-12)/(-6))/(9/(-297)*-22). Suppose -4/11*n**u - 20/11 + 14/11*n**2 + 34/11*n = 0. Calculate n.
-2, 1/2, 5
Let l(m) be the first derivative of m**5/390 - 3*m**4/13 + 35*m**3/39 - 17*m**2 + 296. Let w(a) be the second derivative of l(a). Find c, given that w(c) = 0.
1, 35
Let d be ((-52)/16)/((-2)/8). Let u = d - 8. Factor 0*r**4 - 6*r - 6*r**4 + 0*r**u + 4*r**3 + 4 + 2*r**5 + 4*r**2 - 2.
2*(r - 1)**4*(r + 1)
Let h(p) = -5*p**2 + 690*p - 410. Let o(w) = 2*w**2 - 372*w + 205. Let g(u) = 3*h(u) + 5*o(u). Determine m so that g(m) = 0.
1, 41
Let b(l) be the first derivative of -2*l**3/5 + 3036*l**2/5 - 137. Factor b(t).
-6*t*(t - 1012)/5
Let l(o) = -12*o**3 - 34*o**2 - 165*o - 128. Let t = -165 - -170. Let h(q) = 7*q**3 + 17*q**2 + 83*q + 64. Let g(j) = t*h(j) + 3*l(j). Let g(y) = 0. What is y?
-8, -1
Suppose 3*v - 7*k + 4*k = 15, -3*v + k = -15. Suppose -v = 5*p, -3*p - 13 = -4*i - 6*p. Let 2*f**2 + 0 - 4 + 3*f**2 + i*f - 6*f**2 = 0. Calculate f.
2
Let k(i) = -4*i - 2. Let b(z) be the third derivative of -z**5/60 + 2*z**4/3 + 3*z**3/2 + z**2. Let a = -3516 + 3514. Let y(f) = a*b(f) - 9*k(f). Factor y(w).
2*w*(w + 2)
Suppose -47*c + 554 = 460. Factor -6/7 + p - 1/7*p**c.
-(p - 6)*(p - 1)/7
Factor 13/3*z**2 + 1/3*z**3 + 4*z + 0.
z*(z + 1)*(z + 12)/3
Factor 2/13*g**2 - 40/13 + 16/13*g.
2*(g - 2)*(g + 10)/13
Determine o, given that -118084/13*o**2 + 361128/13*o - 2/13*o**4 - 242064/13 - 978/13*o**3 = 0.
-246, 1, 2
Let o be 505/1212 + 0/1. Let m(a) be the second derivative of 10*a**2 - 8*a + 25/6*a**3 + o*a**4 + 0. Factor m(s).
5*(s + 1)*(s + 4)
Factor -414/7 - 416/7*p - 2/7*p**2.
-2*(p + 1)*(p + 207)/7
Solve -26/7*f + 0 - 2/7*f**2 = 0.
-13, 0
Suppose 0 = -23*r + 15*r + 320. Let x be r/16*(-12)/(-20). Factor x + 1/2*u**2 + 2*u.
(u + 1)*(u + 3)/2
Let i be (-9248)/(-56)*1071/2448. Determine x, given that i*x**2 + 9 + 51*x = 0.
-6/17
Suppose -485*j**3 - 115600 + 1461*j**3 - 487*j**3 - 490*j**3 + 336*j**2 - 27540*j = 0. Calculate j.
-4, 170
Let w = 23001 + -22997. Factor 5/6*y**w - 20/3*y + 35/3*y**2 + 0 - 35/6*y**3.
5*y*(y - 4)*(y - 2)*(y - 1)/6
Let d(v) be the first derivative of v**3 - 21*v**2 - 216*v - 4479. Factor d(p).
3*(p - 18)*(p + 4)
Let s = -1665251/3460 + 63/1730. Let u = 482 + s. Factor -3/4*x**2 + 3/4*x**4 - 3/4*x + u*x**3 + 0.
3*x*(x - 1)*(x + 1)**2/4
Suppose -9*j = 53995 - 54022. Let m(g) be the first derivative of 1/24*g**j + 14 + 1/8*g**2 + 1/8*g. Suppose m(q) = 0. What is q?
-1
Let a(t) be the third derivative of t**6/180 - 29*t**5/45 + 265*t**4/36 - 6*t**2 + t - 20. Factor a(s).
2*s*(s - 53)*(s - 5)/3
Let s(p) be the second derivative of 1/9*p**2 + 7/54*p**4 + 1/10*p**5 + 0 - 1/3*p**3 - 8/135*p**6 + 45*p. Find x, given that s(x) = 0.
-1, 1/8, 1
Factor -366*d**2 + 63*d**4 + 33*d**3 - 475*d**2 + 811*d**2.
