
Let g(p) be the second derivative of -p**6/1980 + p**4/132 + 20*p**3/3 - 11*p. Let l(k) be the second derivative of g(k). Solve l(a) = 0 for a.
-1, 1
Let d = -5 + 6. Suppose -l = -5*k - d, -8*k + 5*l - 5 = -3*k. Solve 36/7*q + 1/7*q**3 + k + 12/7*q**2 = 0 for q.
-6, 0
Let i = 742345 + -8165785/11. Factor 68/11 + 174/11*t + i*t**2.
2*(t + 17)*(5*t + 2)/11
Let i be 6/(-9)*99/6. Let a = i - -13. Factor -10*d**2 - 3*d**a + 10*d - 2*d**2 - 18*d**3 + 23*d**3.
5*d*(d - 2)*(d - 1)
Let r be ((-10)/(-45) - (-101)/(-90))*72/(-324). Let i(y) be the third derivative of 0 - 7*y**2 - r*y**5 + 0*y + 1/80*y**6 - 9/16*y**4 + 0*y**3. Factor i(f).
3*f*(f - 9)*(f + 1)/2
Suppose 0 = 136*k - 126*k - 30. Factor -5 - 84*x**k - 27*x**4 + 5 - 663*x**2 - 1014*x + 24*x**4.
-3*x*(x + 2)*(x + 13)**2
Let k(w) be the third derivative of w**5/80 - 53*w**4/2 + 22472*w**3 - 50*w**2 + 12. Let k(d) = 0. Calculate d.
424
Let a be (-35)/10 + 4 + (-4)/(312/(-33)). Let -2/13*g**2 + a*g + 0 = 0. What is g?
0, 6
Let r be 1/((11025/120)/49). Find m such that -r + 2/15*m**2 + 2/15*m**3 - 8/15*m = 0.
-2, -1, 2
Let q(c) be the first derivative of -c**5/12 - 55*c**4/36 - 5*c**3 - 97*c - 31. Let s(o) be the first derivative of q(o). Factor s(p).
-5*p*(p + 2)*(p + 9)/3
Determine u, given that -168/5*u + 6/5*u**5 + 18/5*u**3 + 102/5*u**2 - 6*u**4 + 72/5 = 0.
-2, 1, 2, 3
Let k(j) be the first derivative of -j**7/189 - 16*j**6/45 - 128*j**5/15 - 2048*j**4/27 - 151*j + 103. Let n(t) be the first derivative of k(t). Factor n(d).
-2*d**2*(d + 16)**3/9
Find c such that 22*c - 22*c + 32098*c**3 - 32093*c**3 + 15*c**2 - 20 = 0.
-2, 1
Let -2/13*f**3 - 2120/13 - 18*f**2 - 2352/13*f = 0. What is f?
-106, -10, -1
Let t(g) be the third derivative of 1/6*g**4 - 10*g**2 + 1/30*g**5 - 3*g - 1/30*g**6 + 0*g**3 + 0 - 1/105*g**7. Factor t(j).
-2*j*(j - 1)*(j + 1)*(j + 2)
Let v be 16/(-60)*1893*-3. Let u = v + -1514. Factor -4/5*z**3 + 4/5*z + 0 + u*z**4 - 2/5*z**2.
2*z*(z - 2)*(z - 1)*(z + 1)/5
Let b(n) be the third derivative of 0 - 11/360*n**5 + 1/420*n**7 - 1/2016*n**8 + 2/9*n**3 - 1/24*n**4 + 7/720*n**6 + 151*n**2 + 0*n. Solve b(c) = 0.
-2, -1, 1, 4
Let j(w) = -w**2 - 766*w - 148996. Let z(i) = -2*i**2 - 1530*i - 297992. Let u(p) = 14*j(p) - 6*z(p). Factor u(r).
-2*(r + 386)**2
Suppose -38 = -5*n - 23. Find g, given that 4*g**2 - 926*g**3 + 925*g**n - 10*g**2 = 0.
-6, 0
Let r = 5987/4 - 1496. Factor 9*x + 33/4 + r*x**2.
3*(x + 1)*(x + 11)/4
Suppose 15*q - 660 = -36*q - 114*q. Let a(t) be the third derivative of 1/5*t**6 + 8/3*t**3 - 22*t**2 + 13/15*t**5 + 2*t**q + 2/105*t**7 + 0*t + 0. Factor a(h).
4*(h + 1)**2*(h + 2)**2
Suppose -2*r + 4*g - 2606 = 0, -r = 3*r + 5*g + 5212. Let h = r - -1308. Find j, given that 0*j + 1/2*j**h + 0*j**3 + 0 + 0*j**4 + 0*j**2 = 0.
