the first derivative of -5 + 0*t + 1/4*t**4 + 0*t**2 + w*t**3. Suppose c(q) = 0. Calculate q.
0
Let d(l) be the first derivative of 1/7*l**4 - 14 - 13500/7*l - 60/7*l**3 + 1350/7*l**2. Factor d(s).
4*(s - 15)**3/7
Let l be (6/(-5))/((-525)/1750). Let c(a) be the second derivative of -1/2*a**l - 3*a**2 + 0 + 7/2*a**3 + 15*a - 9/20*a**5. Factor c(x).
-3*(x - 1)*(x + 2)*(3*x - 1)
Let s = 571 - 565. Suppose 0 + 0 - s*z**2 + 8*z**3 - 3*z - 11*z**3 = 0. What is z?
-1, 0
Let p(z) = -z**4 - 4*z + 2. Let q(v) = 6*v**4 + v**3 + 20*v - 10. Let n(t) = -15*p(t) - 3*q(t). Solve n(j) = 0 for j.
-1, 0
Solve -204*i**2 + 2388/5*i - 96 - 27/5*i**3 = 0.
-40, 2/9, 2
Let m(c) be the third derivative of c**8/420 + c**7/7 + 9*c**6/25 + 28*c**2 + 24*c + 4. Factor m(h).
2*h**3*(h + 36)*(2*h + 3)/5
Suppose -58590 = 67*k + 58526 - 117384. Let -1856/5*y**2 + 324/5*y**5 - 128*y - 1136/5*y**3 + 468/5*y**k - 64/5 = 0. Calculate y.
-2, -1, -2/9, 2
Factor 6/17*i + 0 + 2/17*i**3 + 8/17*i**2.
2*i*(i + 1)*(i + 3)/17
Suppose 493 = 135*l - 152*l. Let s(d) = 7*d + 205. Let k be s(l). Factor -9/5*t**k + 9/5 + 3/5*t**3 - 3/5*t.
3*(t - 3)*(t - 1)*(t + 1)/5
Let d(k) be the third derivative of -k**10/37800 - k**9/5040 + k**8/280 - k**5/60 - 19*k**3/6 + 105*k**2. Let i(l) be the third derivative of d(l). Factor i(w).
-4*w**2*(w - 3)*(w + 6)
Let y(c) = 89*c - 310. Let t(k) = -79*k + 310. Let d(i) = -5*t(i) - 4*y(i). Let w be d(8). Let 1/5*q**w + q + 0 = 0. What is q?
-5, 0
Let m be 189/(-216) + (-644)/(-224). Factor -40/7*q - 24/7 - 18/7*q**m - 2/7*q**3.
-2*(q + 1)*(q + 2)*(q + 6)/7
Factor -13*i + 5*i + 140*i**2 + 29*i**3 + 44*i + 18*i**3 - 7*i**4.
-i*(i - 9)*(i + 2)*(7*i + 2)
Solve 4*z**3 - 2/3*z**4 - 40*z - 200/3 + 22/3*z**2 = 0.
-2, 5
Let d(g) be the third derivative of -11*g**5/90 - g**4/72 + 7*g**3/6 + 120*g**2 + g + 1. What is j in d(j) = 0?
-1, 21/22
Factor 244 + 256*x - 79 - 85 - 80 + 4*x**2.
4*x*(x + 64)
Let r(v) = 2*v**2 - 3*v + 1. Let w(g) = 39*g**2 + 66*g - 810. Let t(c) = 18*r(c) - w(c). Factor t(s).
-3*(s - 6)*(s + 46)
Let p(i) be the second derivative of i**7/1365 - i**5/130 + i**4/78 - 59*i**2/2 + i - 10. Let u(l) be the first derivative of p(l). Factor u(a).
2*a*(a - 1)**2*(a + 2)/13
Suppose 3*o = 2*y + 2 - 112, -o - 18 = 4*y. Let g = 37 + o. What is d in -3*d - d**2 - 454 - g*d + 3*d**2 + 458 = 0?
1, 2
Let q = 470 - -8183. Factor -8653*s - 5*s**4 - 6*s**3 - s**5 + q*s.
-s**3*(s + 2)*(s + 3)
Find f, given that -1/4*f**2 + 0 - 191/4*f = 0.
-191, 0
Factor -218 + 1/8*f**2 + 1743/8*f.
(f - 1)*(f + 1744)/8
Let a = -2461 + 2466. Let h = 10 - 6. Find y, given that -14*y**4 + 2*y**4 - 2*y + h*y**4 - 8*y**2 - 2*y**a - 12*y**3 = 0.
-1, 0
Let o be (-2)/3 + 4/(-3) - -4. Suppose -10 = -4*y + 3*y - 4*u, 0 = 2*y - o*u - 30. Determine m so that 25*m**3 - 10*m - 5*m**5 + y - 10*m - 14 = 0.
