1
Let u(b) = 245*b - 4653. Let a be u(19). Let c(g) be the first derivative of -6/11*g + 6 - 1/22*g**4 + 2/11*g**3 + 1/11*g**a. Factor c(i).
-2*(i - 3)*(i - 1)*(i + 1)/11
Suppose 309*x - 22 = 304*x - 2*h, -4*x + h + 15 = 0. Factor 0*j - 1/5*j**x - 4/5*j**2 + 0 + j**3.
-j**2*(j - 4)*(j - 1)/5
Let t(f) be the second derivative of 21/4*f**4 - 318*f + 0*f**2 + 0*f**3 + 0 + 3*f**5 - 1/10*f**6. Let t(n) = 0. Calculate n.
-1, 0, 21
Let s(u) be the second derivative of u**5/40 + 3*u**4/8 + 9*u**3/4 + 151*u**2 - u - 235. Let d(r) be the first derivative of s(r). What is t in d(t) = 0?
-3
Suppose -4*h = -3*q + 268, q - 4*q + 12 = 0. Let g be h/72 + -5 - (0 - 7). Find i, given that g*i**3 - 2/9*i**5 + 0*i**4 - 8/9*i + 0 + 0*i**2 = 0.
-2, -1, 0, 1, 2
Suppose 0 = -5*j - k + 21 + 11, -3*k + 12 = j. Determine z so that -32*z**2 + 2*z**5 + 10*z + 42*z**3 - j*z**3 - 59*z**4 + 43*z**4 = 0.
0, 1, 5
Let c(d) be the third derivative of 0 - 5/216*d**4 + 3*d**2 - d + 1/90*d**5 + 1/270*d**6 + 0*d**3 + 1/3024*d**8 - 1/315*d**7. Factor c(z).
z*(z - 5)*(z - 1)**2*(z + 1)/9
Let -53*n**2 + 28*n**4 + 24*n**4 - 112 - 296*n + 1015*n**5 + 50*n**3 - 127*n**2 - 1009*n**5 = 0. What is n?
-7, -2, -1, -2/3, 2
Let o be (-5)/(-15) - 104/(-3). Suppose -8 = 2*c + 4*p, 0 = -4*c + 6*p - 2*p + 32. Factor -17*s + 5*s**c + 52*s - 20*s + 65*s**2 - 90 - o*s**3.
5*(s - 3)**2*(s - 2)*(s + 1)
Let c(v) be the third derivative of 0*v**3 + 7*v**2 + 0 + 1/390*v**6 - 1/390*v**5 + 0*v**4 + 0*v - 1/1365*v**7. Suppose c(d) = 0. Calculate d.
0, 1
Solve -156*q**4 - 160*q - 3344/3*q**2 + 896/3 + 20/3*q**5 - 2456/3*q**3 = 0 for q.
-2, -1, 2/5, 28
Let 60/7*p - 446/21*p**3 + 242/21*p**2 + 8/7*p**4 + 0 = 0. What is p?
-5/12, 0, 1, 18
Let a = -35 - -27. Let s = a - -14. Find t, given that -15*t**3 + 12 + 11 - s*t**3 + 1 + 3*t**5 + 36*t - 6*t**2 = 0.
-2, -1, 2
Suppose p = -p - 3*h + 37, 5*h = -4*p + 75. Let 6*s + 2 - p*s**2 - 18*s**2 + 30*s**2 = 0. What is s?
-1/4, 1
Let p(z) be the third derivative of -5*z**8/224 + 37*z**7/140 + 241*z**6/80 - 437*z**5/40 - 26*z**4 + 55*z**3 - 46*z**2 - 3*z. Find y, given that p(y) = 0.
-5, -1, 2/5, 2, 11
Let a be 423/(-24) + 11 + (10 - 3). Let c(t) be the first derivative of 18 - 1/2*t + 3/16*t**4 + a*t**2 + 2/3*t**3. Factor c(k).
(k + 1)*(k + 2)*(3*k - 1)/4
Factor -12/5*w - 1947*w**3 - 696/5*w**2 + 0 + 10443/5*w**4.
3*w*(w - 1)*(59*w + 2)**2/5
Let u(l) be the third derivative of 44*l**2 + 0*l**3 + 0*l**4 + 1/150*l**5 + 0*l**6 + 0 - 1/525*l**7 + 0*l. Factor u(c).
-2*c**2*(c - 1)*(c + 1)/5
Let n(k) be the first derivative of 4/35*k**5 - 63 + 16/7*k - 4/7*k**2 - 20/21*k**3 + 5/14*k**4 - 1/21*k**6. Find v such that n(v) = 0.
-2, -1, 1, 2
Let l(u) be the third derivative of -1/4*u**4 + 0 - 3/40*u**5 + u**3 + 145*u**2 + 0*u. Factor l(a).
