 1/108*i**4. Factor c(m).
m*(5*m + 2)/9
Let c(h) be the first derivative of -1/80*h**6 + 0*h**3 - 9 + 0*h + 2*h**2 + 1/20*h**5 - 1/16*h**4. Let n(g) be the second derivative of c(g). Solve n(b) = 0.
0, 1
Let n = -1188 + 1188. Let u(g) be the second derivative of 0*g**5 + g + n + 1/6*g**6 + 0*g**2 - 5/12*g**4 + 0*g**3. Determine i, given that u(i) = 0.
-1, 0, 1
Solve -25*q**2 - 4*q**3 + 5*q**4 - 16*q**3 - 14*q + 14*q = 0.
-1, 0, 5
Suppose 26*d = 18*d. Let l(r) be the third derivative of -r**2 + 0*r**3 + d*r - 1/180*r**5 + 1/72*r**4 + 0. Let l(a) = 0. What is a?
0, 1
Let r(p) = -p**3 + 45. Let l be r(0). Suppose -5*t = -2*h, l - 12 = 4*t + 5*h. Factor -6*o**2 + 4*o**2 + 3*o**t + o**4 - 2*o**2.
o**2*(o - 1)*(o + 1)
Let o = -14 - -19. Suppose 0 = -5*v - 5*i + 17 - 2, -5 = -o*v + 5*i. Solve -2*r**2 - 1 - 4*r**2 - 4*r + 0*r**v - 12*r**3 - r**4 + 8*r**3 = 0.
-1
Let i(c) = 76*c**2 - 1137*c + 4096. Let y(n) = 77*n**2 - 1140*n + 4096. Let k(f) = -4*i(f) + 5*y(f). Solve k(l) = 0.
64/9
Let c(z) be the first derivative of -4/3*z - 1/9*z**3 + 2/3*z**2 - 3. Factor c(i).
-(i - 2)**2/3
Let u(l) be the second derivative of l**2 + 1/33*l**3 - l - 1/66*l**4 + 0 + 1/330*l**5. Let d(b) be the first derivative of u(b). Factor d(s).
2*(s - 1)**2/11
Let x(l) = 2*l**2 - 1. Let k(u) = 6*u**2 + 180*u - 4054. Let b(q) = k(q) - 4*x(q). Factor b(a).
-2*(a - 45)**2
Let t(j) be the third derivative of j**6/120 - j**5/60 - j**3/3 - 6*j**2. Let z be t(2). Solve -z - 5*n**2 + 4*n**2 + 15*n - 5*n**2 - 13*n**2 - 36*n**3 = 0.
-1, 2/9, 1/4
Suppose 3*a + 0*a - 17 = 4*h, -6 = 3*h. Find t such that 5*t**a - 2*t**2 + t**5 + 23*t**4 + 0*t**3 - 27*t**4 = 0.
0, 1, 2
Let i(a) be the third derivative of -a**5/420 - 3*a**4/28 - 27*a**3/14 - 74*a**2. Factor i(u).
-(u + 9)**2/7
Let o(a) be the first derivative of a**4/18 - 20*a**3/27 + 4*a**2/3 + 16*a - 73. Factor o(r).
2*(r - 6)**2*(r + 2)/9
Suppose -9*p - 25 = -16. Let b be p/5 - (-18)/30. Factor 2/5 - 4/5*o**3 + 2/5*o**5 - 4/5*o**2 + b*o + 2/5*o**4.
2*(o - 1)**2*(o + 1)**3/5
Let j = 23162/7 + -3308. Let -10/7*a**2 + j*a**3 + 2/7*a + 2/7 = 0. Calculate a.
-1/3, 1
Let l(u) be the third derivative of u**6/30 + u**5/15 - 2*u**4/3 - 8*u**3/3 - 3*u**2 + 3*u. Solve l(b) = 0.
-2, -1, 2
Let x(d) = 4*d**2 - 16*d - 17. Let y be x(5). Suppose -4 = 5*r - 7*r. Let 0 + 5/4*b**r + b**y + 1/2*b + 1/4*b**4 = 0. Calculate b.
-2, -1, 0
Let b = -20735/2 - -10368. Find i such that i**2 + 0 + 1/2*i**3 + b*i = 0.
-1, 0
Factor -1/2*t**4 - 13 - 13/2*t**3 + 37/2*t + 3/2*t**2.
-(t - 1)**2*(t + 2)*(t + 13)/2
Suppose 0 = -10*r + 12*r + 6, 2*r = -o - 4. Let i be 2 + -4 + (-33)/(-6). Factor 3/2*j - 1 + 6*j**o + i*j**3.
(j + 1)**2*(7*j - 2)/2
Suppose 0 = 174*n - 69*n - 228 - 192. Factor -30/17*f + 60/17*f**3 + 100/17*f**2 + 98/17*f**5 - 18/17 - 210/17*f**n.
