 Let c(n) be the second derivative of -8/15*n**3 - 1/15*n**p + 0 - 33*n + 0*n**2 + 14/75*n**6 + 2/5*n**5. Factor c(m).
4*m*(m + 1)**2*(7*m - 4)/5
Let c(k) = -k**3 - 11*k**2 - 40*k - 47. Let b be c(-15). Let g = -7251/5 + b. Solve g*j - 2/5*j**3 + 0*j**2 - 12/5 = 0.
-3, 1, 2
Let v(m) be the first derivative of m**6/120 - 11*m**5/4 + 3025*m**4/8 + 200*m**3/3 + 51. Let y(a) be the third derivative of v(a). Solve y(i) = 0 for i.
55
Let t(u) = -u**4 + 2*u**3 - 1. Let x(y) = 11*y**4 - 52*y**3 + 10*y**2 + 400*y - 369. Let w(c) = 6*t(c) + x(c). Factor w(r).
5*(r - 5)**2*(r - 1)*(r + 3)
Let p be (-382)/(-40) + (2595/30275)/(12/7). Let 15*o**2 - 9/5*o**3 - 168/5*o + p = 0. What is o?
1/3, 4
Let v(q) be the third derivative of -q**6/144 + 4*q**5/15 - 319*q**4/144 + 5*q**3/3 + 906*q**2 + 3. Find o such that v(o) = 0.
1/5, 4, 15
Let -59/3*b**2 + 0*b + 0 - 1/9*b**4 + 178/9*b**3 = 0. Calculate b.
0, 1, 177
Let w(n) = 3*n**3 - 61*n**2 + 18*n + 13. Let q be w(20). Let t be 30/(-105) - (q/(-273) - 1). Determine y, given that t*y - 10/13*y**2 + 2/13*y**3 + 0 = 0.
0, 1, 4
Let j(x) be the first derivative of 5*x**3/3 - 1210*x**2 + 292820*x + 1117. Factor j(h).
5*(h - 242)**2
Let n(v) be the first derivative of -19*v**4/18 - 116*v**3/27 + 173*v**2/9 - 64*v/3 - 1903. Factor n(o).
-2*(o - 1)**2*(19*o + 96)/9
Let s(t) be the first derivative of -73 - 1/35*t**5 + 0*t - 1/14*t**2 - 1/7*t**3 - 3/28*t**4. Solve s(x) = 0 for x.
-1, 0
Let m(x) = 490*x**3 + 14700*x**2 + 5402266*x. Let a(o) = -92*o**3 - 2940*o**2 - 1080453*o. Let p(n) = 16*a(n) + 3*m(n). Factor p(j).
-2*j*(j + 735)**2
Let h be (7 + -6 + 4)/1. Let v be h - 0 - -1 - (-1404)/(-312). Factor -v*c**2 - 3/4 - 3/8*c**3 - 15/8*c.
-3*(c + 1)**2*(c + 2)/8
Let a(z) = 2*z**3 + 13*z**2 + 6*z + 5. Let h be a(-6). What is s in -288*s**2 - 80*s + 67*s**h + 56*s**5 + 288*s**4 + 52*s**3 - 95*s**5 = 0?
-10, -1, -2/7, 0, 1
Solve -20*i**2 + 16*i**5 - 336*i - 64 - 403*i**2 - 90*i**2 + 84*i**4 + 193*i**2 + 20*i**3 = 0.
-4, -2, -1, -1/4, 2
Suppose 2*i = -0*i - 0 + 8. Determine b so that -2*b + 10/7*b**2 + 2/7*b**i - 12/7 + 2*b**3 = 0.
-6, -1, 1
Suppose -4*y + 1 = -4*o + 25, 2*y + 4 = -2*o. Solve -4*t**5 + 9 + 48*t**3 - 9 + 64*t**o = 0 for t.
-2, 0, 4
Find x such that -2*x + 12 - 1/6*x**5 - 29/3*x**2 + 0*x**4 + 9/2*x**3 = 0.
-6, -1, 2, 3
Let f = -15252 - -15254. Let t(y) be the second derivative of -5*y - 1/15*y**4 + 0 + 0*y**3 - 1/25*y**5 + 0*y**f. Factor t(w).
-4*w**2*(w + 1)/5
Let x = 1183/1419 - 2/129. Let a = x - -263/55. Solve a*y**3 + 8/5 - 8/5*y**5 - 8*y + 26/5*y**2 - 14/5*y**4 = 0 for y.
-2, 1/4, 1
Let n(g) = 3*g**4 + 612*g**3 - 174*g**2 - 607*g + 161. Let t(k) = -k**4 - 2*k**3 - 2*k**2 + 3*k + 1. Let f(b) = -n(b) + 5*t(b). Let f(w) = 0. What is w?
