Let a be (3*8)/((-6)/45*3). Let x be (-20)/a*1*6. Factor 0 - 4/3*l - 5/3*l**3 + 8/3*l**x + 1/3*l**4.
l*(l - 2)**2*(l - 1)/3
Let w be (-5 - -2) + (-466)/(-126). Let u = -2/63 + w. Suppose 0 - u*j + 2/3*j**2 = 0. Calculate j.
0, 1
Factor 1/10*k**3 + 0*k - 3/10*k**2 + 0.
k**2*(k - 3)/10
Let u(d) be the second derivative of -d**5/5 + 47*d**4/3 + 32*d**3 - 159*d. Determine q, given that u(q) = 0.
-1, 0, 48
Let a be (3/((-18)/(-4)) - (-26)/(-39)) + 2. Factor -4/13 + 2/13*n**a - 2/13*n.
2*(n - 2)*(n + 1)/13
Let a(t) be the third derivative of -t**8/3360 + t**7/1680 + t**6/720 - t**5/240 + 5*t**3/3 + 13*t**2. Let l(u) be the first derivative of a(u). Factor l(h).
-h*(h - 1)**2*(h + 1)/2
Let y(h) be the first derivative of -h**5/30 + h**4/6 - 2*h**2 - 11. Let g(b) be the second derivative of y(b). Solve g(a) = 0 for a.
0, 2
Let w(h) = 5*h**2 - 1. Let m(i) = -i**3 + i**2 + 1. Suppose -23 + 21 = 2*y. Let f(z) = y*w(z) - m(z). Factor f(p).
p**2*(p - 6)
Determine u, given that -1/5*u**2 + 218/5*u - 11881/5 = 0.
109
Let z = 40 + -40. Factor 2/13*u**2 + 4/13*u + z.
2*u*(u + 2)/13
Let x(i) be the second derivative of -i**8/8960 - i**7/672 - 7*i**6/960 - 3*i**5/160 - i**4/6 - 6*i. Let w(a) be the third derivative of x(a). Factor w(c).
-3*(c + 1)**2*(c + 3)/4
Let f = -2/3399 + 30595/6798. Factor -b**2 + 1/2*b**4 + f + 2*b**3 - 6*b.
(b - 1)**2*(b + 3)**2/2
Let a = -1/754 + 9/58. Suppose a*n**4 + 18/13*n + 30/13*n**2 + 0 + 14/13*n**3 = 0. Calculate n.
-3, -1, 0
Let l be ((-21)/98)/(7/(-49)). Solve 0*x - 3*x**2 - l*x**3 + 0 = 0 for x.
-2, 0
Let c(k) be the second derivative of k**4/15 + 218*k**3/15 - 44*k**2 + 847*k. Find o, given that c(o) = 0.
-110, 1
Let u be 9/2*28/42. Let v(a) be the third derivative of 1/4*a**3 - 1/240*a**6 + 1/24*a**5 - 7/48*a**4 + 0*a + 0 + u*a**2. Determine i so that v(i) = 0.
1, 3
Factor -50*n**2 - 99*n**4 - 5*n**2 + 3*n + 94*n**4 - 28*n - 35*n**3.
-5*n*(n + 1)**2*(n + 5)
Let c(z) be the first derivative of -z**6/12 + 3*z**5/5 - 5*z**4/8 - 105. Factor c(s).
-s**3*(s - 5)*(s - 1)/2
Let i = -17 - -15. Let j be i/((-28)/(-6)) - (-15)/21. Factor -j*k**3 + 0 + 0*k + 6/7*k**2.
-2*k**2*(k - 3)/7
Let h = 14/141 - -152/47. Let r(i) be the first derivative of 1/3*i - h*i**4 - 5/3*i**2 - 8 + 11/3*i**3 + 16/15*i**5. Let r(q) = 0. What is q?
1/4, 1
Suppose 279/5*i + 0 - 3/5*i**2 = 0. What is i?
0, 93
Let j(c) be the first derivative of -8*c**5/15 - 4*c**4 - 74*c**3/9 - 7*c**2 - 8*c/3 + 2. Determine s, given that j(s) = 0.
-4, -1, -1/2
Let z = 751229/3570 - -73/510. Let d = z + -210. Factor 0 - 2/7*b**4 - 2/7*b**2 + 0*b + d*b**3.
-2*b**2*(b - 1)**2/7
Suppose 0 = 4*w - 3*z - 26, z + 1005 = 4*w + 975. Suppose -1/3*m**4 - 1/3*m**2 - 16/3 - w*m + 2*m**3 = 0. What is m?
-1, 4
Let m = 27 - 27. What is o in 6*o**2 + 12 + 12*o - 3*o**2 + m*o**2 = 0?
