 3*g**2 + g**2 - 47*g - 18*g = 0. Calculate g.
-39, -3
Let y(l) be the third derivative of l**5/30 - 121*l**4/12 + 40*l**3 + 2722*l**2. Determine j so that y(j) = 0.
1, 120
Let n(b) be the first derivative of 17/15*b**2 + 76/15*b + 114 - 2/45*b**3. Let n(w) = 0. What is w?
-2, 19
Let d be (1 + 2 + -2)*-9. Let m = d + 13. Factor -7*w**5 + 10*w**5 + w**m + 8*w**4.
3*w**4*(w + 3)
Let i(c) be the first derivative of 5 + 1/60*c**5 + 0*c**3 + 0*c + 1/12*c**4 - 3/2*c**2. Let l(u) be the second derivative of i(u). Factor l(z).
z*(z + 2)
Let c be 15/10*(6 + (-742)/126). Let s(n) be the second derivative of 1/6*n**4 - 1/20*n**5 + 0*n**2 - 17*n + 0 - c*n**3. Find l such that s(l) = 0.
0, 1
Let s(c) = -25*c**3 - 1533*c**2 + 614*c - 5. Let a(b) = 87*b**3 + 5364*b**2 - 2148*b + 18. Let l(p) = 5*a(p) + 18*s(p). Solve l(h) = 0 for h.
-52, 0, 2/5
Let 1242*q**4 + 126*q + 1390*q**4 + 130*q**3 - 2630*q**4 + 254*q**2 = 0. What is q?
-63, -1, 0
Suppose -122*t + 296 = 26*t. Let h(u) be the second derivative of 2/11*u**t + 1/110*u**5 + 0 + 1/22*u**4 - 5/33*u**3 - 1/165*u**6 + 8*u. Factor h(w).
-2*(w - 1)**3*(w + 2)/11
Let s(m) be the first derivative of -1/9*m**3 - 2/3*m - 85 - 7/12*m**2 + 1/24*m**4. Factor s(r).
(r - 4)*(r + 1)**2/6
Let f(l) be the third derivative of -l**5/15 - 7*l**4/10 - 8*l**3/15 + 67*l**2 - 7*l. Factor f(d).
-4*(d + 4)*(5*d + 1)/5
Let d(q) be the first derivative of 8/3*q**3 + 0*q - 1/4*q**4 - 97 + 33/2*q**2. Factor d(k).
-k*(k - 11)*(k + 3)
Let j(l) = -5*l**3 - 5*l**2 - 50*l. Suppose -12*p - 789 - 207 = 0. Let d = -84 - p. Let r(b) = -b**2 + b. Let n(f) = d*j(f) - 20*r(f). Let n(i) = 0. What is i?
-3, -2, 0
Factor 467720676/5 - 23476/5*c**3 + 16/5*c**4 + 11483676/5*c**2 - 1873752156/5*c.
4*(c - 489)**3*(4*c - 1)/5
Suppose -11 = -2*z - 6 - 1. Let a(o) be the second derivative of 0 + 1/14*o**4 + 1/70*o**5 + 0*o**3 + 0*o**z + 11*o. Solve a(m) = 0.
-3, 0
Let z(j) be the first derivative of -4*j**3/3 + 234*j**2 - 464*j + 1045. Factor z(n).
-4*(n - 116)*(n - 1)
Suppose 5*w = 5*v - 20, -2*w + 4*v - 16 = w. Let j = 301975/7 + -43139. Suppose -j*m**3 - 4/7*m + 6/7*m**2 + w = 0. What is m?
0, 1, 2
Suppose 1441 = 2*z + 5*y, y - 10 = -7. Let s = -14969/21 + z. Factor 0*b + 0 - 2/7*b**4 - s*b**2 + 10/21*b**3.
-2*b**2*(b - 1)*(3*b - 2)/21
Suppose 733 + 19148 = v. Factor 6*m**3 + 395407 + 450*m**2 - 3*m**3 - 83938 - 27*m**2 + v*m.
3*(m + 47)**3
Let j(c) be the second derivative of c**3 - 3/40*c**5 + 0 + 122*c + 0*c**4 + 0*c**2. Factor j(d).
-3*d*(d - 2)*(d + 2)/2
Let a(j) be the first derivative of -81*j**6/2 - 2646*j**5/5 - 7797*j**4/4 - 2950*j**3 - 2064*j**2 - 672*j + 1127. Let a(n) = 0. Calculate n.
-7, -2, -1, -4/9
Let b(l) be the second derivative of -135*l - 1 + 1/10*l**5 + 8*l**2 + l**4 - 5*l**3. Suppose b(v) = 0. Calculate v.
