3*k + 1920. Let c = k + -1287/2. Solve -c*g + g**2 - 1/2*g**3 + 0 = 0.
0, 1
Let 2/3*m + 50*m**3 + 4/3*m**4 + 26 - 78*m**2 = 0. What is m?
-39, -1/2, 1
Let i = 44 - 44. Suppose -5*x + 22 - 2 = i. Factor -55 - x*l**3 - 2*l**4 + 2*l**2 + 4*l + 55.
-2*l*(l - 1)*(l + 1)*(l + 2)
Let t(p) be the second derivative of -3/56*p**7 + 3/40*p**5 + p - 2 + 0*p**3 + 0*p**2 + 1/40*p**6 + 0*p**4. Factor t(b).
-3*b**3*(b - 1)*(3*b + 2)/4
Let q(x) = 17*x**3 - 529*x**2 + 4832*x - 36. Let j(h) = -19*h**3 + 528*h**2 - 4829*h + 42. Let y(u) = -6*j(u) - 7*q(u). Factor y(n).
-5*n*(n - 97)*(n - 10)
Let z(l) be the second derivative of -l**7/21 + 3*l**6/5 + 21*l**5/10 - 245*l**4/6 - 388*l - 10. Let z(t) = 0. What is t?
-5, 0, 7
Let c = 1078324 + -1078322. Let -10/9*j**4 + 0 + 2/9*j**3 - 2/9*j**5 + 0*j + 10/9*j**c = 0. Calculate j.
-5, -1, 0, 1
Let q(s) = -7*s + 65. Let t be q(9). Factor 0*w**2 - 3*w**3 + 4*w**5 - 9*w**3 - 16*w + 4*w**2 + 8*w**4 - 36*w**t.
4*w*(w - 2)*(w + 1)**2*(w + 2)
Let f(y) = y - 27. Let v(t) = -t + 27. Let b(m) = -3*f(m) - 2*v(m). Let u be b(27). Solve 1/6*w**3 - 1/3*w**2 + 0 + u*w = 0 for w.
0, 2
Let x(w) be the second derivative of 0*w**2 + 1/8*w**4 - 31*w + 0 + 1/60*w**5 + 3*w**3 - 1/360*w**6. Let o(u) be the second derivative of x(u). Factor o(q).
-(q - 3)*(q + 1)
What is w in 16124*w + 751728*w**2 - 751740*w**2 - 1101 + 6477 = 0?
-1/3, 1344
Let l = 94/49 + -3838/2205. Let n(b) be the first derivative of -3 + 0*b**2 + 0*b - l*b**5 + 0*b**3 - 1/27*b**6 - 2/9*b**4. Determine a so that n(a) = 0.
-2, 0
Suppose 4*y - 11 = -3. Let q(b) be the first derivative of 6*b**2 + 0*b**3 - 7*b**2 - 20 - 3*b - b**3 - y*b**2. Factor q(a).
-3*(a + 1)**2
Suppose 8*r + 20 = 52. Let h(o) be the third derivative of 0 + 1/24*o**r + 1/18*o**3 + 0*o + 15*o**2 - 1/120*o**6 + 2/315*o**7 - 1/36*o**5. Factor h(g).
(g - 1)**2*(g + 1)*(4*g + 1)/3
Let v = -156 - -160. Solve v*s**4 + 3*s**5 - 753*s - 6*s**2 + 3*s**4 + 750*s - s**4 = 0 for s.
-1, 0, 1
Let r be (-14)/12 - 23/(5382/(-525)). Let n = 9 - 5. Factor r*j**2 - 4/13*j + 6/13*j**n - 16/13*j**3 + 0.
2*j*(j - 1)**2*(3*j - 2)/13
Let z(s) be the first derivative of -s**3 + 1/5*s**5 - s**4 - 217 + 8*s + 5*s**2. Solve z(l) = 0 for l.
-1, 2, 4
Let v(x) be the second derivative of 1/150*x**4 + 4/25*x**2 - 4/75*x**3 + 0 + 100*x. Determine h, given that v(h) = 0.
2
Let k(l) be the third derivative of l**5/30 + 2009*l**4/6 + 4036081*l**3/3 - 2*l**2 + 24*l - 7. Factor k(w).
2*(w + 2009)**2
Let y(u) = 15182*u + 45546. Let x be y(-3). Factor 0*i - 4/7*i**5 - 8/7*i**3 + 0*i**2 - 12/7*i**4 + x.
-4*i**3*(i + 1)*(i + 2)/7
Let u = -13496 + 13523. Let p(a) be the third derivative of 0 + 0*a + 1/90*a**6 - 1/3*a**4 + 0*a**3 + 1/45*a**5 + u*a**2. Factor p(c).
