0 = 3*y + o - 6365, -4*y - 1663 = 5*o - 10157. Let h = y + -2119. Determine f so that 3/4*f**h + 0*f - 27/4 = 0.
-3, 3
Let n(g) be the third derivative of g**8/1008 + 16*g**7/105 + 47*g**6/90 - g**5/90 - 21*g**4/8 - 47*g**3/9 + 3*g**2 + 26*g. Factor n(a).
(a - 1)*(a + 1)**3*(a + 94)/3
Let t(g) be the third derivative of -g**5/270 - 2479*g**4/54 - 6145441*g**3/27 - 235*g**2 + 16. Factor t(w).
-2*(w + 2479)**2/9
Let s(k) be the second derivative of 1/3*k**3 + 3/2*k**2 - 1/12*k**4 + 0 + 285*k. Factor s(r).
-(r - 3)*(r + 1)
Let v(y) be the second derivative of y**6/480 - y**4/32 - y**3/12 - 27*y**2 + 9*y. Let z(o) be the first derivative of v(o). Solve z(x) = 0 for x.
-1, 2
Let p = -374 + 380. Let f(d) = -3*d + 8*d**3 + 5*d**2 - 9*d - d**3 - 13. Let c(r) = -r**3 - r**2 + 2*r + 2. Let n(y) = p*f(y) + 39*c(y). Solve n(z) = 0 for z.
0, 1, 2
Suppose 0 = 2*t + 9*t - 165. Suppose t*d - 19*d = -8. Factor -25*v + 4*v**2 + 10 + d*v**2 + 9*v**2.
5*(v - 1)*(3*v - 2)
Let q(g) be the third derivative of 44*g**7/525 + 67*g**6/150 + 23*g**5/25 + 5*g**4/6 + 2*g**3/15 - 3200*g**2. Factor q(a).
4*(a + 1)**3*(22*a + 1)/5
Let c = 360392 - 4684998/13. Determine i so that 168/13*i - 54/13*i**2 + 4/13*i**3 + c = 0.
-1/2, 7
Let m(u) be the first derivative of u**6/600 + 23*u**5/200 + 11*u**4/20 - 92*u**3/3 + 30. Let c(k) be the third derivative of m(k). Factor c(o).
3*(o + 1)*(o + 22)/5
Let x(p) be the second derivative of -p**5/60 + 5*p**4/18 - 23*p**3/18 + 7*p**2/3 - 3*p - 205. Factor x(w).
-(w - 7)*(w - 2)*(w - 1)/3
Let i(q) be the third derivative of -45*q**3 + 0*q - 87/25*q**5 - 86*q**2 + 0 - 19/525*q**7 + 1/840*q**8 + 63/4*q**4 + 71/150*q**6. Suppose i(b) = 0. What is b?
3, 5
Let k = -148 + 150. Find j, given that 58*j**2 - 25*j + 25 - 116*j**2 - 5 + 63*j**k = 0.
1, 4
Let w(d) = -d + 26. Let j be w(8). Let s be (-4)/j - 1*(-116)/36. Factor -6*h**2 + 12*h**2 - s*h - 4*h**2 + h**2.
3*h*(h - 1)
Let z(k) be the third derivative of -1/30*k**6 - 1/36*k**4 + 4/315*k**7 + 0*k**3 + 2/45*k**5 + 0*k - 1/504*k**8 - 64*k**2 + 0. Factor z(c).
-2*c*(c - 1)**4/3
Suppose -3*r + 8 = u, -5*u + 7*u + 4*r - 12 = 0. Factor 23 + 7 - 35*p**u - 10*p**2 + 35*p + 10*p**3 + 0*p.
5*(p - 3)*(p - 2)*(2*p + 1)
Factor 3561*n**2 - 3*n**3 + 1433 + 1836*n - 6620*n**2 + 3509*n**2 + 415.
-3*(n - 154)*(n + 2)**2
Let p = -6581 - -51557/7. Let g = p - 784. Factor 0 - g*v**2 + 2*v.
-2*v*(v - 7)/7
Suppose 1/4*q**2 - 601/2*q + 361201/4 = 0. Calculate q.
601
Determine o so that 484/7*o**5 + 0 - 400/7*o**2 + 216*o**3 - 1628/7*o**4 + 32/7*o = 0.
0, 2/11, 1, 2
Let a(s) = 5*s - 6. Let j be a(2). Suppose 11 = 2*i + h - 0*h, -j*h - 4 = 0. Factor -i*d + 20*d**2 - 6*d - 16*d**3 + 8*d.
-4*d*(d - 1)*(4*d - 1)
Let x(c) be the second derivative of 5*c**6/2 + 2103*c**5 - 4212*c**4 + 16856*c**3/5 - 6744*c**2/5 - 3531*c + 2. Suppose x(g) = 0. What is g?
