)*(u + 7)/4
Let f(q) be the first derivative of -q**6/2 + 183*q**5/5 - 2697*q**4/4 - 961*q**3 + 2002. Factor f(v).
-3*v**2*(v - 31)**2*(v + 1)
Let j(f) be the first derivative of -1/120*f**5 + 1/36*f**3 - 1/12*f**2 + 7 + 15*f + 1/72*f**4. Let l(a) be the first derivative of j(a). Factor l(y).
-(y - 1)**2*(y + 1)/6
Let d(t) = -12*t**3 + 6 + 13*t**2 + 8*t - 14*t**3 + 40*t**3 - 13*t**3. Let w(r) = -r**2 + r. Let x(s) = d(s) + 5*w(s). What is i in x(i) = 0?
-6, -1
Let y(t) = -23*t**2 - 5471*t - 3753806. Let r(q) = -131*q**2 - 32829*q - 22522834. Let z(n) = -6*r(n) + 34*y(n). Suppose z(k) = 0. What is k?
-1370
Suppose -1/5*v**3 + 0 - 10*v + 3*v**2 = 0. What is v?
0, 5, 10
Let x = 404/197 + -611/394. Factor x*k**3 + 1/2*k**2 - 1/2*k - 1/2*k**4 + 0.
-k*(k - 1)**2*(k + 1)/2
Let s = 324 + -292. Let 20*q**4 + 12*q**2 + 28*q + 15*q + s*q**4 - 92*q**3 - 8*q**5 - 7*q = 0. Calculate q.
-1/2, 0, 1, 3
Let g be -15 - (-20 - 51/68*-4). Suppose 2*h - 2/3*h**3 + 4/3*h**g + 0 = 0. What is h?
-1, 0, 3
Let z(m) be the first derivative of m**5/5 - 5*m**4/4 - 6*m**3 + 36*m**2 + 452. Let z(q) = 0. Calculate q.
-4, 0, 3, 6
Factor 646*x**5 - 17*x**3 - 364*x**5 - 281*x**5 + 16*x**4.
x**3*(x - 1)*(x + 17)
Let c(q) = -273*q + 3549. Let z be c(13). Let r(x) be the first derivative of 28 + z*x - 5/3*x**3 - 1/2*x**2 - x**4. Determine g so that r(g) = 0.
-1, -1/4, 0
Let v(y) be the second derivative of 51*y**5/160 + 23*y**4/32 + 3*y**3/8 - 500*y + 5. Suppose v(b) = 0. What is b?
-1, -6/17, 0
Let m(n) be the second derivative of -n**7/735 + n**6/420 + n**5/210 - n**4/84 + 47*n**2/2 + 68*n. Let x(a) be the first derivative of m(a). Factor x(k).
-2*k*(k - 1)**2*(k + 1)/7
Let l = 664 + -658. Determine f, given that f**2 - 5*f**2 + 70 + 59*f - f**2 + l*f = 0.
-1, 14
Let h(t) be the third derivative of -t**8/63 + 304*t**7/315 + t**6/30 - 23*t**5/9 + 19*t**4/9 - 276*t**2. Find f such that h(f) = 0.
-1, 0, 1/2, 38
Let v(l) be the second derivative of l**6/80 - 33*l**5/160 + 19*l**4/32 - 9*l**3/16 + 3732*l. Factor v(s).
3*s*(s - 9)*(s - 1)**2/8
Suppose -14 = -3*g + w, g - 6*w = -7*w - 6. Let d(l) be the third derivative of -4*l**g + 1/4*l**4 + 0*l - 4/3*l**3 + 0 - 1/60*l**5. Factor d(r).
-(r - 4)*(r - 2)
Let i be (20/(-12))/((-3)/9). Let b be (-38)/(-12) + ((-248)/48)/31. Find l such that b*l**2 - 8 - 37*l + 27*l - i*l**2 = 0.
-4, -1
Let h = 173204 - 866006/5. Suppose -h*g**2 + 8/5*g + 4/5*g**3 + 0 + 2/5*g**4 = 0. Calculate g.
-4, 0, 1
Let b(n) be the second derivative of -1/25*n**6 + 0 + 0*n**3 - 1/30*n**4 + 0*n**2 + 1/105*n**7 + n + 3/50*n**5. Factor b(u).
2*u**2*(u - 1)**3/5
Suppose -16*b - 67 = 45. Let a(d) = -3*d - 11. Let k be a(b). Factor -18 + 75*z**2 - k*z - 5*z - 72*z**2.
3*(z - 6)*(z + 1)
Determine d so that 56/5*d**2 + 0 + 2/5*d**3 + 0*d = 0.