2*(f - 1)**3*(7*f + 3)**2/17
Let q(h) be the first derivative of 0*h + 0*h**2 + 17 - 2/5*h**3 - 3/20*h**4. Determine i so that q(i) = 0.
-2, 0
Let 33/2 - 3/2*o**2 + 15*o = 0. Calculate o.
-1, 11
Factor 0 - 4/9*s**2 + 46/9*s**3 + 0*s.
2*s**2*(23*s - 2)/9
Suppose -47 = -3*k - 2*k - o, -k - 3*o = -1. Suppose u**4 - 20*u**3 - 3*u**4 - 9*u**2 + u**2 - k*u**4 = 0. Calculate u.
-1, -2/3, 0
Let c(r) = -r**2 + 6*r - 4. Let m be c(3). Suppose 0*f = -m*f + 60. Factor 4 + f*s**3 + 3*s**5 - 8*s**2 - 13*s**2 - 10 - 15*s + 15*s**2 + 12*s**4.
3*(s - 1)*(s + 1)**3*(s + 2)
Solve -2*c**2 + 6*c**2 + 5*c + 3*c**3 + 5*c**2 + c = 0 for c.
-2, -1, 0
Let i be 56/(-7)*7/14. Let w be (34/(-14) + 3)/(i/(-14)). Let -2/7*v + 1/7 + 1/7*v**w = 0. What is v?
1
Let o(n) be the third derivative of -n**8/1512 - 4*n**7/945 + 7*n**5/135 + 17*n**4/108 + 2*n**3/9 - 4*n**2 - n. What is d in o(d) = 0?
-3, -1, 2
Let g = 14635/124 - -348/31. Let w = -129 + g. Determine k, given that 0*k + 0*k**2 + w*k**4 + 0 + 0*k**3 = 0.
0
Let m(o) = 3*o**5 - 42*o**3 + 51*o**2 + 36*o - 48. Let v(i) = -3*i**5 + 41*i**3 - 50*i**2 - 36*i + 48. Let h(t) = -2*m(t) - 3*v(t). Let h(b) = 0. Calculate b.
-4, -1, 1, 2
Let u be 8 + (25 + -13)*(-4)/6. Suppose 3/8*a**3 + 0 + 3/8*a**4 + 0*a + u*a**2 = 0. Calculate a.
-1, 0
Let k(f) = 7*f**2 - 8*f + 1. Let d be (-1)/(-1 + (-125)/(-120)). Let p(u) = -u**2 + u. Let x(s) = d*p(s) - 3*k(s). Factor x(y).
3*(y - 1)*(y + 1)
Suppose 7*t - 67 = 129. Solve 3*s**2 + 131 + t*s - 13*s - 149 = 0 for s.
-6, 1
Let q(s) = 42*s - 96. Let l(a) = 22*a - 48. Let o(v) = -11*l(v) + 6*q(v). Let k be o(5). Determine r, given that 0 - 4/3*r**3 - 2/3*r - k*r**2 = 0.
-1, -1/2, 0
Let w(x) be the third derivative of x**8/1176 + x**7/735 - x**6/140 - x**5/210 + x**4/42 - 69*x**2 + 1. Let w(z) = 0. Calculate z.
-2, -1, 0, 1
Factor -10*a**3 + 18*a - 21*a**2 - 2*a**4 - 20*a**2 - 16*a**2 + 51*a**2.
-2*a*(a - 1)*(a + 3)**2
Let d(u) = u**2 + u. Let i(a) = 5*a**3 - 5*a**2 - 70*a - 60. Let r(v) = 30*d(v) + i(v). Solve r(o) = 0 for o.
-6, -1, 2
Let y(f) be the first derivative of f**4 - 6*f**2 - 8*f + 341. Find k, given that y(k) = 0.
-1, 2
Let i(p) be the first derivative of 7*p**5 + 18*p**4 + 13*p**3 + p**2 + 75. Suppose i(w) = 0. Calculate w.
-1, -2/35, 0
Let t(q) be the second derivative of -q**5/40 + 13*q**4/8 - 19*q**3/6 - 32*q. What is v in t(v) = 0?
0, 1, 38
Let m be 4/(-8) - (-10)/12. Let j(w) = 203*w - 1827. Let a be j(9). Determine h so that a - m*h**3 + 0*h + 1/3*h**2 = 0.
0, 1
Let m = 17 + -17. Let u(c) = -7 + m - c + 8. Let y(q) = q**4 - q**3 + 5*q - 5. Let t(b) = 5*u(b) + y(b). Find n such that t(n) = 0.
0, 1
Let i(z) = 3*z**3 + z. Let r be i(1). Suppose -5*p + 3*b + 20 = 2*b, 0 = p + b + 2. Factor -g**3 + 6*g**2 + p*g + 0*g**3 + r*g**3.
