*r + 2. Let t(o) be the first derivative of 14/3*o**3 + r*o**2 - 23 + 0*o - 3/2*o**4. Factor t(m).
-2*m*(m - 3)*(3*m + 2)
Factor 352*t - 46464 - 2/3*t**2.
-2*(t - 264)**2/3
Let p(x) be the first derivative of -3*x**2 + 0*x + x**3 - 41 + 3/4*x**4. Factor p(o).
3*o*(o - 1)*(o + 2)
Let s(z) = -5*z**4 + z**3 - z + 1. Let p(m) = 24*m**4 - 9*m**3 + 39*m**2 - 49*m - 5. Let x(q) = 2*p(q) + 10*s(q). Factor x(i).
-2*i*(i - 3)*(i - 2)*(i + 9)
Let u(s) be the third derivative of s**8/840 + s**7/75 - 7*s**6/300 - 43*s**5/150 + 7*s**4/10 - 303*s**2. Let u(q) = 0. What is q?
-7, -3, 0, 1, 2
Let l be (1411*20/1020 - 34) + 14/2. Find t such that 4/3*t**2 - 14/3*t**3 + 8*t + l*t**5 - 16/3 + 0*t**4 = 0.
-2, 1, 2
Factor -21 + 26/5*p - 1/5*p**2.
-(p - 21)*(p - 5)/5
Suppose -60*h + 61*h + 5*u + 100 = 0, -h + 100 = -5*u. Find m such that -10/3*m**3 + 2 + 11/3*m - 1/3*m**5 - 2*m**4 + h*m**2 = 0.
-3, -2, -1, 1
Let i(s) be the second derivative of -5*s**4/12 - 165*s**3/2 - 2610*s**2 + 7*s + 469. Let i(b) = 0. Calculate b.
-87, -12
Let b(h) = -15*h**2 + 4*h + 1. Let n be b(-1). Let l be (-415)/(-35) + (n - -7). Factor 2/7*k**3 + 0*k - l*k**2 + 0.
2*k**2*(k - 3)/7
Let q(i) = -9*i**5 - i**4 + 24*i**3 + 3*i**2 + 3*i - 3. Let b(d) = 44*d**5 + 4*d**4 - 112*d**3 - 14*d**2 - 14*d + 14. Let n(c) = -3*b(c) - 14*q(c). Factor n(v).
-2*v**4*(3*v - 1)
Let x be (8/(-42))/(6 - (-986)/(-153)). Factor 0 + x*p**2 - 3/7*p**3 - 3/7*p**4 + 3/7*p.
-3*p*(p - 1)*(p + 1)**2/7
Let h = -637000 + 637003. Factor 24/7 - 2/7*i**h + 16/7*i**2 - 38/7*i.
-2*(i - 4)*(i - 3)*(i - 1)/7
Let o = -11 + 13. Suppose o*p = s + 45, 4*p + 0*p + 2*s - 70 = 0. Factor 6*k**3 + 18*k**2 + p*k + k**3 + 46 + k**4 - 38.
(k + 1)*(k + 2)**3
Suppose 4*q + 3*b - 44 = -0*b, -3*b - 44 = -4*q. Suppose 15*l - q*l = 8. Find n such that 20 + 20*n + 33*n - 13*n - 25*n**l = 0.
-2/5, 2
Let o = -3791/126960 + 18/529. Let w(x) be the third derivative of 0*x + 1/12*x**3 + 0 + o*x**5 + 16*x**2 - 1/32*x**4. Solve w(r) = 0 for r.
1, 2
Let 7*w**2 + 81 + 5787*w - 1416 - 319 = 0. Calculate w.
-827, 2/7
Let n(v) be the first derivative of 8*v**5/5 + v**4/4 - 8*v**3 - 19*v**2/2 - 2*v - 1707. Factor n(l).
(l - 2)*(l + 1)**2*(8*l + 1)
Let b(s) be the second derivative of 9/80*s**5 - 1 - 20*s - 1/2*s**3 + 0*s**2 + 1/40*s**6 + 0*s**4. Suppose b(h) = 0. Calculate h.
-2, 0, 1
Let l(y) be the second derivative of -1/9*y**5 - 14/9*y**3 + 262*y - 8*y**2 + 0 + 26/27*y**4. Factor l(s).
-4*(s - 3)**2*(5*s + 4)/9
Let g(s) be the second derivative of -s**5/10 - 49*s**4/6 - 208*s**3 - 576*s**2 - 1251*s. Find i such that g(i) = 0.
-24, -1
Factor -4833628*p + 4833544*p - 3*p**2 - p**2.
-4*p*(p + 21)
Let b = -609553619/267 + 2282975. Let y = b + 2/89. Let 8/3*h + 4/3*h**4 + 4 - 16/3*h**2 - y*h**3 = 0. Calculate h.