-3*(a + 2)*(3*a - 2)/2
What is v in 550*v**4 - 42*v**5 + 51*v**5 - v**5 - 36*v**5 + 220*v**2 - 705*v**3 - 97*v**5 - 20*v = 0?
0, 1/5, 2
Let g be 68/51 - (-158)/(-6). Let d = 29 + g. Solve -s - d + 0*s - 276*s**2 - 7*s + 272*s**2 = 0 for s.
-1
Suppose 2*c - 6 + 4 = 0. Let o be 1 - (0/c - (16 - 8)). Suppose d**4 - 6 - 4 + 25*d**3 - o*d**2 + 35*d - 36*d**2 - 6*d**4 = 0. Calculate d.
1, 2
Let m(b) = -2*b**3 + 6*b**2 + 8*b + 2. Let i(z) = -2*z**2 + 33*z - 66. Let v be i(14). Let d be m(v). Suppose 0*g + 2/13*g**d + 0 = 0. Calculate g.
0
Let r be 1 + (-518)/(-42) - (-7)/((-35)/30). Factor -r - 2/3*l**2 - 8*l.
-2*(l + 1)*(l + 11)/3
Suppose 5*u + 2*a - 364 = 0, 5*u = -18*a + 20*a + 376. Let 3468*z - 18*z**2 + 19652 - 70*z**3 + u*z**3 + 239*z**2 - 17*z**2 = 0. What is z?
-17
Let n = -1/57563 + 172696/402941. Factor -n*p**5 - 5/7*p**4 + 0*p**2 + 0*p + 0 - 2/7*p**3.
-p**3*(p + 1)*(3*p + 2)/7
Let y be -10*((-156)/50 - (-7 + 4)). Let a = -264 - -266. Factor -y*r**3 - 2/5*r**4 - 2/5*r + 0 - 6/5*r**a.
-2*r*(r + 1)**3/5
Let i(z) be the second derivative of z**8/8960 + 3*z**7/1120 + z**6/120 + 27*z**4/4 + 40*z. Let o(g) be the third derivative of i(g). Factor o(v).
3*v*(v + 1)*(v + 8)/4
Let h(z) be the second derivative of 0 + 64/5*z**2 + 37*z + 32/15*z**3 - 2/25*z**5 - 2/5*z**4 + 1/75*z**6. Factor h(b).
2*(b - 4)**2*(b + 2)**2/5
Factor -3015968/13 - 2/13*i**2 - 4912/13*i.
-2*(i + 1228)**2/13
Let p = 55 - -8. Factor -23*f + 9*f + p*f - 18 + 6 - 4*f**2.
-(f - 12)*(4*f - 1)
Factor -111/2*h**3 - 1/2*h**4 - 327/2*h**2 - 325/2*h - 54.
-(h + 1)**3*(h + 108)/2
Let j(r) be the first derivative of r**5/60 + 11*r**4/24 + 14*r**3/3 + 27*r**2/2 + 32. Let w(y) be the second derivative of j(y). Factor w(x).
(x + 4)*(x + 7)
Let o = -828/11 + 3323/44. Let s be (-2 + 1)/((-61)/488). Determine h so that o*h**4 + s - 11/4*h**3 + 21/2*h**2 - 16*h = 0.
1, 2, 4
Let s(i) = i**3 - 6*i**2 - 10*i + 60. Suppose 122 - 140 = -3*j. Let f be s(j). Factor -2/5*a**5 - 4/5*a**4 + f + 0*a - 2/5*a**3 + 0*a**2.
-2*a**3*(a + 1)**2/5
Let y(t) = -3*t**2 + 628*t - 19833. Let w(o) = -o**2 + o - 6. Let j be 2/(-4) + ((-300)/(-24))/(-25). Let l(r) = j*y(r) - 2*w(r). Factor l(d).
5*(d - 63)**2
Let p(a) be the second derivative of 7*a**4/78 - 1258*a**3/39 - 360*a**2/13 + 2686*a. Suppose p(s) = 0. What is s?
-2/7, 180
Factor -1833/4*g - 8619/4 - 129/4*g**2 - 3/4*g**3.
-3*(g + 13)**2*(g + 17)/4
Let v(j) = -4*j**3 - 22*j**2 + 3*j - 6. Let o(c) = 2*c**2 + c - 2. Let g(q) = 3*o(q) - v(q). Solve g(f) = 0 for f.
-7, 0
Let q(d) be the second derivative of -d**6/90 - 2*d**5/5 - 7*d**4/4 - 2255*d - 2. Factor q(x).
-x**2*(x + 3)*(x + 21)/3
Suppose 2606 - 30*a**2 + 83*a**2 + 879 - 129*a - a**3 + 1930 - 802*a = 0. Calculate a.