-78, -1, 1/4, 1
Let c(y) be the second derivative of -y**6/60 + 2*y**5/5 - 5*y**4/8 - y - 1733. Determine i so that c(i) = 0.
0, 1, 15
Suppose -24*z + 249 - 105 = 0. Let o(s) be the first derivative of 3/5*s**5 - s**3 - 2*s**z + 3*s**4 + 0*s**2 + 0*s - 18. What is p in o(p) = 0?
-1, 0, 1/4, 1
Let 12*o + 1/4*o**3 - 51/4*o**2 + 25 = 0. What is o?
-1, 2, 50
Let z = 1319/2874 + -140/479. What is j in -44/3*j + 968/3 + z*j**2 = 0?
44
Let d be (-304)/(-322) + 120/(-1380). Let p(m) = 118*m + 120. Let c be p(-1). Determine f so that 0 + 2/7*f - 8/7*f**3 - d*f**c = 0.
-1, 0, 1/4
Suppose -13*g + 6*g = 0. Suppose g = 7*y + 12 - 40. Let 1/7*r**y + 3/7*r**3 + 1/7*r + 3/7*r**2 + 0 = 0. Calculate r.
-1, 0
Let r(u) be the second derivative of u**7/28 + 19*u**6/10 + 321*u - 1. Factor r(k).
3*k**4*(k + 38)/2
Let h be 14 + 0 + (-56108)/4056. Let w(x) be the second derivative of -3/2*x**5 - 10*x**3 + 0 + x + 10*x**2 + h*x**6 + 65/12*x**4. Solve w(v) = 0 for v.
1, 2
Let o(n) = n**3 - 2*n**2 + 10*n - 38. Let l be o(4). Suppose l*p - 2 + 2 = 0. Find g, given that p + 4/13*g + 2/13*g**2 = 0.
-2, 0
Let w be 112/40*(-1000)/(-140). Let c(l) be the second derivative of -9/5*l**2 + 0 + 5/4*l**4 + w*l + 1/2*l**3. Find h such that c(h) = 0.
-3/5, 2/5
Let p(s) = s**3 - 5*s**2 + 18. Let l be p(6). Let y be (-24)/l - 1254/(-27). Factor -3*g**3 - y + 46 - g**3 - 36*g**2.
-4*g**2*(g + 9)
Let s(g) = -18*g**3 + 22*g**2 + 26*g - 10. Let f(z) = 19*z - 70*z - 1 + 28*z + 2*z**2 + 24*z. Let k(c) = -10*f(c) + s(c). Factor k(i).
-2*i*(i - 1)*(9*i + 8)
Let g be (20794/(-322307))/(3/(-124)). Let r = -274 + 829/3. Let 2/3*x + 0 + r*x**2 + x**4 + g*x**3 = 0. Calculate x.
-1, -2/3, 0
Let w(l) = 2*l**2 - 9*l + 12. Let f(a) = a**3 - 19*a**2 - a + 27. Let r be f(19). Let y be w(r). Factor -24*x**2 - 24*x + y*x**3 - 8*x - 20*x**4 + 80*x**2.
-4*x*(x - 4)*(x + 1)*(5*x - 2)
Let o(s) be the second derivative of 1/36*s**3 + 1/28*s**7 + 0*s**2 + 11/60*s**5 - 1/9*s**4 - 42*s + 0 - 2/15*s**6. Determine m so that o(m) = 0.
0, 1/3, 1
Let s be -1 + (21/6)/((-2)/(-4)). Let i = -1 - -3. Solve 2*y**4 - s*y**4 - y**2 - y**3 + 5*y**4 - y**i = 0 for y.
-1, 0, 2
Let f be (-1*(7 - 8 - -1))/1. Let p(w) be the first derivative of -2/39*w**3 - 3/13*w**2 + 14 + f*w. Find u such that p(u) = 0.
-3, 0
Let j(p) be the first derivative of -p**3/15 + 17*p**2/10 - 52*p/5 - 174. Let j(s) = 0. Calculate s.
4, 13
Let q(v) = -v**3 - 18*v**2 + 14*v - 24. Let u be q(-19). Find t, given that 49*t**3 - u*t**5 + 76*t**5 - 10*t**2 - 15*t**2 - 35*t**4 + 6*t**3 = 0.
0, 1, 5
Let w(v) be the first derivative of -5/8*v**2 - 85 + 1/12*v**3 + 3/2*v. What is s in w(s) = 0?
2, 3
Find n, given that -28*n + 11/2 + 5/2*n**2 = 0.