-1, 1, 3
Solve 135/7 - 3/7*n**2 + 12/7*n = 0 for n.
-5, 9
Let w be 1/(-3)*3 + 5. Factor 15*c**3 - 60*c + 4*c**w - 40 + 948*c**2 + c**4 - 958*c**2.
5*(c - 2)*(c + 1)*(c + 2)**2
Let c = 5993701/600 + -19979/2. Let o(w) be the third derivative of 0*w + 32*w**2 - c*w**6 + 1/120*w**4 + 0 + 0*w**3 + 0*w**5. Factor o(j).
-j*(j - 1)*(j + 1)/5
Let g(m) be the second derivative of 0 - 20*m**2 + 61*m + 65/6*m**4 - 25/2*m**3 - 3/4*m**5. Determine v, given that g(v) = 0.
-1/3, 1, 8
Factor 1/2*x**2 - 119/2 - 59*x.
(x - 119)*(x + 1)/2
Let k(g) = g + 8. Let f be k(-9). Let c(u) = 7*u + 7. Let p be c(f). Let 8/3*t + p*t**2 + 0 - 50/3*t**3 = 0. Calculate t.
-2/5, 0, 2/5
Let p(h) be the first derivative of h**3/7 - 51*h**2/14 + 48*h/7 - 1028. Factor p(w).
3*(w - 16)*(w - 1)/7
Suppose 17*a = -5*a + 44. Factor 151*j - 111*j - 5*j**3 + 10*j**a + 4*j**2 + 11*j**2 - 60.
-5*(j - 6)*(j - 1)*(j + 2)
Let b = -14033 + 14035. Let y(d) be the second derivative of 2/85*d**6 - 3*d - 5/34*d**4 + 0 + 4/17*d**b - 1/34*d**5 + 0*d**3. Determine w so that y(w) = 0.
-1, -2/3, 1/2, 2
Let w(f) be the second derivative of -f**6/160 - 23*f**5/240 - 13*f**4/96 + 7*f**3/24 + 19*f**2 + 2*f. Let u(y) be the first derivative of w(y). Factor u(z).
-(z + 1)*(z + 7)*(3*z - 1)/4
Factor 1/3*c + 14/3 - 14/3*c**2 - 1/3*c**3.
-(c - 1)*(c + 1)*(c + 14)/3
Suppose -3552 = 10*c - 3572. Let g(d) be the second derivative of -11/30*d**3 + 0 - 3/10*d**c - 2/15*d**4 + 18*d. Suppose g(r) = 0. Calculate r.
-1, -3/8
Suppose -10*v = 57 + 113. Let n be v/4*(-132)/374. Factor 81/2*b**3 + 0 - 729/2*b**2 + 2187/2*b - n*b**4.
-3*b*(b - 9)**3/2
Let v(k) be the third derivative of 2*k**6/45 + 7*k**5/30 - k**4/3 + 6*k**3 + 18*k**2. Let z(b) be the first derivative of v(b). Factor z(x).
4*(x + 2)*(4*x - 1)
Let x(k) be the second derivative of -9/40*k**5 - 2/9*k**3 - 13/24*k**4 + 4*k + 1/45*k**6 + 0*k**2 - 30. What is p in x(p) = 0?
-1, -1/4, 0, 8
Let i(w) be the third derivative of -w**8/1008 + 2*w**7/63 + 7*w**6/120 + 514*w**2 + 1. What is y in i(y) = 0?
-1, 0, 21
Let o(h) be the first derivative of h**5/10 - 27*h**4 + 2592*h**3 - 93312*h**2 + 376. What is r in o(r) = 0?
0, 72
Let j(x) be the third derivative of 2*x**7/105 - 7*x**6/6 + 96*x**5/5 + 54*x**4 + 2*x**2 + 310. Factor j(n).
4*n*(n - 18)**2*(n + 1)
Let l(a) = a**3 + a**2 - a - 9. Let u be l(3). Factor u*j**2 + j**4 + 10*j**3 - 2*j**2 - 10*j + j**4 - 16*j**2 - 8.
2*(j - 1)*(j + 1)**2*(j + 4)
Let p(f) be the second derivative of -37*f**4/60 - 12*f**3/5 + 2*f**2/5 - 16*f + 11. Factor p(w).
-(w + 2)*(37*w - 2)/5
Let m(f) = -157957*f**2 + 6751*f - 79. Let u(r) = 78976*r**2 - 3375*r + 39. Let a(p) = -3*m(p) - 7*u(p). Factor a(o).
-(281*o - 6)**2
Let n(g) be the first derivative of -32 + 59/6*g**2 + 1/18*g**3 + 3481/6*g. Suppose n(q) = 0. What is q?