-2
Let d = 3481/4 + -870. Factor -d*u**3 + 3/4*u**2 + 1/4 - 3/4*u.
-(u - 1)**3/4
Let d = -45517 - -228719/5. Let p = d - 226. Determine b so that -4/5*b**2 + 0*b**3 + p*b**4 + 0 - 2/5*b**5 + 2/5*b = 0.
-1, 0, 1
Let x(y) = -y + 5. Let c be x(0). Suppose c*q - 4 = 3*q. Find p, given that 9*p**3 - 8*p**q - 21*p**4 - 29*p**4 - 49*p**3 = 0.
-2/5, 0
Let m(g) be the third derivative of g**5/9 + g**4/12 - 153*g**2. Find w, given that m(w) = 0.
-3/10, 0
Let u(c) = -3*c**2 - 39*c + 1137. Let h be u(14). Factor 1/7*p**h - 1/7*p**2 - 1/7*p + 1/7.
(p - 1)**2*(p + 1)/7
Factor 160/9*p**2 + 0 + 4/9*p**5 - 8/9*p**4 - 16/3*p**3 - 128/9*p.
4*p*(p - 2)**3*(p + 4)/9
Factor -2*u**2 - 6 + 18 + 3*u**3 - 6*u**3 + 96 + 65*u**2 - 168*u.
-3*(u - 18)*(u - 2)*(u - 1)
Find b such that 3/4*b**4 + 0*b + 0 + 33/4*b**2 - 9*b**3 = 0.
0, 1, 11
Let b(i) = -5*i - 207. Let m be b(-42). Let t(q) be the first derivative of -1/3*q**m + 2 + q**2 + 3*q. Factor t(w).
-(w - 3)*(w + 1)
Let g(d) be the first derivative of d**5/10 + d**4/6 - 2*d**3/3 + 5*d - 13. Let s(x) be the first derivative of g(x). Let s(n) = 0. What is n?
-2, 0, 1
Let o(d) be the second derivative of -2/3*d**3 + 0*d**2 - 7*d - 4 - 1/15*d**4. Find h such that o(h) = 0.
-5, 0
Let x(v) be the first derivative of -v**3/30 - 3*v**2/10 - 4*v/5 - 14. Determine a so that x(a) = 0.
-4, -2
Let p = 35379 + -70755/2. Find u, given that 9/4 + p*u + 1/4*u**2 = 0.
-3
Let r = 1992 - 1990. Determine i so that -1/4 - 1/4*i**3 + 1/4*i + 1/4*i**r = 0.
-1, 1
Let y(q) be the first derivative of 2*q**3/63 + 5*q**2/21 - 16*q/7 + 290. Factor y(w).
2*(w - 3)*(w + 8)/21
Let j(f) = -f**3 - 15*f**2 + 102*f - 8. Let t be j(5). Let p(m) be the first derivative of 0*m**t + 1/8*m**3 - 3/32*m**4 - 2 + 0*m. Factor p(b).
-3*b**2*(b - 1)/8
Let d(l) be the first derivative of 2*l**6/3 + 124*l**5/5 + 283*l**4 + 2692*l**3/3 + 1232*l**2 + 784*l - 56. Factor d(b).
4*(b + 1)**3*(b + 14)**2
Let h = 11 - -61. Suppose 5*m - 35 = -p + 45, 25 = 5*p. Determine s, given that -75*s**2 + 3 - m - 12*s + h*s**2 = 0.
-2
Let t(h) be the first derivative of h**5 - 105*h**4/4 + 165*h**3 - 675*h**2/2 + 452. Factor t(a).
5*a*(a - 15)*(a - 3)**2
Suppose 45/2 + 3/4*x - 3/4*x**2 = 0. What is x?
-5, 6
Let d(l) = 2*l**3 + 82*l**2 + 5*l + 205. Let a be d(-41). Suppose 2/3*p**3 + a + 0*p + 2/3*p**2 - 4/3*p**4 = 0. What is p?
-1/2, 0, 1
Find w, given that -18/5 - 3/5*w**2 + 3*w = 0.
2, 3
Let z(h) = -h**3 + 5*h**2 - 3*h - 1. Let f be z(4). Find c, given that c**f + 3*c**3 - 4*c**2 + 8*c**3 - 8*c = 0.
-2/3, 0, 1
Let s(p) be the first derivative of -2*p**5 + 109*p**4/2 + 84*p**3/5 - 356*p**2/5 + 176*p/5 + 6. Find z, given that s(z) = 0.
-1, 2/5, 22
Let q = 190 + -185. Let v(f) be the second derivative of 9*f - 1/14*f**7 + 3/2*f**3 + 1/2*f**4 + 3/2*f**2 + 0 - 3/10*f**q - 3/10*f**6. Solve v(l) = 0 for l.
