tive of 0 + 241*n**2 - 1/75*n**6 + 0*n**4 + 17/600*n**5 - 1/2100*n**7 + 0*n + 0*n**3. Suppose p(b) = 0. What is b?
-17, 0, 1
Let v(o) be the first derivative of 2*o**3/15 - 646*o**2/5 - 6609. Solve v(y) = 0 for y.
0, 646
Let b(t) be the second derivative of t**6/30 + 179*t**5/20 - t**4/12 - 179*t**3/6 + 7*t - 7. What is o in b(o) = 0?
-179, -1, 0, 1
Let r be (2/(-5))/(54/81 - (-213)/(-225)). Factor r*n + 78/7*n**3 + 18/7*n**4 + 0 - 58/7*n**2.
2*n*(n + 5)*(3*n - 1)**2/7
Let j(g) be the second derivative of 0*g**2 + 89*g - 1/50*g**5 + 0 + 1/30*g**4 + 0*g**3. Factor j(l).
-2*l**2*(l - 1)/5
Suppose 132*v + 54*v - 1132 = -97*v. Let h(p) be the second derivative of p**2 + 0 + 1/40*p**5 + 2*p + 3/4*p**3 + 1/4*p**v. Find f, given that h(f) = 0.
-4, -1
Let g(d) be the second derivative of d**6/10 - 69*d**5/4 - 3*d**4/4 + 347*d**3/2 - 345*d**2 + 6352*d. Factor g(z).
3*(z - 115)*(z - 1)**2*(z + 2)
Let j be (6 + 309)/7*8/6. Find n, given that -j*n + 64*n**3 + 3*n**4 - 32 - 5*n**5 + n**4 + 20*n**4 + n**5 + 8*n**2 = 0.
-1, 1, 8
Let s be ((-4)/(-42))/(5282/87153). Solve s*f - 18/7 - 1/7*f**2 = 0.
2, 9
Let a(t) be the second derivative of 3*t**5/20 - 37*t**4/4 + 83*t**3 - 288*t**2 + 233*t - 2. Suppose a(r) = 0. Calculate r.
2, 3, 32
Let x(h) = -38*h**2 - 34*h + 163. Let d(v) = -27*v**2 - 23*v + 109. Let o(q) = -7*d(q) + 5*x(q). Solve o(l) = 0 for l.
-13, 4
Let o(d) be the third derivative of -d**5/80 - 715*d**4/16 - 511225*d**3/8 + 3199*d**2. Factor o(z).
-3*(z + 715)**2/4
Let l(h) be the second derivative of -2 - 23/4*h**2 - 22*h + 2*h**3 - 1/24*h**4. Factor l(u).
-(u - 23)*(u - 1)/2
Suppose -238*o - 192 = -254*o. Suppose -209 = o*z - 209. Factor -6/7*r**2 - 2/7*r + z.
-2*r*(3*r + 1)/7
Factor -28/3*x**4 - 236/9*x**2 + 2/9*x**5 + 80/3*x**3 + 26/3*x + 0.
2*x*(x - 39)*(x - 1)**3/9
Suppose -61*y = -32*y - 145. Let v be (3/(-63))/(-5*y/75). Factor 1/7*c**2 + 0 - 1/7*c**3 - 1/7*c**4 + v*c.
-c*(c - 1)*(c + 1)**2/7
Let c(p) be the second derivative of -2/3*p**2 + 71*p - 1/10*p**5 + 0 - 1/3*p**3 + 4/9*p**4. Suppose c(u) = 0. What is u?
-1/3, 1, 2
Let p(t) be the third derivative of -t**8/336 + t**7/35 + 43*t**6/120 - t**5/5 - 15*t**4/2 + 764*t**2. Determine s so that p(s) = 0.
-3, 0, 2, 10
Let h(t) be the third derivative of t**8/840 + 3*t**7/560 + t**6/120 + t**5/240 - 7*t**3/3 - t**2 - 3. Let m(u) be the first derivative of h(u). Factor m(g).
g*(g + 1)**2*(4*g + 1)/2
Let u(s) be the first derivative of -5*s**4/8 + 5755*s**3/6 - 2875*s**2/2 - 499. Factor u(d).
-5*d*(d - 1150)*(d - 1)/2
Let m(a) be the first derivative of -a**5/180 - 17*a**4/72 - a**2/2 + 41*a - 188. Let x(q) be the second derivative of m(q). Factor x(z).
-z*(z + 17)/3
Let z(h) be the first derivative of 22 - 1/28*h**4 + 338/7*h - 221/14*h**2 + 4/3*h**3. Factor z(q).