1/5, 11
Let t(k) be the first derivative of -1/6*k**6 + 0*k**2 - 9/2*k**4 + 0*k + 9/5*k**5 + 0*k**3 + 115. Find p, given that t(p) = 0.
0, 3, 6
Let v(n) be the third derivative of -n**6/600 + 9*n**5/100 - 4*n**4/5 - 20*n**3 + n**2 + 77*n. Let m(o) be the first derivative of v(o). Factor m(l).
-3*(l - 16)*(l - 2)/5
Let p(t) be the third derivative of -5*t**8/84 - 29*t**7/35 - 527*t**6/160 - 289*t**5/240 + 896*t**2. Determine r so that p(r) = 0.
-17/4, -1/5, 0
Let o(i) be the second derivative of i**6/40 + 21*i**5/5 + 1991*i**4/8 + 5922*i**3 + 536787*i**2/8 - 3662*i. Let o(l) = 0. What is l?
-47, -9
Let a = -85975/2 + 42989. Determine i, given that a*i**3 + 1/2*i + 0 - 1/2*i**4 - 3/2*i**2 = 0.
0, 1
Let s be (68/6)/(7/84*8). Factor 5014*c**2 - 13*c + 9*c - s*c - 5017*c**2 + 24.
-3*(c - 1)*(c + 8)
Let x = 268 + -272. Let r(s) = -3*s**2 + 38*s - 439. Let z(h) = -7*h**2 + 74*h - 877. Let o(w) = x*z(w) + 10*r(w). Let o(c) = 0. Calculate c.
21
Let j(b) be the second derivative of -b**6/90 - b**5/30 + 259*b**4/36 - 254*b**3/9 + 42*b**2 + 1404*b. Find f such that j(f) = 0.
-18, 1, 14
Let m = 4877 + -4877. Let w(a) be the third derivative of 0*a**3 - 1/42*a**7 + 0*a**5 + m*a + 0*a**4 - 1/24*a**6 + 0 - 13*a**2. Find p, given that w(p) = 0.
-1, 0
Let f = -485 + 365. Let o be 8/(-50)*f/48. Factor 0*y**3 + 1/5*y**4 + o*y + 0 - 3/5*y**2.
y*(y - 1)**2*(y + 2)/5
Let i = 286 - 254. Factor 22 + w**2 + i*w - 1 - 10*w.
(w + 1)*(w + 21)
Let y(g) be the second derivative of 2*g**7/735 + 17*g**6/630 + 2*g**5/105 + 53*g**3/2 - g + 59. Let u(x) be the second derivative of y(x). Factor u(l).
4*l*(l + 4)*(4*l + 1)/7
Let n be 1323/4617 + (-18)/(-114). Let v(p) be the first derivative of -47 + 0*p**2 + 0*p - 8/27*p**3 - 2/9*p**5 - 1/27*p**6 - n*p**4. What is r in v(r) = 0?
-2, -1, 0
Let f(x) be the second derivative of 7*x**5/20 - x**4/4 - x**3/3 - 27*x. Let h(z) = 4*z**3 - z**2 - 2*z. Let n(l) = 6*f(l) - 10*h(l). Factor n(m).
2*m*(m - 2)**2
Let b be 6216/252 + (-4)/(-3). Suppose -33*a + b*a = -14. Factor -9/7*g + 2/7 + 4/7*g**a.
(g - 2)*(4*g - 1)/7
Let z(u) be the second derivative of -5*u**7/42 - 2*u**6/3 + 113*u**5/4 - 110*u**4/3 - 1090*u**3/3 + 1040*u**2 + 134*u. Find q, given that z(q) = 0.
-13, -2, 1, 2, 8
Let t(m) = -365*m**2 + 855*m - 660. Let o(f) = 26*f**2 - 61*f + 47. Let l(p) = -85*o(p) - 6*t(p). Factor l(v).
-5*(v - 1)*(4*v - 7)
Let c(l) = -3*l**3 - 9*l**2 + 15*l + 81. Let k(r) = -r. Let q(v) = v - 7. Let h be q(6). Let n be 1/1 + (3 + -4 - -12). Let i(x) = h*c(x) + n*k(x). Factor i(w).
3*(w - 3)*(w + 3)**2
Let z(d) = -4*d**3 + 3*d**2 - 12*d + 2. Let s be z(2). Let m be (s/(-14) - 4) + 33/19. Suppose -m*c - 18/19*c**2 + 4/19 = 0. Calculate c.
-1, 2/9
Let m = 742375 - 3711872/5. Factor -8/5*l**2 - l**3 + 0 - m*l.
-l*(l + 1)*(5*l + 3)/5
Let m(u) be the third derivative of -u*