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Let s(r) be the first derivative of -r**6/90 - r**5/3 - 7*r**4/2 - 49*r**3 - 56. Let a(w) be the third derivative of s(w). Factor a(f).
-4*(f + 3)*(f + 7)
Let h = -373 - -408. Factor 53*z**3 + 2*z**2 - h*z**3 - 5*z - 6 - 17*z**3.
(z - 2)*(z + 1)*(z + 3)
Let u(g) be the first derivative of g**4/42 - 8*g**3/21 + 16*g**2/7 + 22*g - 31. Let o(l) be the first derivative of u(l). Let o(y) = 0. What is y?
4
Let r(j) be the third derivative of -1/15*j**5 + 2*j - 1/80*j**6 - 1/6*j**3 + 3*j**2 - 7/48*j**4 + 0. Factor r(i).
-(i + 1)**2*(3*i + 2)/2
Let i = -1854 - -1865. Suppose 0 = o + 7 - i. Find h, given that 0*h**3 - 2/5*h**o + 1/5*h - 1/5*h**5 + 0 + 2/5*h**2 = 0.
-1, 0, 1
Let w(g) = 2*g**3 - 7*g**2 - 5*g + 6. Let b be w(-1). Let 6/7 + 12/7*q**3 - 2/7*q**5 - 4/7*q**b - 2/7*q**4 - 10/7*q = 0. What is q?
-3, -1, 1
Let l(b) = -4*b**3 - 440*b**2 - 1150*b + 1730. Let m(q) = 13*q**3 + 1321*q**2 + 3381*q - 5191. Let f(k) = 14*l(k) + 4*m(k). Factor f(h).
-4*(h - 1)*(h + 4)*(h + 216)
Let q = -928579/4 - -232151. Find c such that -24*c**2 - 30*c**4 + 0 - 4*c - q*c**5 - 46*c**3 = 0.
-2, -2/5, 0
Let r(y) be the third derivative of 35/16*y**4 + 0*y - 17*y**2 + 5/8*y**5 + 0 + 49/16*y**3. Factor r(q).
3*(10*q + 7)**2/8
Let c(j) be the first derivative of -36/5*j**3 + 576/5*j**2 + 3/20*j**4 - 3072/5*j + 173. Factor c(h).
3*(h - 16)**2*(h - 4)/5
Let b(h) be the third derivative of -h**6/30 + 1924*h**5/5 - 1850888*h**4 + 14244434048*h**3/3 - 1287*h**2 + h. Let b(u) = 0. What is u?
1924
Let g(p) = -9*p**2 + 169*p + 4. Let i(z) = 2*z**2 - 1. Let m(o) = -g(o) - 4*i(o). Factor m(a).
a*(a - 169)
Let q(w) be the first derivative of w**4/9 + 376*w**3/9 + 248*w**2 + 4448*w/9 - 11274. Factor q(i).
4*(i + 2)**2*(i + 278)/9
Let g(d) = -10*d**2 - 89*d - 22. Let i(v) = 5*v**2 + 44*v + 12. Let w be 1 - -2 - (19 - 5). Let k(u) = w*i(u) - 6*g(u). Factor k(o).
5*o*(o + 10)
Suppose -3216*u + 9*u**4 - 94*u**3 + 20*u**3 - 27*u**3 - 58*u**3 - 2112 - 12*u**4 - 1260*u**2 = 0. What is u?
-44, -4, -1
Let r(f) be the third derivative of -f**5/20 - 34*f**4 + 273*f**3/2 + 5*f**2 - 207*f. Solve r(w) = 0.
-273, 1
Let l be 9 - 1/(1 + 0)*1. Let t be (-32)/(-12)*(190/l - 2). Factor 6*r**3 + 6*r**3 + 52*r - 9*r**4 + 15*r**2 - t*r.
-3*r*(r - 2)*(r + 1)*(3*r - 1)
Let a(i) = -106*i**2 - 5682*i - 5896. Let x(d) = -10*d**2 - 516*d - 536. Let b(c) = -3*a(c) + 32*x(c). Find s such that b(s) = 0.
-1, 268
Suppose a + 153 = 10*a. Factor 3*s**3 + 19*s + a*s - 32*s + 2*s**4 - s**5 - 8*s**2.
-s*(s - 2)*(s - 1)**2*(s + 2)
Let t be (-7 - -8)*80/(-6)*61/(-732). Factor -2/9*g**2 + t + 8/9*g.
-2*(g - 5)*(g + 1)/9
Let y(o) be the first derivative of 4/3*o**2 - 26/9*o + 2/27*o**3 - 45. Find i, given that y(i) = 0.