-28, 0
Let a(k) = k**3 + 4*k**2 - 16*k - 21. Let z be a(-6). Let n be (-99)/77 + (z - 0). Solve -27/7*l**2 + 57/7*l**3 - 48/7*l + 30/7*l**4 - n = 0 for l.
-2, -1/2, -2/5, 1
Let b(n) be the first derivative of -n**8/160 + 9*n**7/560 + n**6/20 - n**5/20 + 4*n**3/3 - 19. Let q(m) be the third derivative of b(m). Solve q(c) = 0 for c.
-1, 0, 2/7, 2
Suppose 2*k - 2*h - 952 = 0, -3*h + 3 = -3. Find j, given that -100*j - 45*j**5 + 2 - 370*j**4 + 1253*j**3 - 2 - k*j**3 - 260*j**2 = 0.
-10, -2/9, 0, 1
Let v(p) be the third derivative of p**7/840 - p**6/240 - p**5/30 + 3*p**4/16 - 3*p**3/8 - 662*p**2 + p. Factor v(j).
(j - 3)*(j - 1)**2*(j + 3)/4
Suppose 23190*s = 23763*s. Factor 0 + s*l + 0*l**2 - 1/3*l**5 - 2/3*l**4 + 0*l**3.
-l**4*(l + 2)/3
What is m in 2217656 + 1592*m + 2/7*m**2 = 0?
-2786
Determine k so that 0 - 84/5*k + 1/5*k**3 + k**2 = 0.
-12, 0, 7
Suppose -3*d - 26*z = -32*z + 6, 12 = 4*z. Find g, given that 246/11*g + 112*g**3 + 288/11*g**d - 90*g**2 - 20/11 = 0.
-5, 2/9, 1/4
Let p(i) = -i**2 + i + 1. Let k(w) = -3*w**2 + 4. Let j(q) = k(q) - 6*p(q). Let y(m) = -8*m**2 + 13*m + 3. Let r(n) = 15*j(n) + 6*y(n). Factor r(g).
-3*(g + 2)**2
Let k(o) be the second derivative of -o + 3/10*o**5 + 65 + 23/6*o**4 + 40/3*o**3 - 16*o**2. Factor k(q).
2*(q + 4)**2*(3*q - 1)
Let a(x) = x**2 - 7*x - 16. Let v be a(9). Suppose v*f + 3*f = 25. Factor f*k + 0*k - 26*k**2 + 6*k**2 + 9*k**4 + 11*k**4 - 5*k**3.
5*k*(k - 1)*(k + 1)*(4*k - 1)
Let c(x) = -x**3 + 16*x**2 - 54*x + 4. Let z be c(12). Let t be 2/3 + -2 + z/(-24). Factor -3/2*i**3 - 9/2*i**2 - t - 9/2*i.
-3*(i + 1)**3/2
Determine k so that 572/3*k**2 + 64/3*k**3 + 2/3*k**4 + 150 + 320*k = 0.
-15, -1
Let v(x) = 539*x + 32882. Let l be v(-61). Let t = 6350/23 - 276. Factor 0*b + t*b**2 - 4/23*b**l + 2/23*b**4 + 0.
2*b**2*(b - 1)**2/23
Let u(z) be the first derivative of 7*z**4/4 + 13*z**3/3 + 5*z**2 - 56. Let j(a) = 190*a**3 + 350*a**2 + 270*a. Let q(b) = -2*j(b) + 55*u(b). Factor q(l).
5*l*(l + 1)*(l + 2)
Let l be 135 - 144 - 606/(-66). Factor l*h**2 + 24/11 - 14/11*h.
2*(h - 4)*(h - 3)/11
Let s(x) be the third derivative of 0*x**4 - 2*x - 16/1155*x**7 + 0 - 1/264*x**8 + 0*x**3 + 1/55*x**5 + 17/660*x**6 + 41*x**2. Solve s(d) = 0.
-3, -2/7, 0, 1
Let c be (-2*1/22)/((-1219)/40227). Determine u so that -2/11*u**c - 2/11*u**2 + 2/11 + 2/11*u = 0.
-1, 1
Suppose 3*s = -k - 12, 5*k - 5*s + 3*s - 8 = 0. Find y such that 1/4*y**5 + 0*y**2 + 0 + 0*y**4 - 1/4*y**3 + k*y = 0.
-1, 0, 1
Determine g, given that -3904576/5 - 4/5*g**2 + 7904/5*g = 0.
988
Let c(j) be the second derivative of 8/3*j**3 - 1/30*j**5 + 0 + 11*j**2 + 19*j - 7/12*j**4. Let g(m) be the first derivative of c(m). Factor g(h).