3*d**2*(d + 1)*(21*d - 10)
Let a = 12415265/1449 + -77122/9. Let i = a + 35/23. Factor i*j**2 - 2/7 - 2/7*j.
2*(j - 1)*(2*j + 1)/7
Let x(y) be the first derivative of 3/20*y**2 + 19 - 1/30*y**3 - 1/5*y. Determine d, given that x(d) = 0.
1, 2
Let l(r) = -r**3 - 486*r**2 + 2. Let v be l(0). Solve 14/9*x**3 - 10/3*x**v + 0 + 2*x - 2/9*x**4 = 0.
0, 1, 3
Let p(a) be the first derivative of -8/11*a + 2/11*a**3 + 0*a**2 + 1/22*a**4 - 41. Solve p(s) = 0.
-2, 1
Determine k, given that 0 - 8*k + 2/7*k**3 - 111/7*k**2 = 0.
-1/2, 0, 56
Let i = 85267 - 85264. Find g such that -10/13*g + 4/13 + 8/13*g**2 - 2/13*g**i = 0.
1, 2
Factor 17640/11*k**3 + 0 + 384/11*k**4 + 0*k + 2/11*k**5 - 76832/11*k**2.
2*k**2*(k - 4)*(k + 98)**2/11
Factor 15/4*d**3 + 33*d + 23*d**2 + 4.
(d + 2)*(d + 4)*(15*d + 2)/4
Factor 154568/19 + 2/19*d**2 - 1112/19*d.
2*(d - 278)**2/19
Let u = 1020033 + -1020001. Determine l, given that -u - 15*l - 1/2*l**4 + 65/2*l**2 + 15*l**3 = 0.
-2, -1, 1, 32
Let x(f) = -f**2 + 11*f - 9. Let l be x(9). Let n(d) = 9*d**3 + 3*d**2 - d. Let p be n(1). Factor -23*r + r**2 + l + 6*r + p*r.
(r - 3)**2
Suppose -74*t + z - 12 = -79*t, t + 36 = 3*z. Factor 0*h**2 + t*h**3 - 4/9*h**4 + 10/9*h**5 + 0*h + 0.
2*h**4*(5*h - 2)/9
Let q = 39 - 53. Let b(r) = -3*r**2 + 92*r - 96. Let z(t) = -t**2 + 31*t - 32. Let c(v) = q*z(v) + 4*b(v). Factor c(k).
2*(k - 32)*(k - 1)
Suppose -8/3*x**3 + 2/3*x**2 + 80/3*x - 25 + 1/3*x**4 = 0. What is x?
-3, 1, 5
Let w(d) = d**2 + 94*d - 1. Let s(a) = -4*a**2 - 351*a - 131. Let j(m) = -2*s(m) - 6*w(m). Factor j(z).
2*(z + 2)*(z + 67)
Let y(g) = 2*g**3 - 2*g**2 - 4. Suppose -7*k + 3*k = -f - 10, 4*f = -4*k. Let a be y(k). Factor 2*q**a + q**4 - 13*q**2 - 8*q**3 + 3*q**2 + 3*q**4 + 4*q.
2*q*(q - 2)*(q + 1)*(3*q - 1)
Let g = 422933/8 + -52864. Factor -9/4 + 9/8*t**2 - g*t.
3*(t - 3)*(3*t + 2)/8
Let c(h) be the second derivative of h**7/2100 + h**6/180 + h**5/50 - 7*h**3/2 + 3*h - 2. Let x(q) be the second derivative of c(q). Factor x(v).
2*v*(v + 2)*(v + 3)/5
Let s(a) be the second derivative of -529*a**6/45 + 23*a**5/5 - 3*a**4/4 + 7*a**3/6 - a**2 - 31*a. Let o(y) be the second derivative of s(y). Factor o(v).
-2*(46*v - 3)**2
Let w(v) = -v**3 - 9*v**2 - 10*v - 14. Let k be w(-8). Suppose 2*d = 3*d - 10. Factor -3*i**2 - i**k + 8*i - 14 + d.
-4*(i - 1)**2
Suppose -26041*u + 26002*u + 117 = 0. Let b = -37 + 55. What is g in b*g**5 + 81/8*g**u - 9/8*g - 51/8*g**2 + 33*g**4 + 3/8 = 0?
-1, -1/3, 1/4
Let o(f) be the first derivative of 0*f + 162 + 0*f**2 + 2/15*f**5 + 32/9*f**3 - 4/3*f**4. Let o(k) = 0. What is k?
0, 4
Suppose 4*l + 2*g = -20, 130*l + 50 = 127*l - 5*g. Solve 1/12*i**3 + 0*i + 25/6*i**2 + l = 0.
