51*v**2/2 - 154*v. Let u(d) be the first derivative of a(d). Factor u(m).
-(m + 52)**2
Let r(l) be the third derivative of -l**5/120 + 337*l**4/48 + 169*l**3/6 + 39*l**2 + 12*l - 1. What is p in r(p) = 0?
-1, 338
Let g(y) = -37*y + 177. Let k be g(-25). Let n = k + -7706/7. Determine v so that 4/7*v**2 - 12/7*v + n = 0.
1, 2
Let h = -51/5 - -362/35. Let q(a) be the first derivative of -8/7*a**3 + 4 + h*a**4 + 24/7*a**2 - 32/7*a. Factor q(p).
4*(p - 2)**3/7
Let i(o) be the first derivative of -o**6/6 - 83*o**5/5 - 1175*o**4/2 - 8046*o**3 - 41553*o**2/2 - 19683*o + 1437. Factor i(k).
-(k + 1)**2*(k + 27)**3
Let n(q) be the first derivative of 2/15*q**4 + 12*q - 4/5*q**2 + 2/15*q**3 - 1/25*q**5 - 15. Let d(h) be the first derivative of n(h). Let d(c) = 0. What is c?
-1, 1, 2
Let b(y) be the second derivative of 49/10*y**2 + 78*y + 3/25*y**5 + 0 + 11/30*y**4 + 1/150*y**6 - 14/5*y**3. Factor b(x).
(x - 1)**2*(x + 7)**2/5
Let r be 864/(-378)*((-6)/8)/((-18)/(-72)). Find g, given that 52/7*g**2 + 18/7*g + 12/7*g**4 + r*g**3 + 0 - 2/7*g**5 = 0.
-1, 0, 9
Let i(j) be the third derivative of 1/42*j**7 + 1/4*j**5 + 46*j**2 + 0*j - 1/8*j**6 + 0 + 0*j**3 - 5/24*j**4. Factor i(p).
5*p*(p - 1)**3
Let z(u) = u**2 - 4*u - 12. Let c be (4 - 5)*12*-1. Let a be z(c). Suppose -9*o**2 + 20 + 6*o**2 + a*o + 19*o**2 = 0. Calculate o.
-5, -1/4
Suppose -4*r + 3*r = -5, 3*r - 23 = -2*a. Factor 12*n**3 + 0*n**3 + 32*n**2 + 8*n**4 - 16*n - 87*n**2 - a*n**5 + 39*n**2.
-4*n*(n - 2)**2*(n + 1)**2
Suppose -309*j + 78 = -283*j. Let n(g) be the third derivative of 1/525*g**7 + 0*g**6 + 0*g + 0*g**j - 1/30*g**4 - 1/50*g**5 + 14*g**2 + 0. Factor n(w).
2*w*(w - 2)*(w + 1)**2/5
Let c(b) be the second derivative of -b**5/100 + 9*b**4/20 + 19*b**3/10 - 3971*b**2/10 - 49*b - 65. Find q such that c(q) = 0.
-11, 19
Let t(r) = -r**3 + 2*r**2 + 8*r - 10. Let s be t(3). Suppose -2128 = -s*z - 2113. Factor 0*b - 4/3*b**4 - 2/3*b**2 - 2*b**z + 0.
-2*b**2*(b + 1)*(2*b + 1)/3
Let k(s) be the second derivative of s**6/900 - 11*s**5/300 + 5*s**3/6 - 5*s**2 - 3*s - 41. Let z(u) be the second derivative of k(u). Factor z(o).
2*o*(o - 11)/5
Suppose -96*k + 105*k = 27. Find w such that w - 6*w**2 + w**3 - k*w**2 + 11*w**2 = 0.
-1, 0
Let l(d) = -3*d + 63. Let j be l(-8). Factor 102*n**2 - j*n**3 + 10*n**4 + 155*n**3 - 8 + 40*n + 4*n**4.
2*(n + 1)*(n + 2)**2*(7*n - 1)
Factor -468/5*c**3 + 8640*c + 0 + 2592*c**2 + 4/5*c**4.
4*c*(c - 60)**2*(c + 3)/5
Let r(g) be the second derivative of -2/9*g**3 + 2*g**2 + 1/15*g**5 - 1/3*g**4 + 0 - 54*g. Find f such that r(f) = 0.
-1, 1, 3
Factor -448109 - 586*n + 189*n**2 - 2*n**3 + 107*n**2 + 448401.
-2*(n - 146)*(n - 1)**2
Let i be 2136/(-420)*-1 + 4 + (-420)/98. Let -9/5 - 18/5*h**2 + i*h + 0*h**3 + 3/5*h**4 = 0. Calculate h.