4*c*(c - 2)*(c + 3)/3
Let g(o) be the third derivative of o**8/840 + 2*o**7/525 - 13*o**6/300 - 13*o**5/75 + 3*o**4/5 + 24*o**3/5 + 10701*o**2. Determine v, given that g(v) = 0.
-3, -2, 2, 3
Let k = -713419 - -6422140/9. Factor 74/9*p + k + 1/9*p**2.
(p + 37)**2/9
Solve -2/13*w**3 + 144/13 + 28/13*w**2 - 114/13*w = 0.
3, 8
Let y(b) be the third derivative of 16/9*b**3 - 1/540*b**6 + 2/27*b**4 - 81*b - 1/54*b**5 + 0 + b**2. Suppose y(c) = 0. What is c?
-4, 3
Let b(c) be the second derivative of c**5/200 + 17*c**4/120 - 28*c**3/15 - 539*c**2/5 - 7160*c. Let b(s) = 0. What is s?
-14, 11
Let x be (-1359)/(-90) + (-6873)/474. Determine a so that -3/5*a**4 + 9/5*a**2 - 3/5*a**3 + x*a - 6/5 = 0.
-2, -1, 1
Suppose -189*q + 1485 = -134*q. Let l(c) be the first derivative of -1/27*c**3 + 4/9*c - 1/6*c**2 + q. Factor l(w).
-(w - 1)*(w + 4)/9
Let n(u) be the first derivative of -u**4/42 + 808*u**3/63 - 5771*u**2/3 - 23548*u/3 + 2997. Determine x, given that n(x) = 0.
-2, 203
Find j, given that 344/19*j - 2/19*j**3 + 360/19 - 18/19*j**2 = 0.
-18, -1, 10
Let d(n) be the first derivative of 3*n**4/4 - 8*n**3 - 1305*n**2/2 + 14850*n - 4337. Factor d(j).
3*(j - 15)**2*(j + 22)
Let j(f) = -2*f**3 + 10*f**2 + 13*f - 3. Let a be j(6). Determine u, given that -40 + 12*u + 24*u**2 - 6*u**3 + a*u**3 + 7*u**3 = 0.
-5, -2, 1
Suppose 72*b = 18*b - 50*b - 13*b. Factor -c**4 + 0 + b*c**2 - 1/6*c**5 + 0*c - 3/2*c**3.
-c**3*(c + 3)**2/6
Let w(u) = -4*u - 8. Let j be w(-23). Let n be j/240 + (-3)/(-12). Suppose -3/5 + n*g**2 - 3/5*g + 3/5*g**3 = 0. What is g?
-1, 1
Determine u so that -102/5*u**4 + 60*u**2 + 3/5*u**5 + 666/5 + 1203/5*u - 342/5*u**3 = 0.
-3, -1, 2, 37
Let m be (-48)/21 - (-1036)/196. Let u(t) be the second derivative of 1/3*t**4 - 2*t + 5/6*t**6 - t**5 + 0*t**m + 0*t**2 + 0. Suppose u(g) = 0. What is g?
0, 2/5
Let c be -3 + -3 + -6 + 671/55. Factor 1/5*m**3 + 1/5*m**2 - 1/5*m + 0 - c*m**4.
-m*(m - 1)**2*(m + 1)/5
Let u(o) be the second derivative of 11881*o**4/6 + 218*o**3 + 9*o**2 - 1226*o. Determine q, given that u(q) = 0.
-3/109
Let c = 126 - 122. What is i in -5*i**5 - 2*i**c - 1 + 1 + 103*i**3 - 106*i**3 + 6*i**5 = 0?
-1, 0, 3
Suppose -3*d**5 + 11652*d**2 - 5880*d**2 - 5916*d**2 + 18*d**4 + 42*d**3 + 126 - 39*d = 0. What is d?
-3, -1, 1, 2, 7
Let v(n) be the second derivative of -n**4/12 - 50*n**3/3 + 1332*n. Find r such that v(r) = 0.
-100, 0
Let p = 42453 + -42450. Factor 0*r + 0 - 3/4*r**p + 1/2*r**2 + 1/4*r**4.
r**2*(r - 2)*(r - 1)/4
Let w(d) be the first derivative of -115 + 1/10*d**5 - 5*d + 3/2*d**3 + 11/4*d**2 - 11/8*d**4. Factor w(s).
(s - 10)*(s - 1)**2*(s + 1)/2
Let g(q) be the first derivative of -14*q**2 - 5*q - 11*q**3 + 3*q - 221 + 23*q**3 - 6*q. Find j, given that g(j) = 0.
