8/(-315). Factor 96/5*s - n*s**2 + 4/5*s**3 - 64/5.
4*(s - 4)**2*(s - 1)/5
Let n(c) be the second derivative of -2*c**6/15 - 2*c**5/5 + 4*c**3/3 + 2*c**2 - 23*c. Factor n(r).
-4*(r - 1)*(r + 1)**3
Solve -20/13*y + 2/13*y**2 + 16/13 + 2/13*y**3 = 0.
-4, 1, 2
Let i(f) be the first derivative of -f**5/100 + f**4/20 + 3*f**3/10 + f**2/2 - 13. Let a(m) be the second derivative of i(m). Factor a(d).
-3*(d - 3)*(d + 1)/5
Determine a so that 0 + 12/11*a**2 - 2/11*a**3 + 54/11*a = 0.
-3, 0, 9
Let u(o) be the second derivative of 2*o**6/15 - 133*o**5/20 - 81*o**4/4 - 71*o**3/6 + 35*o**2/2 - 215*o. Determine l so that u(l) = 0.
-1, 1/4, 35
Let u = -138 + 24. Let q = 114 + u. Factor 4/7*z**5 + q*z + 0*z**3 + 0 + 0*z**2 + 2/7*z**4.
2*z**4*(2*z + 1)/7
Let k(u) be the third derivative of -u**6/300 - u**5/150 - 44*u**2 + 2*u. Determine j, given that k(j) = 0.
-1, 0
Let d be (-5)/(-10)*0 + (-20)/(-165). Let m(a) be the second derivative of 1/66*a**4 + 6*a + 0 + d*a**3 + 4/11*a**2. Factor m(o).
2*(o + 2)**2/11
Suppose -y = -1 - 1. Factor -57 + 3*q + 57 - 3*q**y.
-3*q*(q - 1)
Let n(k) be the third derivative of -k**7/490 + 41*k**6/140 - 81*k**5/5 + 10935*k**4/28 - 19683*k**3/14 - 128*k**2. Let n(v) = 0. What is v?
1, 27
Let i(s) be the first derivative of -s**4/20 + 2*s**3/15 + 7*s**2/10 + 4*s/5 - 89. Factor i(w).
-(w - 4)*(w + 1)**2/5
Let p = -913 - -1293. Find t such that -380 + p + 4*t**3 = 0.
0
Factor 0*z + 0 + 968/5*z**2 - 1056/5*z**3 - 2/5*z**5 + 18*z**4.
-2*z**2*(z - 22)**2*(z - 1)/5
Suppose 4*m + 16 = 8*m. Factor 16*l - m*l**2 - 64 + 22*l - 6*l.
-4*(l - 4)**2
Suppose 0 = -5*h + 5*w + 15 + 5, -h - 5*w = -4. Suppose 4*f**3 - h*f + 4/3*f**2 - 4/3 = 0. What is f?
-1, -1/3, 1
Let d(y) be the first derivative of -2*y**3/39 - 2*y**2 + 54*y/13 + 50. Factor d(f).
-2*(f - 1)*(f + 27)/13
Suppose -1060 = -259*d - 59*d + 53*d. Factor 10/3*p**d + 2/15*p**5 + 172/3*p**2 + 76/3*p**3 + 242/15 + 154/3*p.
2*(p + 1)**3*(p + 11)**2/15
Let m(u) be the first derivative of -4/9*u**3 + 0*u + 0*u**2 + 18. Factor m(y).
-4*y**2/3
Let d(b) be the third derivative of b**2 - 11/30*b**5 + 5/12*b**4 - 1/105*b**7 + 7/60*b**6 + 0*b + 0*b**3 + 0. Factor d(f).
-2*f*(f - 5)*(f - 1)**2
Let f be (6/7)/(2/28 - 0). Suppose -f*y - 20*y + 64 = 0. Solve 1/2*q + 0*q**3 + q**4 - q**y + 0 - 1/2*q**5 = 0.
-1, 0, 1
Let s(u) be the first derivative of -u**9/16632 - u**8/2310 - u**7/924 - u**6/990 + u**3/3 - 11. Let j(y) be the third derivative of s(y). Factor j(n).
-2*n**2*(n + 1)**2*(n + 2)/11
Suppose -4*t**4 - 120/7 - 1004/7*t**2 + 668/7*t + 484/7*t**3 = 0. Calculate t.
2/7, 1, 15
Let p(x) be the first derivative of x**6/8 + 29*x**5/20 - 43*x**4/16 + 11*x**3/12 - 171. Determine o so that p(o) = 0.