-(q - 13)**2*(q - 2)/7
Let x be (54/8)/(3/16). Suppose 3*z - x = -27. Factor k**4 - k - 9*k**z - k**2 + 17*k**3 - 7*k**3.
k*(k - 1)*(k + 1)**2
Let t(y) be the second derivative of y**6/30 - 9*y**5/10 + 77*y**4/12 - 10*y**3 - 8*y + 18. Suppose t(j) = 0. Calculate j.
0, 1, 5, 12
Let n be (-4 - (2322/(-105) + 4)) + ((-144)/42)/(-12). Factor -n + 84/5*m + 4/5*m**3 - 32/5*m**2.
4*(m - 3)**2*(m - 2)/5
Let o(a) be the third derivative of 2*a**7/21 - 17*a**6/30 + 7*a**5/5 - 11*a**4/6 + 4*a**3/3 + 132*a**2 - 5*a. Suppose o(y) = 0. Calculate y.
2/5, 1
Factor -2430 - 27*b + 1968*b**4 + 1968*b**4 - 25*b**3 + 1976*b**4 - 5911*b**4 + 177*b**2.
(b - 10)*(b - 9)**2*(b + 3)
Suppose 2*m = 4*a + 2, 3*a - 2*m + 4 = -0*m. Determine h so that 3*h**a + 0*h + h + 10*h + 4*h = 0.
-5, 0
Suppose 2*x + 1128 = -2*z, -4*x + 3*z = -0*x + 2284. Let d = x - -570. Factor -2/7*w**3 + 4/7*w**d - 2/7*w + 0.
-2*w*(w - 1)**2/7
Let z(r) = -18*r**5 + 66*r**4 - 76*r**3 + 26*r**2 + 44*r + 7. Let o(t) = -t**5 + t**4 + t**3 - t**2 - 6*t - 1. Let w(q) = 21*o(q) + 3*z(q). Factor w(y).
-3*y*(y - 1)**3*(25*y + 2)
Let n(a) = -7*a**3 + 12*a**2 + 21*a - 44. Suppose 0 = 14*c + 25 - 81. Let q(u) = -8*u**3 + 12*u**2 + 20*u - 48. Let d(w) = c*n(w) - 3*q(w). Factor d(g).
-4*(g - 4)*(g - 1)*(g + 2)
Let f(a) be the first derivative of -a**6/120 - a**5/20 + 3*a**4/8 + 2*a**3/3 + 14*a - 90. Let o(r) be the third derivative of f(r). Factor o(z).
-3*(z - 1)*(z + 3)
Let s = 404538 + -1618149/4. Solve -3/2*c**2 + 0 - s*c - 3/4*c**3 = 0 for c.
-1, 0
Let q(n) = -2*n + 12. Let w be q(6). Suppose -2*j + w*j + j = 0. Solve j*g**4 - 6*g**3 + 12*g + 3*g**4 + 12 - 2*g**4 - 9*g**2 + 2*g**4 = 0 for g.
-1, 2
Let a(w) be the second derivative of -w**6/32 + 21*w**5/80 - 7*w**4/8 + 3*w**3/2 + 25*w**2/2 - 15*w. Let l(c) be the first derivative of a(c). Factor l(o).
-3*(o - 2)*(o - 1)*(5*o - 6)/4
Let z = -128 - -131. Let 4*y**3 - 5*y**3 - 12*y**2 + 5*y**3 - 21*y - 5*y**z - 10 = 0. Calculate y.
-10, -1
Let j(f) = f**2 + 99*f + 440. Let a(r) = -2*r**2 - 297*r - 1330. Let z(p) = 2*a(p) + 7*j(p). Factor z(u).
3*(u + 5)*(u + 28)
Let f(r) be the first derivative of -r**6/3 + 53*r**4/2 - 144*r**3 + 308*r**2 - 288*r - 1641. Solve f(z) = 0.
-9, 1, 2, 4
Let t be (-33 - -32) + 7*1 + -6. Suppose -13*f + 39 = -t*f. Let 8/7*u**2 + 0*u + 0 + 12/7*u**f + 1/7*u**5 + 6/7*u**4 = 0. What is u?
-2, 0
Let h = 426 + -418. Let c(g) = -15*g**2 - 181*g - 262. Let q(s) = 10*s**2 + 120*s + 175. Let a(o) = h*q(o) + 5*c(o). Determine u, given that a(u) = 0.
-9, -2
Let a = 162624 - 162619. What is w in w**2 + 0 - 1/7*w**4 - 2/7*w - 6/7*w**3 + 2/7*w**a = 0?