-50, 0
Factor -5111*c**2 + 8127*c**2 - 1500*c**3 - 2456*c + 924*c + 91 - 75.
-4*(c - 1)**2*(375*c - 4)
Let s(d) be the second derivative of d**4/6 - 506*d**3/3 + 505*d**2 + 4228*d. Factor s(g).
2*(g - 505)*(g - 1)
Let w be (-100)/(-8)*(12/(-33))/((-6)/33). Let t(s) be the first derivative of -2/11*s**3 + 0*s - w + 21/11*s**2. Factor t(x).
-6*x*(x - 7)/11
Let h(u) be the second derivative of -u**7/21 + 3*u**6/5 + 8*u**5/5 - 52*u**4 + 240*u**3 - 432*u**2 - 1976*u. Solve h(i) = 0.
-6, 1, 2, 6
Determine u so that -866/9*u**2 - 2/9*u**3 - 93310/9*u + 94178/9 = 0.
-217, 1
Let u(g) = 375*g**4 - 17532*g**3 + 215424*g**2 - 76668*g + 6912. Let s(a) = -a**4 - 2*a**3 + a**2 + 5*a. Let b(p) = 12*s(p) + u(p). Factor b(k).
3*(k - 24)**2*(11*k - 2)**2
Let z(f) = -1875*f + 10605 + 8932 + 6873 - 6*f**2 + 14273. Let p(b) = b**2 + 268*b - 5812. Let y(c) = 27*p(c) + 4*z(c). Let y(a) = 0. Calculate a.
44
Let f(h) be the third derivative of 1/588*h**8 + 2*h**2 - 23*h + 0*h**3 + 0 + 1/210*h**5 + 1/105*h**6 + 0*h**4 + 1/147*h**7. Factor f(w).
2*w**2*(w + 1)**2*(2*w + 1)/7
Let z(a) be the third derivative of -a**6/240 - a**5/20 + 3*a**4/2 - 1513*a**2. Solve z(u) = 0 for u.
-12, 0, 6
Let o(p) be the second derivative of -p**5/10 - 32*p**4 - 127*p**3 - 190*p**2 + 167*p + 3. Factor o(v).
-2*(v + 1)**2*(v + 190)
Factor 128*d - 4*d**4 + 96*d**2 - 25*d**3 - 7*d**3 + 84 - 404.
-4*(d - 2)**2*(d + 2)*(d + 10)
Let n(x) be the third derivative of 3*x**8/896 + 17*x**7/40 + 113*x**6/160 - 9*x**5/2 - 1181*x**4/64 - 235*x**3/8 + 4329*x**2. Find k such that n(k) = 0.
-235/3, -1, 2
Find s, given that -2263*s**5 - 2260*s**5 + 4529*s**5 + 716*s - 1434*s**3 - 1066*s**4 + 354*s**2 = 0.
-1, 0, 2/3, 179
Suppose -5*m + 240 = -o + 6*o, -2*m = -10. Factor -100*p**2 + 4*p - 29*p + 52*p**2 + o*p**2.
-5*p*(p + 5)
Let a = 2037 - 2034. Let x(o) be the second derivative of -3/8*o**4 + 13*o - 1/4*o**a + 0 + 0*o**2. Factor x(b).
-3*b*(3*b + 1)/2
Let z(d) = 2*d**4 + 636*d**3 - 3528*d**2 + 6871*d - 4491. Let m(y) = 2*y**4 + 424*y**3 - 2352*y**2 + 4581*y - 2993. Let s(h) = -7*m(h) + 5*z(h). Factor s(o).
-4*(o - 47)*(o - 2)**3
Determine a so that 13*a**4 - 2088*a - 1260 + 24*a**2 - 444*a**2 + 409*a**3 + 20*a**2 + 15*a**3 - 17*a**4 = 0.
-1, 3, 105
Suppose -j + 3*o + 26 = 0, -657*o = -4*j - 654*o + 32. Factor 9/2*m - 3/2*m**j + 60.
-3*(m - 8)*(m + 5)/2
Let d(k) = 6*k**2 + 349*k - 295. Let h be d(-59). Let y(n) be the first derivative of -1/2*n**6 + 0*n - 8 + 3/2*n**4 - 3/2*n**2 + 0*n**3 + h*n**5. Factor y(c).
-3*c*(c - 1)**2*(c + 1)**2
Let d = 234873 - 466101/2. Factor d + 5/2*t**2 - 135*t.
5*(t - 27)**2/2
Let u(j) be the second derivative of 195*j + 0 - 1/2*j**2 + 5/16*j**3 + 3/160*j**5 + 13/48*j**4. Let u(a) = 0. What is a?
-8, -1, 1/3
Let h = -63 + 65. Suppose h*n = -4*t + 10, -5*t + 5*n