-2*(h - 1)*(h + 8)
Let g(d) be the first derivative of -d**6/240 + d**5/20 + 3*d**2/2 - 11*d + 15. Let l(z) be the second derivative of g(z). Suppose l(o) = 0. What is o?
0, 6
Let u(i) be the second derivative of -i**5/15 + 17*i**4/9 + 4*i**3 - 6037*i. What is z in u(z) = 0?
-1, 0, 18
Let a(s) be the second derivative of -3*s - 14 + 0*s**2 - 1/95*s**6 + 0*s**3 - 2/19*s**4 - 2/19*s**5. Factor a(j).
-2*j**2*(j + 6)*(3*j + 2)/19
Let n(v) be the third derivative of -v**8/60480 + 7*v**6/6480 + v**5/180 - v**4/2 - v**3/6 + 21*v**2. Let u(c) be the second derivative of n(c). Factor u(b).
-(b - 3)*(b + 1)*(b + 2)/9
Let z = 109 - 107. Let n(p) be the first derivative of -p**3 - p**3 - 38 + 2*p**z + 2*p**2 - 2*p + 36. Factor n(r).
-2*(r - 1)*(3*r - 1)
Let r(w) = 2*w**4 - 5*w**3 + 3*w**2 + w + 1. Let o(y) = 33*y**4 - 152*y**3 + 561*y**2 - 591*y - 1167. Let i(q) = o(q) - 17*r(q). Suppose i(h) = 0. Calculate h.
-74, -1, 4
Let p(x) = -x**2 + 15*x + 12. Let a be p(15). Suppose 3*d = c + a, -2*d + 4*c + 0*c = -18. Factor -5 + 5 + w**3 - 3*w + 0*w**d + 2.
(w - 1)**2*(w + 2)
Let d = -25 - -27. Let i be -8*(-91)/104 + (-184)/48 + -3. Factor 0*s - i*s**d + 1/6.
-(s - 1)*(s + 1)/6
Let k be (-24 + (-33097)/(-1380))/((-3)/72). Factor 72/5 - 8*m + k*m**2.
2*(m - 18)*(m - 2)/5
Let u = -224 + 224. Factor q**3 + 9*q**3 - 8 - 12*q**2 + 38*q**2 + u*q**3 + 8*q.
2*(q + 1)*(q + 2)*(5*q - 2)
Factor -58*j**2 - 447 + 5*j**3 - 1553 + 226*j - 62*j**2 + 261*j + 413*j.
5*(j - 10)**2*(j - 4)
Let i(z) be the first derivative of 2*z**5/5 - 31*z**4/2 + 206*z**3/3 + 135*z**2 - 2897. Determine v, given that i(v) = 0.
-1, 0, 5, 27
Let k = -4 - -4. Suppose -12*n + 13*n = k. Factor n - 13/4*v + 1/4*v**2.
v*(v - 13)/4
Let h = 10399 + -10397. Let b(s) be the first derivative of -1/2*s**6 + 16*s**3 - 9/5*s**5 - 4 + 3*s**4 - 48*s + 0*s**h. Suppose b(g) = 0. What is g?
-2, 1, 2
Let r(d) be the first derivative of 2*d**3/3 + 66*d**2 + 2178*d - 13754. Factor r(t).
2*(t + 33)**2
Let g = -3/3487 + 3505/20922. Let p(j) be the second derivative of g*j**4 - 4/3*j**3 + 0 + 13*j - 5*j**2. Factor p(u).
2*(u - 5)*(u + 1)
Let w(y) = -2003*y + 218329. Let b be w(109). Find h, given that -11/4*h**b - 6*h + 7 + 3/2*h**3 + 1/4*h**4 = 0.
-7, -2, 1, 2
Let c(u) be the second derivative of u**5/10 + 731*u**4/6 + 133955*u**3/3 + 133225*u**2 - 242*u - 2. Factor c(y).
2*(y + 1)*(y + 365)**2
Let w(s) be the second derivative of -s**5/100 + 19*s**4/20 - 261*s**3/10 - 841*s**2/10 + 1149*s. Let w(f) = 0. What is f?
-1, 29
Let o(t) be the first derivative of t**4 - 28*t**3 + 100*t**2 + 288*t + 2377. Factor o(m).
4*(m - 18)*(m - 4)*(m + 1)
Suppose -16*u - 10 = 6. Let l be ((-1)/(-1)*u)/((-40)/80). Suppose -1/3*o**5 + 2/3*o**l + 0*o**3 + 0 - 2/3*o**4 + 1/3*o = 0. Calculate o.
-1, 0, 1
Let c be ((