-11, 0, 1/3, 1
Suppose 0 = -5*u + 2*q, u - 3*q = q. Let b(t) be the first derivative of 0*t**2 - 1/4*t**6 + 0*t**4 + 7 - 3/10*t**5 + u*t**3 + 0*t. Factor b(p).
-3*p**4*(p + 1)/2
Let x = -2 + -1. Let c be (-1 - -7)/(x - -5). Determine k so that -2*k**2 - k**3 + 2*k**3 + 3*k**c - 2*k**4 = 0.
0, 1
Let x(q) be the third derivative of 0*q + 0 + 16*q**2 - 1/15*q**5 + 1/21*q**4 + 2/21*q**3 + 2/105*q**6. What is u in x(u) = 0?
-1/4, 1
Let v(l) be the second derivative of -l**4/9 + 23*l**3/3 - 34*l**2/3 + 200*l. Determine t so that v(t) = 0.
1/2, 34
Factor -2/9*p**3 - 10/9 - 2/3*p**2 + 2*p.
-2*(p - 1)**2*(p + 5)/9
Let u = 223/146 + -2/73. Let y(b) be the first derivative of 5 + 0*b + b**3 - u*b**2. Suppose y(g) = 0. What is g?
0, 1
Let r(u) be the third derivative of -u**6/420 + u**4/84 + 68*u**2. Let r(f) = 0. Calculate f.
-1, 0, 1
Solve m**5 + 8*m**2 + 2*m**4 - 38602*m**3 + 0*m**4 + 38599*m**3 - 4*m**4 - 4*m = 0.
-2, 0, 1, 2
Let f(s) be the second derivative of s**7/84 - s**6/20 + s**5/40 + s**4/8 - s**3/6 - 81*s. Suppose f(r) = 0. Calculate r.
-1, 0, 1, 2
Suppose 49 = 97*f - 74 - 168. Determine q so that -3/5*q**4 + 0*q + 7/5*q**2 + 1/5*q**5 - 1/5*q**f - 4/5 = 0.
-1, 1, 2
Suppose 5*k = 3*j - 23, 7*j - 4*j - 25 = 4*k. Determine s, given that -4*s - 13*s**3 - s - j*s**2 - 4*s**4 + 3*s = 0.
-2, -1, -1/4, 0
Let u be 3/4*1200/540. Factor -5/3*v + 0 - u*v**2.
-5*v*(v + 1)/3
Let c(b) be the first derivative of -5043*b**3/7 - 246*b**2/7 - 4*b/7 - 457. Factor c(i).
-(123*i + 2)**2/7
Let u(t) be the second derivative of 5/6*t**4 + 37*t + 6*t**2 + 0 + 23/6*t**3 - 1/20*t**5. Factor u(v).
-(v - 12)*(v + 1)**2
Let r(j) be the third derivative of j**10/378000 + j**9/75600 + j**8/50400 + 31*j**5/60 + 29*j**2. Let p(k) be the third derivative of r(k). Factor p(z).
2*z**2*(z + 1)**2/5
Let h(j) be the second derivative of -1/10*j**3 + 1/100*j**5 + 0 + 1/5*j**2 + 2*j + 0*j**4. Factor h(k).
(k - 1)**2*(k + 2)/5
Find b, given that -60*b**2 + 66*b + 48 - 267*b**3 - 28*b**4 + 387*b**3 - 226*b = 0.
-1, 2/7, 2, 3
Suppose -5*u + 60 = -3*k, 0 = 3*k + u + 6 + 36. Let p be ((-40)/k)/(6/9). Factor 3*t**3 - 3*t**2 + p*t**4 - 8*t**3 + 4*t**2.
t**2*(t - 1)*(4*t - 1)
Let y(c) be the first derivative of -c**6/30 + 13*c**5/25 - 3*c**4/5 - 16. Let y(p) = 0. Calculate p.
0, 1, 12
Find q, given that -981/2*q**2 - 1/2*q**4 + 187/6*q**3 + 279/2*q + 961/3 = 0.
-2/3, 1, 31
Suppose 6*q - 3*q - 24 = 0. Factor 2*k + 2*k + 0 - 8 - 4*k**3 + q*k**2.
-4*(k - 2)*(k - 1)*(k + 1)
Let x(p) be the first derivative of -3/2*p**2 + 5/3*p - 9 + 1/12*p**4 + 1/3*p**3. Suppose x(q) = 0. What is q?
-5, 1
Solve -5*v**2 + 2*v**2 + 0*v**2 - 60*v + 27 + 0*v**2 + 36 = 0.
-21, 1
Suppose 5*q = -2*m + 40 - 9, -4*m + q + 7 = 0. Factor 0 + 3/4*b**2 + 0*b - 1/4*b**4 - 1/2*b**m.