-8, 1
Let x(f) = -4*f - 30. Let i be x(-8). Suppose -4*y**3 + 12*y + 11*y**2 - 12*y**2 + 2*y**4 - 9*y**i = 0. What is y?
-2, 0, 1, 3
Factor -711/2*f**2 - 15753*f + 7921/2 - 2*f**3.
-(f + 89)**2*(4*f - 1)/2
Suppose -179 - 303 + 2*u**2 + 255*u + 323*u - 98*u = 0. What is u?
-241, 1
Let k(n) = -3*n**4 + 8*n**3 + 6*n**2 - 8*n + 2. Let y(g) = -g**4 + 3*g**3 + g**2 + 1. Suppose 120 = 6*m + 14*m. Let p(o) = m*y(o) - 3*k(o). Factor p(c).
3*c*(c - 2)**2*(c + 2)
Suppose -120*o + 127*o = 486822. Suppose o - 69546 - 5*c**4 + 20*c**3 - 20*c**2 = 0. What is c?
0, 2
What is z in 4/7*z**2 + 496/7 - 256/7*z = 0?
2, 62
Let b(c) be the first derivative of c**4/14 - 10*c**3/21 - 4*c**2/7 + 40*c/7 - 204. Suppose b(z) = 0. Calculate z.
-2, 2, 5
Let q(y) be the first derivative of -4*y**5/5 + 111*y**4 - 4032*y**3 - 6272*y**2 - 934. Suppose q(m) = 0. Calculate m.
-1, 0, 56
Let q(p) = -11*p**4 - 50*p**3 + 72*p**2 + 475*p + 379. Let u(f) = 6*f**4 + 27*f**3 - 36*f**2 - 237*f - 189. Let r(i) = -3*q(i) - 5*u(i). Factor r(o).
3*(o - 4)*(o + 1)*(o + 4)**2
Let w(d) be the second derivative of d**5/15 + 11*d**4/18 - 28*d**3/3 - 156*d**2 - 900*d. Factor w(b).
2*(b + 6)**2*(2*b - 13)/3
Let s(v) = -v**3 + 66*v**2 - 121*v - 443. Let w be s(64). Let a(z) be the second derivative of 0*z**2 + 0*z**3 + 0 - 21*z + 1/20*z**w + 1/12*z**4. Factor a(b).
b**2*(b + 1)
Factor -53/2*t - 3/2*t**2 + 105.
-(t + 21)*(3*t - 10)/2
Let b(r) be the third derivative of -7*r**5/60 - 187*r**4/24 + 97*r**3/3 - 2*r**2 - 2*r + 2748. Suppose b(w) = 0. What is w?
-194/7, 1
Let b(n) = -710*n**2 - 70670*n - 6748835. Let v(p) = 19*p**2 + 1910*p + 182401. Let q(y) = -2*b(y) - 75*v(y). Factor q(s).
-5*(s + 191)**2
Let u(p) = 3*p**2 - p - 1. Let g(h) = 8*h**2 + 4*h - 43. Let a(o) = g(o) - u(o). Let r(z) = 6*z**2 + 6*z - 45. Let f(n) = 3*a(n) - 2*r(n). Factor f(m).
3*(m - 3)*(m + 4)
Let t be (-270)/30*(-12)/324. Factor -1/9*r**2 - t - 4/9*r.
-(r + 1)*(r + 3)/9
Suppose -750 = 28*m + 230. Let t be (50/(-175))/(30/m). Solve -l - 2/3 - t*l**2 = 0 for l.
-2, -1
Factor 92/3*p**4 + 0 - 8/3*p**3 + 0*p**2 + 0*p.
4*p**3*(23*p - 2)/3
Let n = -6 + 8. Let x = n + 2. Factor 3*r**5 + 12*r**x - 6*r**2 - 25*r**4 + 16*r**4 - 6*r**3 + 3 + 3*r.
3*(r - 1)**2*(r + 1)**3
Suppose -866 - 683 + 1413 - 268*n + 4*n**3 - 128*n**2 = 0. Calculate n.
-1, 34
Let c = 278 + -248. Factor -c*v + 47*v + v**2 + 100 - 37*v.
(v - 10)**2
Let m(b) = -11*b**2 - 96*b - 610. Let c(x) = 25*x**2 + 190*x + 1218. Let j(n) = -6*c(n) - 14*m(n). Factor j(k).
4*(k + 7)*(k + 44)
Determine p so that -23/2 + 125/3*p + 11/6*p**2 = 0.
-23, 3/11
Let h(y) be the second derivative of -3