-2, -1, 0, 1, 2
Let x(m) = 9*m**2 + 790*m + 1562. Let y(g) = 56*g**2 + 4740*g + 9373. Let h(t) = -13*x(t) + 2*y(t). Factor h(o).
-5*(o + 2)*(o + 156)
Find h such that -2508*h**2 + 8 - 460*h + 932 + 1249*h**2 + 1254*h**2 = 0.
-94, 2
Find s such that -1/7*s**3 - 477/7 - 47/7*s**2 + 309/7*s = 0.
-53, 3
Suppose 0 = 8*b + b - 243. Suppose -14 = -4*x + 2*h, 4*x - b = -2*h - 9. Let -35*o**3 + 0 + 35*o - 10 + 85*o**2 - 21*o**4 - 5*o**x - 49*o**4 = 0. What is o?
-1, -2/3, 1/5, 1
Let t(y) = -2*y**2 + 283*y + 1167. Let k be t(-4). Let 1/2*i**2 + 0 + 0*i + 1/2*i**k = 0. What is i?
-1, 0
Let b = 43 + -39. Let n be ((-52)/39)/(b/(-6)). Suppose n*r - 6 + 8*r**2 + 9 - 35*r**2 - 27*r**3 + r = 0. What is r?
-1, -1/3, 1/3
Let y be 0/(1/(0 + -1)). Let c be (-429)/(-36) + (13 - (-235)/(-15)) - 9. Factor 0 + c*w**4 - 3/4*w**3 + 1/2*w**2 + y*w.
w**2*(w - 2)*(w - 1)/4
Let v(j) be the first derivative of 2*j**5/5 + 9*j**4/2 + 16*j**3 + 16*j**2 + 4038. Factor v(c).
2*c*(c + 1)*(c + 4)**2
Let u(s) be the third derivative of 7/66*s**4 + 0*s**3 + 31*s + 0 + 2*s**2 + 1/330*s**5. Factor u(a).
2*a*(a + 14)/11
Let q be 10/(-35) - 14960/(-9240). Suppose 4/9*j**2 - 2/9*j**3 + 10/9*j - q = 0. What is j?
-2, 1, 3
Suppose -587*f + 585*f = -4. Let s(z) be the first derivative of -4*z**3 + 0*z + 8 + 1/2*z**4 + 9*z**f. Factor s(x).
2*x*(x - 3)**2
Let j = 1814828 + -1814826. Factor -3/5*p**3 + 253125 - 10125*p + 135*p**j.
-3*(p - 75)**3/5
Let s(r) be the third derivative of r**5/60 - 37*r**4/15 - 8*r**3 - 6*r**2 - 59*r. Factor s(x).
(x - 60)*(5*x + 4)/5
Suppose -32*b - 57076 = -57236. Factor -575/7*q**3 - 1/7*q**b + 0 + 529/7*q**2 + 47/7*q**4 + 0*q.
-q**2*(q - 23)**2*(q - 1)/7
Let 180 + 190*j - 2*j**2 - 6*j**2 - 5*j**2 + 18*j**2 + 345 = 0. Calculate j.
-35, -3
Let p(q) = -q**2 + 34*q + 879. Let t be p(51). Let b(d) be the third derivative of 0*d + 0 + t*d**2 + 5*d**3 - 1/12*d**5 + 5/24*d**4. Factor b(f).
-5*(f - 3)*(f + 2)
Let r be (3*(-5 - -4))/(5/(-15)). Suppose -5*i - 15 = 5*p, -r = -i + 5*p + 6. Factor -1/5*m**5 - 1/5*m**4 + 1/5*m**2 + 0 + i*m + 1/5*m**3.
-m**2*(m - 1)*(m + 1)**2/5
Let p(y) = 29*y - 388. Let s be p(-40). Let l = 1548 + s. Suppose -8/3*z**2 - 7/3*z**4 + 19/3*z**3 + l - 4/3*z = 0. Calculate z.
-2/7, 0, 1, 2
Let -384/7*c - 1552/7*c**3 + 16/7*c**5 - 272*c**2 + 0 - 316/7*c**4 = 0. Calculate c.
-2, -1/4, 0, 24
Let b = -328321 + 1641607/5. Factor b*q**4 + 10092/5*q**2 + 195112/5*q + 232/5*q**3 + 1414562/5.
2*(q + 29)**4/5
Let q be (-1)/(3/(-6)) + (-1 - -3). Suppose 0 = 5*j - 11 - q, 5*l + 5*j = 35. Factor l*t**3 - 2 - 13*t + 2*t**4 - t + 10*t.