-b**2*(b - 1)*(b + 3)/4
Let p(h) be the third derivative of -h**5/4 - 5*h**4/24 + 10*h**3/3 - 36*h**2. Let p(k) = 0. What is k?
-4/3, 1
Let g(j) be the third derivative of -j**6/120 + j**5/12 + 93*j**2. Let g(f) = 0. Calculate f.
0, 5
Let x be (6/212)/((-198)/(-24)). Let v = x - -2326/1749. Factor -8/3*g**2 - 4/3*g**5 + 4*g**4 + 4*g - v - 8/3*g**3.
-4*(g - 1)**4*(g + 1)/3
Let b(f) = -5*f**4 + 2*f**3 + 4*f - 1. Let r(z) = 13*z**4 - 5*z**3 + z**2 - 11*z + 2. Let m(p) = 8*b(p) + 3*r(p). Let m(k) = 0. Calculate k.
-1, 1, 2
Suppose 14*b - 286 = b. Suppose 5*h = -3*f + h + b, -5*f + 3*h = 2. Find x such that 2*x + 1/3*x**f + 3 = 0.
-3
Let d(w) be the second derivative of -w**4/36 + w**3/2 - 7*w**2/3 - 107*w. Suppose d(o) = 0. Calculate o.
2, 7
Find d, given that -52/3 - 50/3*d + 2/3*d**2 = 0.
-1, 26
Let n(t) be the first derivative of t**4/36 + 14*t**3/27 + 43*t**2/18 + 10*t/3 - 197. Factor n(z).
(z + 1)*(z + 3)*(z + 10)/9
Let c(t) = t**3 - 8*t**2 - 24. Let p(x) = x**3 - 8*x**2 + x - 24. Let i(s) = -2*c(s) + 3*p(s). Let b be i(8). Factor b + 1/3*w + 1/3*w**2.
w*(w + 1)/3
Let c = 48 + -46. Factor 12 + 4*w - c*w**2 - 14 + 3 + 5.
-2*(w - 3)*(w + 1)
Factor -5/2*h**2 + 50*h + 105/2.
-5*(h - 21)*(h + 1)/2
Determine u, given that -1/7*u + 1/7*u**3 + 4/7*u**2 - 4/7 = 0.
-4, -1, 1
Factor -10*c + 1/5*c**2 + 125.
(c - 25)**2/5
Let x(q) = q**3 - 7*q**2 - 4*q - 4. Let g be x(8). Suppose 0 = u - 32 + g. Factor -6/17*k**3 + 0 - 2/17*k**u - 2/17*k - 6/17*k**2.
-2*k*(k + 1)**3/17
Let i(o) be the third derivative of o**7/2240 - o**6/160 + 9*o**5/320 - o**4/16 + o**3/2 - 4*o**2. Let r(c) be the first derivative of i(c). Factor r(y).
3*(y - 4)*(y - 1)**2/8
Factor -640*k**3 + 12*k**4 + 21125 + 10125*k**2 + 0*k**4 + 9705*k**2 + 41600*k - 3*k**4 - 4*k**4.
5*(k - 65)**2*(k + 1)**2
Factor 107*j + 3025 + 9*j**2 + 0*j**2 - 8*j**2 + 3*j.
(j + 55)**2
Let n(k) be the second derivative of -k**8/1344 - k**7/504 + 5*k**4/12 + 11*k. Let o(i) be the third derivative of n(i). Factor o(j).
-5*j**2*(j + 1)
Let s(q) be the second derivative of -q**6/120 - q**5/20 + q**4/16 + 7*q**3/12 + q**2 - 5*q + 13. Factor s(u).
-(u - 2)*(u + 1)**2*(u + 4)/4
Let i(t) = -t**5 + 7*t**4 - 2*t**2 - 4*t + 5. Let r(f) = f**4 - f + 1. Let k = 44 - 29. Let n(w) = k*r(w) - 3*i(w). Factor n(c).
3*c*(c - 1)**3*(c + 1)
Let s = -24 + 73/3. Let d(a) be the third derivative of 4*a**2 - 1/12*a**4 + 1/120*a**5 + 0 + 0*a + s*a**3. Factor d(r).
(r - 2)**2/2
Let q(b) be the first derivative of 2*b**5/5 + 637*b**4/8 + 11289*b**3/2 + 603935*b**2/4 + 148877*b/2 + 361. Suppose q(c) = 0. What is c?
-53, -1/4
Let p(t) be the second derivative of t**10/40320 + t**9/20160 - t**8/8960 - t**7/3360 - 11*t**4/12 + 8*t. Let y(u) be the third derivative of p(u). Factor y(k).
3*k**2*(k - 1)*(k + 1)**2