-562, 2/5
Suppose 0 = 3*l + 3*n - 6, 2*l - 1 = 4*l + n. Let i be (l/(-9) + (-2)/3)*-9. Determine f so that -36*f**2 + 13*f + 28*f - 9 - i*f**4 + 18*f**3 - 11*f = 0.
1, 3
Let s(w) = -1. Let j(v) = -119 + 2*v**2 + 0*v + 79 + 17*v. Let g(z) = -j(z) - 2*s(z). Factor g(d).
-(d - 2)*(2*d + 21)
Suppose 983620*a + 162 = 983701*a. Factor -2/7*n**a + 26/7*n - 24/7.
-2*(n - 12)*(n - 1)/7
Suppose 88 = 11198*a - 11176*a. Let z(b) be the second derivative of 169/6*b**2 + 0 + 29*b + 1/36*b**a + 13/9*b**3. Find s such that z(s) = 0.
-13
Let s = 410 - 408. Suppose -6 - 12*t**3 - 5 - 12*t**3 - 34*t + 10*t**3 - 36*t**s - t**4 = 0. What is t?
-11, -1
Let r = 41 - 38. Let m be 564/9 - (-1)/r. Let 74*s - 1029 + 250*s + 3*s**3 - m*s**2 + 238*s - 121*s = 0. What is s?
7
Let c(y) = 3*y**2 + 540*y + 3636. Let m be c(-7). What is b in 0*b + 32/9*b**m + 10/9*b**5 + 34/9*b**4 + 8/9*b**2 + 0 = 0?
-2, -1, -2/5, 0
Let m be 2/1*(-11 - 14497/(-38)). Suppose -4*r = -611 - m. Solve -r + 78*a + 2/13*a**3 - 6*a**2 = 0.
13
Let n(v) be the first derivative of 1/25*v**5 - 1/4*v**4 - 2/5*v**2 - 12 + 0*v + 8/15*v**3. Factor n(g).
g*(g - 2)**2*(g - 1)/5
Solve -1/2*u**3 + 147/2*u - 23*u**2 + 0 = 0.
-49, 0, 3
Let q = 188 - 186. Factor -16*m**q - 8*m**2 + 30 + 19*m**2 - 5*m.
-5*(m - 2)*(m + 3)
Let n be -176 - (-1044856)/5895 - ((-2)/(-15))/1. Find s, given that 4*s**3 + 32/9*s**2 + 0 + 2/9*s**5 + n*s + 16/9*s**4 = 0.
-5, -1, 0
Let n(a) be the third derivative of a**5/15 + 742*a**4/3 + 1101128*a**3/3 - 1274*a**2. Suppose n(w) = 0. What is w?
-742
Let -2*n**4 + 4*n**4 + 96*n**2 + 248*n - 81*n**2 + 115*n**2 + 28*n**3 + 168 = 0. Calculate n.
-7, -3, -2
What is b in 16/3*b**2 + 0*b + 28/3*b**3 - 56/3*b**4 + 0 + 4*b**5 = 0?
-1/3, 0, 1, 4
Let b(k) be the second derivative of k**5/120 - k**4/72 - 2*k**3/3 - 3*k**2 + 3*k - 97. Determine s, given that b(s) = 0.
-3, -2, 6
Let r(t) be the third derivative of t**8/336 - 19*t**7/105 + 3*t**6 + 19*t**5/30 - 361*t**4/24 + 2*t**2 - 52*t - 4. Find w, given that r(w) = 0.
-1, 0, 1, 19
Let u = -591 + 1185/2. Let x(g) = -g**3 - 8*g**2 + 33*g + 4. Let o be x(-11). Find v, given that -u*v**o + 3*v**2 + 0*v**3 + 0*v - 3/2 = 0.
-1, 1
Let z(s) = -s**2 - 14*s + 18. Let q be z(4). Let l be ((-336)/q - 6)/((-15)/(-99)). Solve -l*y**2 - 4/15 + 26/15*y = 0 for y.
2/11, 1
Let h(t) be the third derivative of 0*t**4 + 77*t**2 + 2/525*t**7 + 0 + t + 0*t**3 + 1/168*t**8 + 0*t**5 + 0*t**6. Factor h(q).
2*q**4*(5*q + 2)/5
Let d(l) be the second derivative of 1/50*l**4 + 8*l + 3/25*l**3 - 27/25*l**2 - 1/250*l**5 - 1. Factor d(w).
-2*(w - 3)**2*(w + 3)/25
Factor -114/5*k**2 - 2/5*k**3 + 25432/5 - 816/5*k.
