c) be the third derivative of 1/33*c**4 + 0 + 0*c + 0*c**3 - 1/330*c**5 - 31*c**2. Solve j(i) = 0.
0, 4
Suppose 6*v = 462 - 138. Suppose -6*o = 12*o - v. Let 2/13*k**o + 0 + 0*k**2 - 2/13*k = 0. Calculate k.
-1, 0, 1
Let b be ((-44)/44)/((-2)/(-1078)). Let d be 4/35*(b/(-14) + -11). Factor -2/7*m**3 - 12/7 - 12/7*m**2 - d*m.
-2*(m + 1)*(m + 2)*(m + 3)/7
Let d(m) be the second derivative of -m**6/150 - 81*m**5/50 - 153*m**4 - 33813*m**3/5 - 1193859*m**2/10 + 10181*m. Let d(y) = 0. What is y?
-51, -9
Suppose 0 = -182219*s + 182235*s. Factor 4/9*g**3 + s*g + 2/9*g**2 + 2/9*g**4 + 0.
2*g**2*(g + 1)**2/9
Suppose -487/3*r + 196 - 67/2*r**2 - 1/6*r**3 = 0. What is r?
-196, -6, 1
Determine a, given that 0 + 9/4*a**2 - 1/4*a**3 + 11/2*a = 0.
-2, 0, 11
Let n(z) be the second derivative of z**6/30 - 25*z**5/2 + 62*z**4/3 + 125*z**3/3 - 249*z**2/2 - 6*z - 207. Suppose n(u) = 0. Calculate u.
-1, 1, 249
Suppose 4*n + 52 = -184*f + 188*f, n - 2 = -4*f. Factor 2 - 5/4*g**2 + 1/2*g + 1/4*g**f.
(g - 4)*(g - 2)*(g + 1)/4
Suppose 2*v - 24 = 0, j + 0*v - 16 = -0*v - v. Solve 12/7*k**3 + 224 + 2/7*k**j - 48*k - 94/7*k**2 = 0 for k.
-7, 4
Let b(s) be the second derivative of 4/5*s**5 - 4/3*s**4 - 5*s + 0*s**2 + 2/15*s**6 + 1 - 2/21*s**7 + 0*s**3. Determine t so that b(t) = 0.
-2, 0, 1, 2
Let l be 9/21 + (-10506)/24416. Let p = 13997/26160 + l. Solve 2/15*x**3 + 12/5 - p*x**2 - 2/5*x = 0 for x.
-2, 3
Let k(b) be the second derivative of b**4/12 + 253*b**3/3 + 64009*b**2/2 - 8*b - 9. What is r in k(r) = 0?
-253
Solve -5/3*a**2 + 0 + 2*a + 1/3*a**3 = 0 for a.
0, 2, 3
Let p(v) be the second derivative of 0*v**2 - 5*v - 5/6*v**4 + 0*v**3 - 1/2*v**6 - 9/8*v**5 + 0 - 5/84*v**7. What is w in p(w) = 0?
-4, -1, 0
Let s(l) = 8*l**2 + 27*l + 13. Let w be s(-3). Let i(n) be the second derivative of 1/4*n**w + 0 - 6*n**2 + 9*n + 0*n**3. Factor i(h).
3*(h - 2)*(h + 2)
Let j(r) be the first derivative of 2*r**5/5 - 77*r**4/6 + 472*r**3/9 + 140*r**2/3 - 352*r/3 + 11259. Determine z, given that j(z) = 0.
-1, 2/3, 4, 22
Let j be 28/21 + 150/(-180). Determine q so that -q**2 + 23/2*q - 5*q**4 + j*q**5 - 12*q**3 + 6 = 0.
-1, 1, 12
Let q(p) = 7*p**3 - 159*p**2 + 599*p - 741. Let u(l) = 76*l**3 - 1648*l**2 + 6588*l - 8152. Let a(w) = 32*q(w) - 3*u(w). Factor a(s).
-4*(s - 1)*(s + 6)*(s + 31)
Let x**2 - 277*x - 544 - x**2 + 300*x + x**2 + 520 = 0. What is x?
-24, 1
Let u(o) be the third derivative of 5*o**8/1008 + o**7/35 - 103*o**6/360 + 3*o**5/5 - 7*o**4/18 - 5*o**2 - 2*o - 15. Let u(x) = 0. Calculate x.
-7, 0, 2/5, 1, 2
Let h = 223777 + -223777. Factor -4/3*z**3 + h + 6*z**2 - 6*z.
-2*z*(z - 3)*(2*z - 3)/3
Let k = -632 + 635. Factor -4989*s**3 - 9*s**4 - 63*s**2 + 30*s + 4938*s**k - 3*s.