15, 19
Let c(a) be the first derivative of -a**4/18 - 686*a**3/27 - 29240*a**2/9 + 59168*a/9 + 461. Let c(b) = 0. What is b?
-172, 1
Let v(z) = 7*z**5 - 53*z**4 + 516*z**3 + 582*z**2 - 6*z + 6. Let b(y) = -y**5 + y**4 + 2*y**3 - y**2 + y - 1. Let k(c) = -6*b(c) - v(c). What is n in k(n) = 0?
-1, 0, 24
Let i(y) be the second derivative of -83*y**4/36 + 28*y**3/3 - 2*y**2/3 + 3528*y. Factor i(f).
-(f - 2)*(83*f - 2)/3
Let f = -359 - -364. Let -5*m**3 - 12*m**3 + 10*m**2 + 32*m**3 + f*m**4 = 0. What is m?
-2, -1, 0
Let t(q) be the second derivative of -131*q + 0*q**2 + 3/11*q**3 - 1/66*q**4 + 0. Factor t(s).
-2*s*(s - 9)/11
Let s(y) be the third derivative of 0 + 167/510*y**5 + 124*y - 115/204*y**4 + 6/17*y**3 - 3/595*y**7 - 61/1020*y**6 - y**2. Solve s(x) = 0 for x.
-9, 2/9, 1
Let q = 2279 + -2276. Let s(u) be the second derivative of 0 + 9/4*u**2 - 16*u - u**q + 1/8*u**4. Factor s(m).
3*(m - 3)*(m - 1)/2
Let z = -89697 - -89700. Factor 0 - 1/4*x + 7/4*x**2 - 3/2*x**z.
-x*(x - 1)*(6*x - 1)/4
Let g(w) be the second derivative of 42*w**3 + 98*w**2 + 9/10*w**5 + 109/12*w**4 + 1/30*w**6 + 5*w - 4. What is a in g(a) = 0?
-7, -2
Let l be ((-181)/10 - (-64)/(-160))/(3/(-6)). Let s(o) be the third derivative of 0 + 1/24*o**6 + 1/3*o**3 - 2/15*o**5 + 0*o + 1/24*o**4 + l*o**2. Factor s(p).
(p - 1)**2*(5*p + 2)
Let p(w) be the third derivative of 0*w**3 - 6*w**2 - 2/3*w**4 - 1/30*w**5 + 0 + 0*w. Find r, given that p(r) = 0.
-8, 0
Let z(r) be the third derivative of 0 - 16*r - 5/3*r**3 - r**2 + 2/15*r**5 + 1/10*r**6 - 1/2*r**4 + 1/105*r**7. Factor z(u).
2*(u - 1)*(u + 1)**2*(u + 5)
Let d(p) = 4*p**3 - 249*p**2 + 14160*p - 13921. Let h(v) = 23*v**3 - 1490*v**2 + 84960*v - 83527. Let x(y) = -17*d(y) + 3*h(y). Factor x(f).
(f - 118)**2*(f - 1)
Let a(c) = 16*c - 1278. Let p be a(80). Factor -216/11 - 6/11*n**p - 72/11*n.
-6*(n + 6)**2/11
Let h be 2/(-2)*(-108)/252. Find n such that 3/7 + 3/7*n**3 - h*n**2 - 3/7*n = 0.
-1, 1
Let a(z) = -2736*z + 131330. Let w be a(48). Determine q so that 96/5 + 4/5*q**3 + 152/5*q + 12*q**w = 0.
-12, -2, -1
Let n(j) be the first derivative of -9*j**5/25 - 25*j**4/4 + 302*j**3/15 - 16*j**2/5 - 4245. Determine m so that n(m) = 0.
-16, 0, 1/9, 2
Let b(d) be the first derivative of -104 - 93*d**2 + 41*d**2 + 4*d**3 + 44*d**2 + d**4. Factor b(f).
4*f*(f - 1)*(f + 4)
Find r such that -302*r + 204*r**2 - 4*r**4 + 6*r**4 - 9*r**3 - 43*r**3 + 204*r**2 - 706*r = 0.
0, 6, 14
Let y = 211963/145 - 22893/29. Factor -164/5*x - y - 2/5*x**2.
-2*(x + 41)**2/5
Factor -1700*v**3 + 108853*v - 16*v**4 - 11*v**4 - 1505*v**3 - 2069*v**3 - 28812 - 255783*v**2 + 63431*v.
-3*(v + 98)**2*(3*v - 1)**2
Let h be 7 - (6 - 1742/(-1110)). Let l = 26/37 + h. Let 8/15 - 8/15*m + l*m**2 = 0. What is m?
2
Let b(p) = 