2*(t - 1)*(t + 1)**3
Let f(x) be the third derivative of -4/315*x**7 + 10*x**2 + 1/25*x**5 + 0*x + 13/180*x**4 - 5 - 1/225*x**6 + 2/45*x**3 - 1/280*x**8. Let f(m) = 0. What is m?
-1, -2/9, 1
Let r be (1/((-8)/(-10)))/((-501)/(-3006)). Solve 0 - 4*s + r*s**3 + 3/2*s**5 - 8*s**4 + 3*s**2 = 0 for s.
-2/3, 0, 1, 4
Let b(j) be the first derivative of j**7/21 - 3*j**6/20 + j**5/20 - 101*j - 65. Let c(l) be the first derivative of b(l). Factor c(v).
v**3*(v - 2)*(4*v - 1)/2
Let c(z) = 9*z - 60. Let k be c(7). Suppose 12*j**4 - 12*j**2 - 6*j**4 + 4 - 6*j + k*j + 6*j**3 + 2 - 3*j**5 = 0. What is j?
-1, 1, 2
Determine v so that 49*v + 20 + 2171*v - 19 + 3357*v**2 - 13 = 0.
-2/3, 2/373
Let l be 3*(-3 + 7) - 7. Let c be -7*l/(-150) - (-4)/24. Solve 0 - c*h + 2/5*h**2 = 0.
0, 1
Let h = -43 - -79. Suppose 27*a + 282*a**2 - 207*a**2 + 15 - 48*a**4 - 168*a**3 - h*a + 258*a**2 - 123*a = 0. Calculate a.
-5, 1/4, 1
What is j in 69/4*j**2 - 1/4*j**3 - 1155/4*j - 1225/4 = 0?
-1, 35
Let a = -7032 + 7038. Let h(p) be the third derivative of 1/480*p**6 + 0*p - a*p**2 + 0 + 0*p**4 - 1/80*p**5 + 1/6*p**3. Factor h(l).
(l - 2)**2*(l + 1)/4
Let 50*l + 19*l + 48 - 180*l**2 + 82*l**2 + l**3 - 138 + 82*l**2 = 0. What is l?
3, 10
Let x(b) = 2*b**2 - b + 1. Let k(h) = 7*h**2 - 5*h + 8. Suppose -38*i - 9 + 47 = 0. Let f(n) = i*k(n) - 5*x(n). Factor f(c).
-3*(c - 1)*(c + 1)
Factor 2/7*g**3 + 24/7*g**2 + 18/7*g - 44/7.
2*(g - 1)*(g + 2)*(g + 11)/7
Let l(i) be the first derivative of i**7/560 - i**6/12 + 19*i**5/80 + 15*i**3 - 33. Let h(w) be the third derivative of l(w). Find g, given that h(g) = 0.
0, 1, 19
Let s be ((-2)/52*(-3)/(-9))/(3/(-24)). Let n(t) be the third derivative of 0 - 13*t**2 + 2/195*t**5 - 1/780*t**6 + 0*t + 1/156*t**4 - s*t**3. Factor n(x).
-2*(x - 4)*(x - 1)*(x + 1)/13
Let b(w) be the second derivative of -3*w**6/10 + 21*w**5/20 + 219*w**4/2 + 354*w**3 + 420*w**2 + w - 1286. Determine r, given that b(r) = 0.
-10, -1, -2/3, 14
Suppose 5*u + 3*h + 2432 = 0, 7*h - 2439 = 5*u + 3*h. Let b = -484 - u. Factor 0 + 0*p**4 - p**2 + 3/2*p**b - 1/2*p**5 + 0*p.
-p**2*(p - 1)**2*(p + 2)/2
Let k(v) = 17*v**2 - 35*v - 19. Let f = 183 - 186. Let i(x) = -188*x**2 + 384*x + 208. Let a(s) = f*i(s) - 32*k(s). Factor a(o).
4*(o - 2)*(5*o + 2)
Let q(p) be the first derivative of -p**4/2 + 98*p**3/3 - 300*p**2 + 504*p + 946. Determine u, given that q(u) = 0.
1, 6, 42
Find g such that -1743753*g - 21 - 11 + 1743735*g - g**2 = 0.
-16, -2
Let n be (231 - -1)/(-4) - 0. Let h = n - -61. Find w, given that 25/2*w**2 - 5/2*w**h - 25/2*w**4 + 0 - 5*w + 15/2*w**5 = 0.
-1, 0, 2/3, 1
Suppose 120*c - 2*m = 125*c - 234, -c = -5*m - 63. Suppose 70 + 122 = c*n. Determine x so that 3/4*x**3 - 2 + 1/4*x**n - 3*x - 1/2*x**2 = 0.
-2, -1, 2
Factor -30*b + 3/4*b**2 + 525/4.
3*(b - 35)*(b - 5)/4
Let r(j) = j**3 + 5*j**2 - 4*j - 4. Let q be r(4).