-3*s*(s + 3)**2*(3*s - 1)
Let y be (-3)/(-7)*(-12020)/(-1803). Let y*c**2 + 64/7 - 64/7*c - 2/7*c**3 = 0. What is c?
2, 4
Let d(c) be the first derivative of -c**4/6 - 122*c**3/3 - 2632*c**2 + 88360*c/3 - 5179. Factor d(w).
-2*(w - 5)*(w + 94)**2/3
Let h(m) be the first derivative of 441*m**5/10 - 231*m**4 + 1052*m**3/3 - 88*m**2 + 8*m - 481. Suppose h(b) = 0. What is b?
2/21, 2
Let r(b) = -106*b**2 + 4*b - 36. Let g be r(4). Let d = -15428/9 - g. Factor -2/3*p**2 - 8/9 - d*p.
-2*(p + 2)*(3*p + 2)/9
Suppose -16*w - 155*w = 43*w + 113*w + 40*w. Factor 2/3*d**3 + 0*d + w - 2*d**2.
2*d**2*(d - 3)/3
Suppose -11*a + 2783 = 95*a + 147*a. Solve -19/2*j**2 + 5/4*j**3 + 6 + a*j = 0.
-2/5, 2, 6
Let d be (-760)/(-175) - 2048/640. Let 0 + 2/7*z**2 - d*z = 0. Calculate z.
0, 4
Let q = -132626 - -132628. Determine n so that 50/3 + 2/3*n**q - 20/3*n = 0.
5
Let f(q) = 1531 - 1521 + 0*q - 2*q + 0*q. Let x be f(5). Solve 14/5*u**4 + 0*u - 6/5*u**5 + 0*u**3 - 8/5*u**2 + x = 0 for u.
-2/3, 0, 1, 2
Suppose 0 = 21*f - 29*f + 40. Suppose -f*d**2 + 20*d + 10*d**2 + 610 - 635 = 0. Calculate d.
-5, 1
Let j(x) = 26*x**2 + 5210*x - 4868. Let t(b) = -5*b**2 - 1042*b + 978. Let h(s) = -3*j(s) - 16*t(s). Factor h(d).
2*(d - 1)*(d + 522)
Let k = -449641 + 3147490/7. Factor -k*h**3 - 9/7*h**2 + 0 + 0*h.
-3*h**2*(h + 3)/7
Let u(d) be the first derivative of -d**6/33 - 16*d**5/55 + d**4/22 + 16*d**3/33 - 1817. Determine l so that u(l) = 0.
-8, -1, 0, 1
Suppose 49*g**4 - 2*g**3 - 466*g**2 + 36*g + 451*g**2 - 48*g**4 = 0. What is g?
-4, 0, 3
Let h(y) be the second derivative of -2/105*y**6 + 0 + 132*y + 4/7*y**3 + 8/35*y**5 - 13/21*y**4 + 0*y**2. Solve h(d) = 0 for d.
0, 1, 6
Let q(t) be the first derivative of -7*t**5/5 + 13*t**4/2 - 9*t**3 + 2*t**2 + 4*t + 1443. Factor q(k).
-(k - 2)*(k - 1)**2*(7*k + 2)
Factor 284/5*k + 576/5 - 2/5*k**2.
-2*(k - 144)*(k + 2)/5
Let z = -100 - -104. Let w be ((-23)/z - 1)*-24. Factor -81*o + 21*o**3 + w + 10*o**2 - 3*o**4 - 54*o**2 + 17*o**2.
-3*(o - 3)**3*(o + 2)
Let d(s) be the second derivative of -s**6/225 + s**5/50 + 8*s**4/5 + 28*s**3/9 + 4073*s. What is y in d(y) = 0?
-10, -1, 0, 14
Find s such that -6644352*s - 17952*s**3 - 11244288 - 545952*s**2 - 267*s**4 - 3/2*s**5 = 0.
-44, -2
Let g be (4 - (-1 + 1))/16. Let m(h) be the second derivative of -8*h + g*h**4 + 3/2*h**2 - h**3 + 0. Solve m(j) = 0 for j.
1
Let h(j) be the third derivative of -j**5/60 - 23*j**4/24 - 19*j**3/6 - 5*j**2. Let q be h(-20). Factor -c - 49*c**3 + q*c**3 - 2*c**4 - 10*c**2 - 3*c.
-2*c*(c + 1)**2*(c + 2)
Let c(v) be the first derivative of -v**3/18 + 437*v**2/6 - 190969*v/6 + 300. Suppose c(h) = 0. Calculate h.
437
Let z be (765/1785)/((-5)/(-7)). Factor 3/5 - 12/5*m - z*m**2 + 12/5*m**3.