-3, 1
Let u be (55/(-110))/(1499/2). Let d = u - -1501/2998. Find k, given that 7/2*k - d - 63/4*k**3 - 13/8*k**2 - 81/8*k**4 = 0.
-1, 2/9
Suppose -11*b + 8 = -3. Let q(k) = -2*k**2 - k - 1. Let t(h) = 2*h**3 - 34*h**2 + 42*h - 26. Let z(r) = b*t(r) - 4*q(r). Suppose z(x) = 0. Calculate x.
1, 11
Suppose 2*c + 15 = -q, -2*q = -11*c + 13*c + 26. Let y be 3/(-15) - q/30. Factor -y*k**2 + 1/6*k**3 - 1/3*k + 0.
k*(k - 2)*(k + 1)/6
Let v be (0*2/(-12))/(-283 - -281). Find x such that -2/5*x**4 + 0 + 4/5*x**3 - 2/5*x**2 + v*x = 0.
0, 1
Let r be -2*520/(-160) - (10/2)/20. Factor -r*s**2 - 15/2*s - 5/4.
-5*(s + 1)*(5*s + 1)/4
Let v = 1117951/7 - 159707. Factor -18/7*s - 4*s**3 - v*s**5 - 12/7*s**4 - 4/7 - 32/7*s**2.
-2*(s + 1)**4*(s + 2)/7
Let t(x) be the third derivative of x**5/12 - 115*x**4/8 + 170*x**3/3 - x**2 + 63. Suppose t(c) = 0. What is c?
1, 68
Factor 3/4*h**2 - 2*h + 3/4 + 1/2*h**3.
(h - 1)*(h + 3)*(2*h - 1)/4
Let i(n) be the third derivative of n**6/80 - 6*n**5/5 + 93*n**4/16 - 23*n**3/2 + n**2 - 540*n - 3. Factor i(d).
3*(d - 46)*(d - 1)**2/2
Let l(j) be the first derivative of 2*j**3/3 - 2*j**2 - 2*j - 30. Let g be l(-1). Suppose 225*u**5 + 7*u**g - 17*u**4 - 230*u**5 = 0. Calculate u.
-2, 0
Let o(h) be the third derivative of h**6/420 + 41*h**5/105 + 745*h**4/84 + 600*h**3/7 - h**2 + 177*h + 3. Factor o(x).
2*(x + 5)**2*(x + 72)/7
Let w be -1 - 6 - (-27 + 2646/231). Find b, given that -8/11*b - w*b**2 - 42/11*b**3 + 24/11 = 0.
-2, -2/3, 3/7
Let t(u) be the first derivative of -u**6/27 + 74*u**5/45 - 35*u**4/18 - 74*u**3/27 + 4*u**2 + 4043. Suppose t(f) = 0. Calculate f.
-1, 0, 1, 36
Let l(c) be the second derivative of 3*c**5/20 + c**4/2 - 3*c**3/2 - 675*c + 2. Find k such that l(k) = 0.
-3, 0, 1
Let t be (-117)/26 + 60/8. Suppose -44*d + t*n - 24 = -48*d, d = 3*n - 9. Factor -4 + 9/2*b**3 - 10*b - d*b**2.
(b - 2)*(3*b + 2)**2/2
Let y(n) be the first derivative of -n**5/30 - 19*n**4/24 + 98*n**3/9 - 131*n**2/3 + 72*n - 5963. Suppose y(g) = 0. Calculate g.
-27, 2, 4
Let s be ((-5016)/399 - -12) + (-25)/(-7). Determine v so that 64/7*v**s + 12/7*v + 80/7*v**2 + 0 - 256/7*v**4 = 0.
-1/4, 0, 3/4
Let m be 9 + 0 + 9637/(-690) + 5. Let j(z) be the third derivative of 1/4*z**4 + 0 + m*z**5 + 18*z**2 + 0*z + 2/3*z**3. Suppose j(u) = 0. What is u?
-2, -1
Let u(m) = -9993 - 6*m**2 - 143*m - m**2 - 271*m + 2*m**2 - 6*m**2. Let i(z) = 10*z**2 + 412*z + 9994. Let c(q) = 7*i(q) + 6*u(q). Find t such that c(t) = 0.
-50
Let x be (-4)/48*3*(-536)/603. Factor 1/9*k**4 + 0*k + x*k**2 - 1/3*k**3 + 0.
k**2*(k - 2)*(k - 1)/9
Suppose -56/11*r**3 - 554/11*r**2 - 2/11*r**4 - 2196/11*r - 2592/11 = 0. Calculate r.
-9, -8, -2
Let z = -40944 - -368498/9. Suppose 0*l - z*l**2 + 0 - 2/9*l**3 = 0. Calculate l.