-1, 1
Let h(p) be the third derivative of -p**7/105 - p**6/10 - p**5/10 + 5*p**4/6 + 42*p**2. Factor h(y).
-2*y*(y - 1)*(y + 2)*(y + 5)
Let o = -25/12 - -127/60. Let d(n) be the third derivative of 0*n**3 + 0*n**4 + 0*n + o*n**5 + 0*n**6 - 1/105*n**7 + n**2 + 0. Factor d(q).
-2*q**2*(q - 1)*(q + 1)
Suppose 65*y = 101*y - 180. Let p(c) be the second derivative of 0 - 96/5*c**2 - 24/5*c**3 - 3/100*c**y - 3/5*c**4 - 4*c. Factor p(t).
-3*(t + 4)**3/5
Let t be 13*4*3/36 + 14 + -18. Solve 0 + 2/3*m - t*m**3 + 1/3*m**2 = 0.
-1, 0, 2
Let d(o) = o + 6. Let j be d(-4). Determine w, given that 6*w**3 - 4*w**2 + 15*w**4 - 17*w**4 + j*w**3 - 2*w**2 = 0.
0, 1, 3
Let t = 547 - 547. Let u = 4 + -2. Determine b, given that -2/13 + 2/13*b**u + t*b = 0.
-1, 1
Let j(p) be the second derivative of -4*p + 0 + 4/15*p**6 - 2/3*p**4 + 0*p**2 - 1/5*p**5 + 2/21*p**7 + 0*p**3. Factor j(c).
4*c**2*(c - 1)*(c + 1)*(c + 2)
Factor -48/7 + 4/7*t**2 - 4/7*t.
4*(t - 4)*(t + 3)/7
Suppose 0*h + 3*h + k + 35 = 0, 3*h = -4*k - 23. Let c be (-26)/(-6) + h/39. Factor -1/5*a**2 + 3/5*a**c - 2/5 - a**3 + a.
(a - 1)**2*(a + 1)*(3*a - 2)/5
Let 2400 + 9*t**3 - 1140*t - 2817*t**2 - 300*t + 2943*t**2 - 12*t**3 = 0. What is t?
2, 20
Let v(g) = -7*g**3 + 15*g**2 - 24*g + 16. Let k(f) = 30*f**2 - 18*f - 30*f - 20*f**3 + 33 + 5*f**3. Let i = 159 - 155. Let l(r) = i*k(r) - 9*v(r). Factor l(y).
3*(y - 2)**2*(y - 1)
Let g(o) be the first derivative of -o**4/14 - 6*o**3/7 - 11*o**2/7 + 6*o + 664. Let g(m) = 0. Calculate m.
-7, -3, 1
Solve -6 + 5 - 25*d + 19 - 3*d**2 = 0 for d.
-9, 2/3
Let c(k) = -k**3 + 11*k**2 - 5*k - 12. Let s be c(9). Let h = 107 - s. Let h*f**3 + 0 + 2*f**4 + 0*f + 1/2*f**2 = 0. What is f?
-1/2, 0
Let v(q) = -q**3 - 7*q**2 - 7*q - 6. Let x be v(-6). Let u be (0 - -1) + (-24)/32. Solve u*y**3 + y + x - y**2 = 0 for y.
0, 2
Let j(o) = -11*o**4 - 35*o**3 - 396*o**2 - 911*o - 581. Let b(p) = -9*p**4 - 36*p**3 - 396*p**2 - 912*p - 579. Let f(d) = 7*b(d) - 6*j(d). Factor f(g).
3*(g - 21)*(g + 1)*(g + 3)**2
Let v(c) be the second derivative of -2*c**5/45 + 29*c**4/54 - 47*c**3/27 + 10*c**2/9 - c - 261. Factor v(r).
-2*(r - 5)*(r - 2)*(4*r - 1)/9
Let x be 31/((-899)/(-87)) - 87/30. Suppose 1/10*c**2 - x*c - 1/5 = 0. Calculate c.
-1, 2
Let y be (-6*7/(-84))/(24/9). Let r(n) be the first derivative of -y*n**4 + 1/4*n**2 + 1/24*n**6 + 0*n - 9 + 1/20*n**5 - 1/12*n**3. Factor r(m).
m*(m - 1)**2*(m + 1)*(m + 2)/4
Let l be ((-90)/(-7))/(18/168). What is q in -5*q**2 + 12*q**2 + 48*q**2 + 20 - l*q = 0?
2/11, 2
Factor 43*l + 112*l**3 - 41*l**2 - 47*l**2 + 16*l**5 - 38*l**4 - 4 - 11*l - 66*l**4 + 36*l**4.
4*(