0
Let o(z) be the first derivative of -2*z**3/9 - 19*z**2 + 2516*z/3 - 11110. Determine k, given that o(k) = 0.
-74, 17
Let x(g) = -19*g**2 - 15*g + 34. Let j be x(6). Let p be j/(-4329)*(-18)/(-4). Let 2/13*u**2 + 12/13*u + p = 0. What is u?
-5, -1
Let g(z) = -z**3 + 3*z. Let n(u) = 15*u**3 + 3*u**2 + 7*u - 3. Let i(c) = -22*g(c) + 2*n(c). Factor i(p).
2*(p - 1)*(p + 1)*(26*p + 3)
Let j(y) be the second derivative of y**6/20 - 21*y**5/8 + 63*y**4/8 + 99*y**3/4 - 38*y - 16. Factor j(b).
3*b*(b - 33)*(b - 3)*(b + 1)/2
Let y = 14 + -12. Let b(m) = -6*m**2 + 211*m - 30. Let s be b(35). Factor -11*n**5 + 219*n**3 + 15*n**5 + 3*n**5 + 48*n - 126*n**4 + 20*n**s - 168*n**y.
3*n*(n - 1)**2*(3*n - 4)**2
Let k(s) be the third derivative of -1/36*s**5 + 0*s + 0 + 1/72*s**6 + 0*s**3 + 107*s**2 + 1/126*s**7 - 5/72*s**4. Factor k(h).
5*h*(h - 1)*(h + 1)**2/3
Let q be ((809/(-11326))/(3/7))/(2/(-9)). Factor 243/4*n + 27/2*n**2 + 0 + q*n**3.
3*n*(n + 9)**2/4
Let i(p) = 487*p - 8763. Let h be i(18). Find t such that 0 + 6/7*t**2 - 6/7*t**4 - 2/7*t**h + 0*t + 2/7*t**5 = 0.
-1, 0, 1, 3
Let k(d) = -14*d**4 + 390*d**3 - 6886*d**2 + 18034*d - 11516. Let h(i) = 5*i**4 - 130*i**3 + 2295*i**2 - 6011*i + 3838. Let b(g) = 8*h(g) + 3*k(g). Factor b(r).
-2*(r - 31)**2*(r - 2)*(r - 1)
Let g(f) be the first derivative of 7*f**6/3 - 234*f**5/5 + 39*f**4 + 64*f**3/3 + 1113. Solve g(b) = 0.
-2/7, 0, 1, 16
Let n(m) be the second derivative of -m**5/45 + m**4/6 - 3*m**2 + m - 1155. Factor n(a).
-2*(a - 3)**2*(2*a + 3)/9
Let h = 49010/6783 + -80/969. Solve 208/7*f + 40/7 + 290/7*f**2 + h*f**3 = 0 for f.
-5, -2/5
Let w(t) be the third derivative of 0 + 1/3*t**4 + 0*t**3 + 1/15*t**5 + 2*t - 49*t**2. Factor w(o).
4*o*(o + 2)
Let v(d) be the first derivative of 6*d**4 + 12*d**2 - 107 + 0*d - 4/5*d**5 - 44/3*d**3. Determine t so that v(t) = 0.
0, 1, 2, 3
Let z(c) be the first derivative of -c**4 - 130*c**3/3 - 256*c**2 - 224*c + 5648. Let z(a) = 0. Calculate a.
-28, -4, -1/2
Let u(x) be the first derivative of 2*x**3/3 - 30*x**2 + 288*x + 911. Factor u(o).
2*(o - 24)*(o - 6)
Suppose 6*v - 2*v = 68. Suppose v*p + 3 = 18*p. Let -1 - 10*f**3 + 0*f**5 - 6*f + 18*f**p - 2*f**5 - 3 + 4*f**2 = 0. What is f?
-1, 1, 2
Let o(n) = n**3 - 576*n**2 - 3287*n - 5018. Let w(h) = 2*h**3 - 576*h**2 - 3265*h - 5017. Let i(f) = -5*o(f) + 4*w(f). Let i(a) = 0. Calculate a.
-186, -3
Let y(p) be the first derivative of 3 + 0*p**3 + 12*p**4 + 0*p - 8/5*p**5 + 1/18*p**6 + 0*p**2. Solve y(h) = 0.
0, 12
Let r(h) be the second derivative of -1/12*h**6 + 25/12*h**4 - 52*h + 2 + 1/8*h**5 + 10/3*h**3 + 0*h**2. Factor r(v).
-5*v*(v - 4)*(v + 1)*(v + 2)/2
Let g(b) be the first derivative of 2*b**3/21 - 330*b**2/7 + 94*b - 488. Find x such that g(x) = 0.