-2, 0, 1/2, 1
Let d(a) be the first derivative of 2*a**7/105 - 23*a**6/120 + a**5/2 + 3*a**4/8 + 13*a**2/2 + 51. Let h(c) be the second derivative of d(c). Factor h(p).
p*(p - 3)**2*(4*p + 1)
Let c = 11150 + -11127. Let y(i) be the second derivative of -1/60*i**5 + 0 + c*i - 1/12*i**2 + 1/18*i**3 + 0*i**4 + 1/180*i**6. Factor y(g).
(g - 1)**3*(g + 1)/6
Let a = -179 - -184. Suppose a*s = 2*s - 5*p + 6, 5*s - 10 = 3*p. Factor 12/7*x + 0 - 2/7*x**s.
-2*x*(x - 6)/7
Let f(x) be the second derivative of 1/10*x**6 + 89*x - 7/4*x**4 + 0 + 0*x**2 - 3/5*x**5 + 5*x**3. Factor f(z).
3*z*(z - 5)*(z - 1)*(z + 2)
Let k(r) be the first derivative of -r**5 - 25*r**4/4 + 15*r**3 + 405*r**2/2 + 540*r + 229. Suppose k(c) = 0. Calculate c.
-3, 4
Factor 668 + 338*l + 175/4*l**2 + 1/4*l**3.
(l + 4)**2*(l + 167)/4
Determine n, given that 24*n**2 + 1204*n + 275 + 458 - 533 = 0.
-50, -1/6
Let s(p) = 17*p - 728. Let c be s(43). Let l(a) be the first derivative of -4/21*a**c - 4/7*a - 8 - 5/7*a**2. Factor l(y).
-2*(y + 2)*(2*y + 1)/7
Let k(r) = -3*r**3 - 21*r**2 + 17*r + 10. Let a be k(-10). Let y = -5176/7 + a. Determine n, given that 0 + y*n**2 + 8/7*n = 0.
-2, 0
Let r(q) be the second derivative of q**5/50 + 41*q**4/15 + 157*q**3/15 - 48*q**2 - 3525*q. Factor r(g).
2*(g - 1)*(g + 3)*(g + 80)/5
Let w = 25722277/228 - 112816. Let a = w - 7/12. Factor -8/19*b - a*b**3 + 2/19*b**4 + 12/19*b**2 + 2/19.
2*(b - 1)**4/19
Factor -2/7*z**3 + 260/7*z**2 + 0*z + 0.
-2*z**2*(z - 130)/7
Factor 5/2*g**3 - 1365/2 - 2725/2*g - 1355/2*g**2.
5*(g - 273)*(g + 1)**2/2
Let b be (412/(-1854))/((-8)/(-534)) - -15. Suppose b*w**2 - 7/2 - 10/3*w = 0. Calculate w.
-1, 21
Let i(r) be the first derivative of -r**4/24 - 1315*r**3/18 + 2633*r**2/12 - 439*r/2 - 2385. Determine k, given that i(k) = 0.
-1317, 1
Let b(k) be the first derivative of -k**4/16 + 15*k**3/4 - 11*k**2/2 - 523. Factor b(u).
-u*(u - 44)*(u - 1)/4
Let f(h) be the second derivative of 0*h**2 + 1/14*h**4 + 28*h + 0 + 5/7*h**3. Factor f(s).
6*s*(s + 5)/7
Let s(m) be the first derivative of m**5/5 + 19*m**4/4 + 119*m**3/3 + 245*m**2/2 - 1532. Determine c, given that s(c) = 0.
-7, -5, 0
Let t be 12/2 + (1015 - 7)/16. Suppose -150*a = -127*a - t. Factor 1/3*i**4 + 1/3*i**3 - a*i**2 + 11/3*i - 4/3.
(i - 1)**3*(i + 4)/3
Let y(v) = 2*v**2 + 6*v + 6. Let a be y(5). Factor -66*q**3 - 12 - 64*q - 68*q**2 - 36*q**3 + a*q**3.
-4*(q + 1)*(q + 3)*(4*q + 1)
Let c(h) = -h**2 + h - 1. Suppose -4 = -2*o + 4*p, -4*p = -4*o + 9 - 1. Let g(i) = 4*i**3 - 18*i**2 + 18*i - 2. Let j(f) = o*c(f) - g(f). Factor j(z).
-4*z*(z - 2)**2
Let b(f) be the third derivative of -7/12*f**4 + 0 + 1/168*f**8 - 12*f**2 - 2*f - 1/21*f**7 + f**3 + 1/10*f**6 + 1/15*f**5. Determine k, given that b(k) = 0.
-1, 1, 3
Let s be 2 - 36/19 - 369/2736*-2. Factor 3/8*y**2 - s + 1/8*y**3 - 1/8*y.
(y - 1)*(y + 1)*(y + 3)/8
Let r(h) 