-13, 1
Let m(h) be the second derivative of 8 - 2*h + 0*h**2 + 1/132*h**4 + 4/11*h**3. Factor m(l).
l*(l + 24)/11
Find o, given that 83*o**4 - 710*o**2 + 268*o**3 + 110*o**3 - 786*o - 124 - 56 + 15*o**4 = 0.
-5, -3/7, 2
Suppose 0 = g - 3*z - 1 - 5, -2*g + 12 = 5*z. Let w = -53 + 58. Factor g*r**3 - 9*r - 2*r**3 + 0*r**3 + w*r.
4*r*(r - 1)*(r + 1)
Let c be -2 - -2*762/20*5. Let l = c + -1893/5. Let -l*b**3 - 8/5*b - 8/5*b**2 + 0 = 0. Calculate b.
-2, 0
Let f = 11226 - 11224. Let l be (-10)/(-36) + (-9)/54. Factor 1/3*s**f + 1/9*s**4 + 1/3*s**3 + 0 + l*s.
s*(s + 1)**3/9
Let v(l) be the first derivative of -4*l**3/21 + 54*l**2/7 + 232*l/7 + 492. Factor v(d).
-4*(d - 29)*(d + 2)/7
Let o(c) be the third derivative of c**6/180 - c**5/45 - 13*c**4/36 - 10*c**3/9 - 4*c**2 - 476*c. Factor o(w).
2*(w - 5)*(w + 1)*(w + 2)/3
Let d(s) be the second derivative of 8/3*s**3 + 22/5*s**6 - 71/5*s**5 + 0 - 10/21*s**7 - 44*s + 17*s**4 - 24*s**2. Suppose d(x) = 0. What is x?
-2/5, 1, 2, 3
Let f(a) be the second derivative of -a**7/21 + 13*a**6/15 - 61*a**5/10 + 127*a**4/6 - 118*a**3/3 + 40*a**2 - 1025*a. Let f(p) = 0. Calculate p.
1, 2, 4, 5
Suppose -3*i - 30 = -8*i. Suppose -7*o - i + 174 = 0. Factor 4*m**4 + 28*m**3 - 12*m**2 - o*m**4 + 3*m + 8*m**4 - 10*m**3 + 3*m**5.
3*m*(m - 1)**4
Let l(z) be the second derivative of -z**6/120 + z**4/24 + 21*z**2 + 73*z. Let x(g) be the first derivative of l(g). Factor x(v).
-v*(v - 1)*(v + 1)
Let w be (-8)/12*27/6. Let d(m) = 4*m**2 - 18*m - 16. Let t(v) = -7*v**2 + 36*v + 33. Let a(r) = w*t(r) - 5*d(r). Suppose a(u) = 0. What is u?
-1, 19
Let x = 111493 - 668957/6. Find z, given that 0 + x*z**2 + 1/6*z = 0.
-1, 0
Let w(b) be the second derivative of b**6/160 - b**5/60 - b**4/32 + b**3/6 - 60*b**2 + 2*b + 15. Let o(c) be the first derivative of w(c). Factor o(l).
(l - 1)*(l + 1)*(3*l - 4)/4
Let h(y) be the first derivative of 220 + 0*y**2 + 0*y - 24/5*y**5 + 1/3*y**6 - 1/2*y**4 + 8*y**3. Let h(w) = 0. What is w?
-1, 0, 1, 12
Suppose 0 = 2*f - d - 2, f - 68*d + 64*d = -6. Suppose -336/13*x - 2/13*x**3 + 50/13*x**f + 288/13 = 0. Calculate x.
1, 12
Let m(n) be the third derivative of n**8/10080 - n**6/270 + n**4/12 - 5*n**3/2 - 8*n**2. Let k(c) be the second derivative of m(c). Solve k(z) = 0 for z.
-2, 0, 2
Let v(b) be the third derivative of b**5/135 - b**4/27 - 10*b**3/9 - 1580*b**2. Find u, given that v(u) = 0.
-3, 5
Let b = 28 - 25. Factor 617*h + 16*h**4 - 617*h + 20*h**b + 4*h**5 + 8*h**2.
4*h**2*(h + 1)**2*(h + 2)
Let s(d) be the first derivative of -d**5/25 - 133*d**4/20 - 521*d**3/15 - 647*d**2/10 - 258*d/5 + 1772. Find u, given that s(u) = 0.
-129, -2, -1
Suppose -545 = -188*x - 72 + 279. Factor -1/2*f**x + 17*f**2 + 0*f - 15/2*f**3 + 0.