1, 329
Suppose 399*u = 74*u - 96*u + 842. Suppose -2/3*m**u - 52/3*m - 338/3 = 0. Calculate m.
-13
Suppose -3*n = 5*v + 8 - 44, -38 = -5*v - 4*n. Let 16*p**3 + 5*p**2 - v*p**5 - 12*p - 8 + 3*p**2 + 2*p**5 = 0. What is p?
-1, 1, 2
Let v(p) be the second derivative of -2*p - 4/15*p**6 - 2/21*p**7 + 40/3*p**4 + 0*p**2 + 12/5*p**5 + 64/3*p**3 + 8. Solve v(u) = 0.
-2, 0, 4
Suppose -47*p = -56*p + 279. Factor 0*m**2 + 208*m**4 - 14*m**2 - p*m**3 - 7*m**2 - 219*m**4 - m**5.
-m**2*(m + 1)*(m + 3)*(m + 7)
Suppose 45*f - 67*f + 41*f = 38. Solve -15*q**f + 0 - 5*q**3 - 10/3*q + 20/3*q**4 = 0 for q.
-1, -1/4, 0, 2
Let y(w) be the second derivative of w**7/126 + 2*w**6/45 - w**5/20 - 7*w**4/18 - 4*w**3/9 + w - 205. Suppose y(o) = 0. What is o?
-4, -1, 0, 2
Let m(z) = -z**3 - 6*z**2 - 9*z + 6. Let a be m(-5). Let 830*f**2 + 2*f**5 + 6*f - 1614*f**2 + a*f + 832*f**2 + 2*f**3 - 12*f**4 = 0. What is f?
-1, 0, 4
Find r such that -219/8*r**2 - 15/2*r - 63/8*r**4 + 123/4*r**3 + 9/2 = 0.
-3/7, 1/3, 2
Suppose 24 = 3*w + 142*k - 139*k, 0 = -2*w + 4*k - 2. Let y(b) be the second derivative of 1/6*b**3 + 0 + 1/2*b**4 + 0*b**2 - w*b. What is p in y(p) = 0?
-1/6, 0
Let g(v) be the second derivative of v**5/5 - 63*v**4 + 250*v**3 - 374*v**2 + 2672*v. Factor g(f).
4*(f - 187)*(f - 1)**2
Let p(n) = n**3 - 17*n**2 + 23*n - 37. Let o be p(16). Factor 9*a + 26*a**2 + o + 11 - 14 - 105*a - 2*a**3.
-2*(a - 6)**2*(a - 1)
Let m(l) be the second derivative of 0 - 419/42*l**4 + 10*l - 3/70*l**6 - 12*l**3 - 81/14*l**2 - 6/5*l**5. Let m(j) = 0. What is j?
-9, -1/3
Let b(j) = 5*j**2 - 578*j + 3602. Let q be b(109). Suppose 6/13*p**3 - 2/13*p**q + 2/13*p**4 - 2/13*p**2 + 0 - 4/13*p = 0. Calculate p.
-1, 0, 1, 2
Let z(n) = 225*n + 1354. Let r be z(-6). Let d(u) be the first derivative of 1/4*u**r + 1/2*u**2 + 2/3*u**3 - 2 + 0*u. Factor d(t).
t*(t + 1)**2
Let n(j) = -324*j + 13335. Let k be n(41). Factor -12 - k*r + 27/2*r**2.
3*(r - 4)*(9*r + 2)/2
Let -30/11*u**5 + 672/11*u**2 - 320/11*u - 568/11*u**3 + 32/11 + 214/11*u**4 = 0. Calculate u.
2/15, 1, 2
Let m(c) be the third derivative of -c**6/300 + 12*c**5/25 + 15*c**4/4 - 46*c**2 - 7*c. Suppose m(l) = 0. What is l?
-3, 0, 75
Let s be (-1300)/(-33) + -39 - 1/(-3). Factor 1/11*w**3 - s*w + 0 - 2/11*w**2.
w*(w - 4)*(w + 2)/11
Suppose 24 = -l + 5*l. Let 7*j**2 - 188 + 186 + l*j**2 - 11*j**2 = 0. Calculate j.
-1, 1
Let t(n) be the second derivative of -n**4/12 - 5*n**3/3 + 23*n. Let h be t(-9). Factor 8*r**4 - 3*r - 2*r**5 - 4 + 4*r - 8*r**3 - 4*r**2 + h*r.
-2*(r - 2)*(r - 1)**3*(r + 1)
Let c(w) = -75*w**2 - 65845*w + 21935. Let k(a) = 56*a**2 + 49382*a - 16451. Let r(s) = 11*c(s) + 15*k(s). Factor r(b).
5*(b + 1096)*(3*b - 1)
Let v(f) = -6*f**3 + 423*f**2 - 852*f + 