-59
Let b(y) = -66*y - 786. Let o be b(-12). Let z(v) be the first derivative of -1/2*v**o + 0*v**2 + 27 + 0*v + 0*v**3 - 3/5*v**5 + 0*v**4. Factor z(m).
-3*m**4*(m + 1)
Let u(p) = -14*p + 31. Let z be u(-35). Let c = z - 2541/5. Factor -c*q**2 + 0*q + 32/5*q**3 + 0 - 4/5*q**4.
-4*q**2*(q - 4)**2/5
Let s(i) be the second derivative of 0*i**2 + 0 - 24*i - 1/135*i**6 - 1/90*i**5 - 1/9*i**3 + 5/54*i**4. Factor s(v).
-2*v*(v - 1)**2*(v + 3)/9
Let n(p) = -3*p - 1. Let a be n(-2). Let h = 653069 - 3265343/5. Solve -h*o**2 + 2/5*o**3 + 0*o - 2/5*o**a + 2/5*o**4 + 0 = 0 for o.
-1, 0, 1
Suppose -10*g + 1507 = 297. Determine m, given that 3*m**4 - 257*m - 18 + 121*m + 15*m**3 + 15*m**2 + g*m = 0.
-3, -2, -1, 1
Let i(t) be the third derivative of t**8/252 + 541*t**7/630 + 667*t**6/360 - 407*t**5/180 - 671*t**4/72 - 67*t**3/9 - 3*t**2 + 1344. Solve i(j) = 0 for j.
-134, -1, -1/4, 1
Solve 1840/3*j - 320 - 775/3*j**2 + 20/3*j**4 - 85/2*j**3 + 5/6*j**5 = 0 for j.
-8, 1, 6
Let p(k) be the third derivative of -2/105*k**7 + 1/15*k**5 - 1/112*k**8 - 1/6*k**4 + 0*k**3 + 67*k**2 + 7/120*k**6 + 0*k + 0. Let p(b) = 0. Calculate b.
-2, -1, 0, 2/3, 1
Factor 753001/2*r**2 + 377504*r - 1001/2*r**4 + 1/2*r**5 + 248995/2*r**3 + 126002.
(r - 502)**2*(r + 1)**3/2
Let v be 5/25*(-52)/(-65). Let c(b) be the first derivative of -2/5*b**2 + 0*b + 4/15*b**3 - v*b**5 + 1/5*b**4 + 4. Solve c(w) = 0 for w.
-1, 0, 1
Suppose 3*b - 4*j + 8 = -2*b, -3*b - 5*j = -10. Suppose b = -z + 24 - 20. Factor -1/4*x + 1/4*x**3 - 1/4*x**2 + 0 + 1/4*x**z.
x*(x - 1)*(x + 1)**2/4
Let t(f) be the third derivative of -2*f**2 - 209*f + 0 - 17405/6*f**3 - 1/12*f**5 + 295/12*f**4. Find j, given that t(j) = 0.
59
Let j(y) be the third derivative of y**7/735 - 19*y**6/140 - 31*y**5/105 + 19*y**4/7 + 232*y**3/21 - 724*y**2. Solve j(n) = 0 for n.
-2, -1, 2, 58
Let d(f) be the third derivative of f**5/90 + 55*f**4/36 - 58*f**3/3 - 24*f**2 - 30*f. Solve d(w) = 0.
-58, 3
Let x = 71 + 23. Solve 2*k - x*k**3 + 177*k**3 - 81*k**3 + 4*k**2 = 0 for k.
-1, 0
Let w be 3*3*(36 - 33). Let s be (-27 + w)*2/(-4). Factor 1/8*u**3 + 3/8*u**2 + s + 1/4*u.
u*(u + 1)*(u + 2)/8
Let d(o) be the third derivative of o**6/840 - 43*o**5/420 - o**4/42 + 86*o**3/21 + 70*o**2. Find f such that d(f) = 0.
-2, 2, 43
Factor -1475*m**2 + 8*m**4 - 4*m**3 + 90*m - 5*m**4 - 2*m**3 + 1388*m**2.
3*m*(m - 6)*(m - 1)*(m + 5)
Let 6384*u**2 + 1/2*u**4 + 6498*u - 227/2*u**3 + 0 = 0. What is u?
-1, 0, 114
Let h(t) = -6*t**2 + 267*t + 67. Let d(z) = z**2 + 12*z + 3. Let f(w) = -4*d(w) - 2*h(w). Determine q, given that f(q) = 0.
-1/4, 73
Suppose 3*n + w + 6 = -8, -5*w - 70 = 0. Factor -3/4*a**4 - 15/8*a**5 + 0*a + 0 + 0*a**3 + n*a**2.
-3*