-2/9, 1
Let c(p) be the third derivative of -p**8/672 - p**7/84 + p**6/16 + 13*p**5/24 + 35*p**4/24 + 2*p**3 + 1170*p**2. Solve c(w) = 0.
-6, -1, 4
Let l be 8 + -5 + (-4 - -3). Suppose -30*g**3 + 21*g**4 - 2*g**5 + 10227*g**2 - 3*g**5 - g**4 - 10207*g**l - 5*g = 0. What is g?
0, 1
Let n(z) be the first derivative of z**5/100 - 19*z**4/20 + 361*z**3/10 + z**2/2 + 13*z + 19. Let s(q) be the second derivative of n(q). Factor s(o).
3*(o - 19)**2/5
Let y(a) = -506*a - 2024. Let b be y(-4). Let r(v) be the third derivative of b*v**3 - 1/180*v**6 + 0*v - 1/36*v**4 + 17*v**2 + 0 + 1/45*v**5. Factor r(c).
-2*c*(c - 1)**2/3
Let w(k) = -k**2 + 11*k - 8. Let j be w(7). Let z = j - 17. Factor -8*d**z + 83*d - 7*d**4 - 83*d + 3*d**4.
-4*d**3*(d + 2)
Let c(o) be the second derivative of o**4/12 + 115*o**3/3 - 4*o - 142. What is w in c(w) = 0?
-230, 0
Solve 2/9*v**3 - 5476 + 440/9*v**2 + 7918/3*v = 0.
-111, 2
Let v(o) be the first derivative of -o**5/10 + 8*o**4/9 + 4*o**3/3 + 36*o - 40. Let t(l) be the first derivative of v(l). Let t(n) = 0. What is n?
-2/3, 0, 6
Suppose -1789*t = -1856*t + 201. Let -6/7*q**t + 4*q**2 + 46/7*q + 12/7 = 0. Calculate q.
-1, -1/3, 6
Let i(p) be the third derivative of -215*p**2 + 4/9*p**3 + 1/6*p**4 + 0 + 1/40*p**5 + 0*p. Factor i(l).
(3*l + 4)**2/6
Let y(w) be the first derivative of 12*w**2 - 5/6*w**4 + 4/5*w**5 - 132 - 1/9*w**6 + 0*w - 16/3*w**3. Suppose y(t) = 0. Calculate t.
-2, 0, 2, 3
Let d(v) = -4*v**3 - 312*v**2 + 2688*v - 5508. Let i(o) = -1. Let n(m) = d(m) - 4*i(m). Factor n(c).
-4*(c - 4)**2*(c + 86)
Let i be (-812)/(-6902) + (-678)/(-595) - 6/7. Let 2/5*m**3 + 0*m**2 + 1/5*m**4 - i*m - 1/5 = 0. What is m?
-1, 1
Let j(p) be the third derivative of -7*p**8/2880 + p**7/360 - p**6/720 - 13*p**5/12 + 2*p**2 + 38. Let y(t) be the third derivative of j(t). Factor y(i).
-(7*i - 1)**2
Solve p**5 - 631120*p + 304460*p**3 + 19637*p**2 - 92872*p**3 + 423200 + 1840*p**4 + 3*p**5 - 25149*p**2 = 0.
-230, -2, 1
Let s = 1415653/9 - 157293. Find g such that -4/9*g**3 + 8/9*g**2 + s + 28/9*g = 0.
-1, 4
Let h = -12149/5 + 2430. Let k be (-6 - -3)/(2/(-3 + 1)). Factor -h*y**k - y**2 - 4/5 - 8/5*y.
-(y + 1)*(y + 2)**2/5
Let c be ((-277)/(-9418))/(6/153). Suppose c*l**2 - 33/2 - 27/4*l = 0. What is l?
-2, 11
Let o(c) be the first derivative of -2*c**5/15 - 7*c**4/6 + 20*c**3/9 + 16*c**2/3 + 3928. Solve o(l) = 0 for l.
-8, -1, 0, 2
Let v = -522 + 525. Let z**4 - 268*z**v - 267*z**3 - 4*z + 538*z**3 = 0. Calculate z.
-2, 0, 1
Suppose -5*g = -5, -3*b - 5*g - 63 = -68. Suppose -9*q**2 + 0*q + b - 12*q**4 + 39/2*q**3 + 3/2*q**5 = 0. What is q?
0, 1, 6
Let u(j) = -j**4 - j - 1. Let p(r) = -43*r**2 + 40*r**3 + 53*r + 26*r**2 - 48*r - 13*r**4 + 3. Let v(y) = 2*p(y) + 6*u(y). Factor v(h).
-2*h*(h - 2)*(4*h - 1)*