-1, 0
Let r(a) be the first derivative of -52441*a**4 + 141064*a**3 - 3672*a**2 + 32*a + 593. Factor r(p).
-4*(p - 2)*(229*p - 2)**2
Let o(x) = 4*x**2 - 32*x - 56. Let b(i) be the third derivative of 0 - 1/6*i**3 + 24*i**2 + 0*i. Let f(g) = 20*b(g) - o(g). Solve f(w) = 0 for w.
-1, 9
Let n = -9191 + 9227. Let z(u) be the first derivative of n*u + 4/3*u**3 + 12*u**2 - 13. What is r in z(r) = 0?
-3
Suppose -5*s + 3*s - 3*q = -71, -5*q + 5 = 0. Suppose -s = -14*r - 3*r. Factor 2/5*g + 4/5 - 2/5*g**r.
-2*(g - 2)*(g + 1)/5
Let r(j) be the third derivative of -j**8/63 - 4*j**7/315 + 13*j**6/120 - 17*j**5/180 + j**4/36 + 2222*j**2. Let r(b) = 0. Calculate b.
-2, 0, 1/4, 1
Let r(k) be the third derivative of k**7/840 - k**6/480 - k**5/12 + 8338*k**2. Factor r(h).
h**2*(h - 5)*(h + 4)/4
Find s, given that -2/7*s**2 - 72/7 - 30/7*s = 0.
-12, -3
Let a(h) be the third derivative of h**6/480 - h**4/32 - h**3/12 + 689*h**2. Suppose a(r) = 0. Calculate r.
-1, 2
Let b = 572/347695 - -2190508821/1461014390. Let r = -2/2101 + b. Factor -r*w**4 + 0 + 0*w**2 + 9/4*w**3 + 0*w - 3/4*w**5.
-3*w**3*(w - 1)*(w + 3)/4
Suppose 22*w + 399*w**2 - 2*w**4 - 406*w**2 - 2*w**3 - 2*w**3 + 24 + 3*w**4 = 0. Calculate w.
-2, -1, 3, 4
Let p(d) be the third derivative of -2*d**7/105 - 7*d**6/30 + 137*d**5/15 - 175*d**4/2 + 408*d**3 + 13*d**2 + 222*d - 1. Factor p(f).
-4*(f - 4)*(f - 3)**2*(f + 17)
Let n(h) be the first derivative of -4*h**5/25 - 3*h**4/5 + 12*h**3 - 162*h**2/5 - 1292. Factor n(s).
-4*s*(s - 3)**2*(s + 9)/5
Let q be (-9 + (-202)/(-22))*(-26)/104*-11. Let z be (-2)/6 - (-7)/12. Suppose -2*w + q*w**3 - 3/4*w**2 - 1 + z*w**4 = 0. Calculate w.
-2, -1, 2
Factor -659883/2 + 1407/2*b - 3/8*b**2.
-3*(b - 938)**2/8
Factor 80040/7*j**2 - 692/7*j**3 - 3121100/7*j + 2/7*j**4 + 3041750/7.
2*(j - 115)**3*(j - 1)/7
Let d(n) = 9430*n - 9428. Let r be d(1). Find o such that 12/11*o - 2/11*o**r + 14/11 = 0.
-1, 7
Let v(o) be the second derivative of o**7/63 + o**6/15 - o**5/5 - 14*o**4/9 - 8*o**3/3 - 33*o - 2. Factor v(n).
2*n*(n - 3)*(n + 2)**3/3
Suppose -10 = -2*v - u, -v - 5*u - 40 = -6*v. Let w be 4 - (-5)/v*(19 - 22). Factor -3*z**2 - w*z + 3*z**3 - 3/2*z**5 + 3/2*z**4 + 3/2.
-3*(z - 1)**3*(z + 1)**2/2
Let m be (-4)/(11 - 3)*-4. Let i(z) = -2 + 6 - 3 - m*z. Let q(l) = -l**2 - 16*l - 82. Let x(h) = -5*i(h) - 5*q(h). Factor x(r).
5*(r + 9)**2
Let j(m) be the second derivative of 149*m - 5/4*m**2 + 7/20*m**5 + 19/12*m**3 - 1/60*m**6 - 13/12*m**4 - 1/84*m**7 + 0. Factor j(l).
-(l - 1)**4*(l + 5)/2
Let s be (-6 - (-2 + -8)) + (-1)/4. Let m be ((-148)/(-40) + 0)/((-30)/(-75)). Suppose m*n**2 + 9/4*n**4 - 33/4*n**3 + 1/2 - s*n = 0. Calculate n.
1/3, 1, 2
Let c(n) be the third derivative of -n**5/75 -