-2*(k - 11)*(k + 34)**2/5
Let j(o) = -o**2 + o - 1. Let c(f) = -f**3 - 5*f**2 + 3*f**2 - 4 + 3*f + 1 - 2*f**4. Let p(q) = -2*c(q) + 6*j(q). Factor p(t).
2*t**2*(t + 1)*(2*t - 1)
Let f(y) = 9*y**2 + 234*y + 2149. Let j(q) = 20*q**2 + 470*q + 4300. Let i(m) = -5*f(m) + 2*j(m). Find o, given that i(o) = 0.
-33, -13
Let c = -1348226 + 1348298. Find p such that -c + 2197/3*p**3 - 1014*p**2 + 468*p = 0.
6/13
Let o = -3121 - -3121. Let d(a) be the first derivative of -2/55*a**5 + 1/11*a**2 - 15 + o*a - 2/11*a**3 + 3/22*a**4. Factor d(k).
-2*k*(k - 1)**3/11
Let s be 0 + 12*4/12. Factor -7 - 6 + s*j + 7 - 10*j**2 - 18*j - 2*j**3.
-2*(j + 1)**2*(j + 3)
Let l(w) = 85*w**4 - 9625*w**3 - 29285*w**2 - 29255*w - 9755. Let v(q) = 7*q**4 - 802*q**3 - 2440*q**2 - 2438*q - 813. Let b(i) = 2*l(i) - 25*v(i). Factor b(t).
-5*(t - 163)*(t + 1)**3
Let v(q) = 6*q**4 + 6*q**3 + 3. Suppose -9*s - 49 + 4 = 0. Let k(t) = -11*t**4 - 11*t**3 + t**2 + t - 5. Let c(n) = s*v(n) - 3*k(n). Let c(i) = 0. What is i?
-1, 0, 1
Suppose 574*m - 345*m + 1292*m + 280*m = 0. Let m + 9/4*h + 1/4*h**3 + 5/2*h**2 = 0. Calculate h.
-9, -1, 0
Let u(f) be the first derivative of -f**3/33 - 1345*f**2/22 + 1346*f/11 + 1605. Let u(s) = 0. Calculate s.
-1346, 1
Let q = 49 + -31. Factor 31*a**2 - 16900 - 17*a**2 - q*a**2 - 567*a + 47*a.
-4*(a + 65)**2
Let a(f) be the first derivative of 3*f**6/4 - 147*f**5/5 + 1095*f**4/4 - 750*f**3 + 3561*f**2/4 - 483*f - 14874. Find z, given that a(z) = 0.
2/3, 1, 7, 23
Let s(d) be the second derivative of -29*d - 1/2*d**2 + 0 + 4*d**4 - 4/3*d**3. Find g, given that s(g) = 0.
-1/12, 1/4
Let t be (3/(-15) - -4*141/(-180))*-3. Let b(l) be the first derivative of -8*l + 2*l**2 + t + 4/3*l**3. Let b(z) = 0. Calculate z.
-2, 1
Suppose -86*p + 63 = -77*p. Factor -28*o**3 + 21*o**3 + p*o**4 - 2 - 3*o**2 + 7*o - 2*o**4.
(o - 1)**2*(o + 1)*(5*o - 2)
Let f(j) be the third derivative of -j**10/37800 - j**9/1440 + 11*j**8/10080 - j**5/15 - 12*j**2 - 1. Let a(d) be the third derivative of f(d). Factor a(v).
-2*v**2*(v + 11)*(2*v - 1)
Suppose -14 + 109 = 19*v. Factor -79 + 73 - 75*t**3 - 186 + 0*t**5 + 60*t**2 - 30*t**4 - 3*t**v + 240*t.
-3*(t - 1)**2*(t + 4)**3
Let k = 32162 + -32159. Factor 9/4*z + 3*z**2 + 3/4*z**k + 0.
3*z*(z + 1)*(z + 3)/4
Let s = -12/2293 - -2473/34395. Let u(d) be the first derivative of -22 - 1/9*d**3 - 4/3*d - 4/3*d**2 + s*d**5 - 1/18*d**6 + 5/12*d**4. Let u(g) = 0. What is g?
-1, 2
Factor 96123/5*y**3 + 0 + 1074/5*y**4 + 3/5*y**5 + 0*y + 0*y**2.
3*y**3*(y + 179)**2/5
Let w(f) = -f**3 + 10*f**2 + 4*f + 2. Let c be w(6). Suppose -50*k - 70 + c = 0. Factor -1 - b - 1/4*b**k.
-(b + 2)**2/4
Factor 133*h - 30*h - 48 + 51*h - 614*h - 112*h**2.
-4*(h + 4)*(28*h + 3)
Determine a so that 2 - 21/2*a**2 - 9*a - 11/4*a**3 =