3*g*(g + 1)**2
Let z(p) be the third derivative of -p**5/15 + p**4/2 - 4*p**3/3 - 75*p**2. Factor z(x).
-4*(x - 2)*(x - 1)
Suppose -221*b**2 - 5184 + 461206*b - 515*b**2 - 465814*b + 128*b**3 - 4*b**4 = 0. What is b?
-2, 18
Suppose -552*k + 565*k - 2 - 7*k**2 + 0*k**2 - 4 = 0. Calculate k.
6/7, 1
Let c = 5 + -3. Let f be 1 + 0 - 7/(7/(-3)). Let f*j**3 - 18*j + j**3 + 10*j**c + 18*j = 0. What is j?
-2, 0
Suppose -4*v**2 + 206*v**3 - 408*v**3 + v**4 + v**4 + 204*v**3 = 0. Calculate v.
-2, 0, 1
Let c be 222*1/(-16) + 14. Factor 0 - 3/8*q**2 + 1/4*q + c*q**3.
q*(q - 2)*(q - 1)/8
Suppose 8 + 6 = 7*a. Let y(h) be the first derivative of 0*h + 1 + 0*h**a + 2/9*h**3. Solve y(j) = 0.
0
Let -w**3 - 4/5 + 1/5*w**4 - 1/5*w**2 + 1/5*w**5 + 8/5*w = 0. What is w?
-2, 1
Let d(c) be the third derivative of -c**8/672 - c**7/120 - c**6/120 + c**5/60 - 56*c**2. Factor d(t).
-t**2*(t + 2)**2*(2*t - 1)/4
Let h = 132 - 130. Let q(c) be the first derivative of -1/8*c**4 + 1/3*c**3 + 0*c - 3 - 1/4*c**h. Factor q(f).
-f*(f - 1)**2/2
Suppose -55/2*i + 25 + 5/2*i**2 = 0. Calculate i.
1, 10
Factor 49*c**2 - 17*c**4 - 6*c**3 + 48 - 8*c**4 + 32*c**4 - 10*c**4 - 4*c**2 + 96*c.
-3*(c - 4)*(c + 1)**2*(c + 4)
Suppose -152 = -3*y - 146. Let s = -3 - -6. Factor 5*z**3 - 3*z**s + 4*z - 7*z**2 + 13*z**y.
2*z*(z + 1)*(z + 2)
Let j be 177*(-6)/360 + 3. Let z(v) be the second derivative of 1/2*v**3 - 6*v + 0 + 1/2*v**2 + j*v**5 + 1/4*v**4. Factor z(n).
(n + 1)**3
Find s, given that 2*s**2 + 17/2*s - 3 - 3/2*s**3 = 0.
-2, 1/3, 3
Let w(k) be the first derivative of 5*k**4/4 - 10*k**3/3 - 7*k - 19. Let h(q) = 2*q**3 - 5*q**2 - 3. Let b(i) = 14*h(i) - 6*w(i). Factor b(m).
-2*m**2*(m + 5)
Let v(g) = g**2 - 2*g - 1. Let d be (-6)/30 + 16/5. Let b be v(d). What is x in -1/2*x**5 + 0*x**b + 0*x**4 + 1/2*x**3 + 0*x + 0 = 0?
-1, 0, 1
Let q(n) = n**2 - n - 9. Let a be q(4). Factor -t**3 - 2*t**2 + t**3 + t**a.
t**2*(t - 2)
Let g be (18/(-42))/(-4 - (-4)/(32/20)). What is b in 4/7*b + 2/7*b**2 + g = 0?
-1
Let s(b) = 39*b**2 + 1086*b + 20511. Let p(h) = -8*h**2 - 217*h - 4102. Let y(v) = -24*p(v) - 5*s(v). Let y(o) = 0. Calculate o.
-37
Let n(y) be the third derivative of y**7/840 - 7*y**6/480 + y**5/30 + y**4/6 + 66*y**2. Factor n(u).
u*(u - 4)**2*(u + 1)/4
Suppose h + 4*h - 30 = 0. Let x be h/(-39) - (-558)/78. Find q, given that -q**2 - 4 + x*q**2 + q**3 - 4*q**3 + q**2 = 0.
-2/3, 1, 2
Let z be (0 + (-4)/(-22))/((-42)/(-22)). Let 0*y**3 + 0 - 8/21*y**2 + z*y**4 + 0*y = 0. Calculate y.
-2, 0, 2
Let c(d) be the third derivative of 1/16*d**4 + 0*d - 1/160*d**5 - 11*d**2 + 0 - 1/4*d**3. Determine g so that c(g) = 0.
2
Suppose 4*m - 5*m = -23. Suppose 0 = -5*p + c + 55, -4*c = -4*p + c 