3*(m - 1)*(m + 1)*(4*m - 1)/5
Let h be ((-768)/11712)/((-270)/915). Find k such that 2/9*k**2 - 82/9*k**3 + 0 + 70/9*k**5 + 4/3*k - h*k**4 = 0.
-1, -2/5, 0, 3/7, 1
Suppose -4 = -2*z, -4*m - 9 = 3*z - 27. Suppose 2*d - 4*p - 228 = 0, -5*d + 234 = -m*d - p. Factor -119*q**2 + 3*q**3 + d*q**2 - 2*q**4 + q**4 - q**3.
-q**2*(q - 1)**2
Let k = -695 - -706. Let o(w) = 7*w**4 + 11*w**3 - 3*w**2 + w - 4. Let z(s) = 13*s**4 + 21*s**3 - 5*s**2 + s - 8. Let x(d) = k*o(d) - 6*z(d). Factor x(l).
-(l - 1)*(l + 1)**2*(l + 4)
Let n(g) be the third derivative of g**6/360 - 7*g**5/6 + 1377*g**2. Solve n(f) = 0 for f.
0, 210
Suppose 2*h = h + 4. Let j(y) = 55*y**3 + 30*y**2 - 5*y - 5. Let l(k) = -139*k - 1 + 9*k**3 - 135*k + 273*k + 5*k**2. Let f(w) = h*j(w) - 25*l(w). Factor f(i).
-5*(i - 1)*(i + 1)**2
Suppose -118*y = -121*y + 3. Let w(v) = 3*v**3 + v + 1. Let f(k) = 8*k**3 - 35*k**2 + 36*k + 76. Let p(z) = y*f(z) - w(z). Suppose p(r) = 0. Calculate r.
-1, 3, 5
Let g(q) be the third derivative of q**6/60 + 29*q**5/30 - 67*q**4/4 + 105*q**3 - 2*q**2 + 27*q + 12. Solve g(v) = 0.
-35, 3
Let v = -83309/60 - -2777/2. Let i(k) be the second derivative of 0 - 5*k - 1/20*k**5 + 1/84*k**7 - 1/4*k**2 + 1/12*k**4 - v*k**6 + 1/12*k**3. Factor i(b).
(b - 1)**3*(b + 1)**2/2
Factor 649794*t**2 + 4271*t**3 - 1306448*t - 1987*t**3 + 2*t**4 - 215828 + 870196.
2*(t - 1)**2*(t + 572)**2
Let b(w) be the third derivative of -w**6/30 + 29*w**5/15 - 30*w**4 - 6*w**2 - 3*w. Suppose b(q) = 0. Calculate q.
0, 9, 20
Let a = -974209/4 - -243553. Let -a*s**2 + 1 + 0*s + 1/4*s**3 = 0. Calculate s.
-1, 2
Let -4/7*l**4 - 40/7*l + 44/7*l**3 + 32/7 - 4*l**2 - 4/7*l**5 = 0. What is l?
-4, -1, 1, 2
Factor 48582831 + 2388*l**2 + 579838*l - 3757*l - 111*l**2 + 3*l**3.
3*(l + 253)**3
Let q be -3 - -2 - -24 - 21. Factor 117*a**q - 405/4*a - 28*a**3 - 16*a**4 + 27.
-(a + 4)*(4*a - 3)**3/4
Let r be 19706/14696 - 3/12. Factor 34/11*g - r + 46/11*g**2.
2*(g + 1)*(23*g - 6)/11
What is c in 5/3*c**4 + 0*c + c**3 - 3*c**2 + 0 + 1/3*c**5 = 0?
-3, 0, 1
Let m(t) be the first derivative of -t**4/32 - 7*t**3/6 + t**2/4 + 14*t - 4065. Suppose m(q) = 0. What is q?
-28, -2, 2
Let x = 2771/4912 + -154/307. Let o(n) be the second derivative of 0 + 5/4*n**3 + 14*n - 33/8*n**2 + x*n**4. Factor o(c).
3*(c - 1)*(c + 11)/4
Solve 121/10*h**3 - 407/2*h**2 - 373/10*h - 17/10 = 0.
-1/11, 17
Suppose -o = o + 50. Let i = 28 + o. What is q in -15*q**2 - q**3 + 5*q**2 + 4*q**2 - i*q - 2*q**3 = 0?
-1, 0
Let z(k) be the first derivative of 32*k**2 - 218 - 8*k - 82/3*k**3 + 13/2*k**4. What is v in z(v) = 0?
2/13, 1, 2
Let c(y) be the first derivative of 5*y**3/3 - 25*y**2 - 1000*y - 2051. Find i such that c(i) = 0.
-10, 20
Factor 6*u**2 + 45*u + 14*u + 4*u**2 + 29*u + 87 - 9*u**2.
(u + 1)*(u + 87)
Let u(x) = -7*x**2 + 65*x - 