-f**2*(f - 2)*(f + 17)/2
Let t(b) be the first derivative of -4*b**3/21 - 46*b**2/7 - 88*b/7 - 8817. Determine v so that t(v) = 0.
-22, -1
Let a(i) be the first derivative of -2*i**5/5 - 2*i**4 - 2*i**3 + 330. Factor a(j).
-2*j**2*(j + 1)*(j + 3)
Let i(p) be the first derivative of p**3/6 + 122*p**2 + 29768*p + 393. Factor i(m).
(m + 244)**2/2
Suppose 15*x - 76*x = 888 - 1193. Determine b so that 0*b + 4*b**3 + 0 - 3/2*b**x - 1/2*b**4 - 2*b**2 = 0.
-2, 0, 2/3, 1
Factor 4/5*h**2 - 2568/5 - 1276/5*h.
4*(h - 321)*(h + 2)/5
Let t(i) be the second derivative of -1/6*i**4 + 0*i**2 + 0*i**3 + 0 + 1/12*i**5 + 1/45*i**6 - 1/126*i**7 - 169*i. Determine b, given that t(b) = 0.
-2, 0, 1, 3
Let h = -14825/8 + 104159/56. Factor -2/7*f**3 - 8*f + h + 20/7*f**2.
-2*(f - 6)*(f - 2)**2/7
Let r(y) be the first derivative of 3*y**5/20 + 9*y**4/4 - 125*y**3/4 + 63*y**2 + 228*y - 2167. Suppose r(d) = 0. Calculate d.
-19, -1, 4
Let r(w) = -w**3 - w + 1. Let z(d) = -42*d**2 - 80*d + 39. Let q(p) = -r(p) - z(p). Let j(s) be the first derivative of q(s). Factor j(i).
3*(i + 1)*(i + 27)
Suppose d + c = 23 - 12, -4*d + 2*c = -74. Suppose 2*x + y = 9, 0 = d*x - 11*x + y - 15. Determine k, given that -4/7*k - 2/7 - 2/7*k**x = 0.
-1
Let q(h) = -29*h**3 - 3818*h**2 + 1283136*h + 2582008. Let y(a) = 18*a**3 + 2550*a**2 - 855424*a - 1721339. Let t(o) = -5*q(o) - 8*y(o). Factor t(f).
(f - 656)**2*(f + 2)
Factor 1/8*i**4 - 343/8*i**3 + 0 + 0*i + 0*i**2.
i**3*(i - 343)/8
Let q(y) be the third derivative of 3/2*y**3 + 0*y + 1/60*y**5 - 48*y**2 + 0 - 1/4*y**4. Let q(l) = 0. What is l?
3
Let u(l) be the first derivative of 2/9*l**3 + 4/3*l**2 + 8/3*l - 142. Factor u(i).
2*(i + 2)**2/3
Let u(z) be the third derivative of 2*z**2 - 4/7*z**3 + 0*z - 1/42*z**4 + 1/105*z**5 + 12. What is y in u(y) = 0?
-2, 3
Suppose -5*v - 11*q + 13*q + 230 = 0, 63 = 2*v + 5*q. Determine s so that -v*s**2 - 66 - 56*s**2 - 67*s + 99*s**2 = 0.
-66, -1
Let d(u) = 3*u**3 - u + 1. Let q(i) = 55*i**3 - 1160*i**2 + 3505*i + 20. Let m(h) = 20*d(h) - q(h). Factor m(z).
5*z*(z - 3)*(z + 235)
Let r(k) = 2*k**4 - k**3 - k**2 - k + 1. Let q(s) = -3*s**4 + 619*s**3 - 3821*s**2 + 5809*s - 4. Let y(g) = q(g) + 4*r(g). Suppose y(z) = 0. Calculate z.
-129, 0, 3
Let s(b) be the second derivative of -b**4/6 - 53*b**3/6 - 293*b**2/2 + 36*b. Let k(p) = p**2 + 26*p + 146. Let t(h) = -5*k(h) - 2*s(h). What is j in t(j) = 0?
-12
Let -2376*g**2 + 483*g**3 - 436*g**3 - 4*g**5 - 1011*g**3 + 1767 - 112*g**4 + 1689 = 0. What is g?
-12, -3, -2, 1
Let w(v) be the third derivative of v**5/75 + 2*v**4/5 - 192*v**3/5 + 740*v**2 - 2*v + 1. Find q, given that w(q) = 0.
-24, 12
Factor -11 + 209 - 270*o**2 - 198 - 5*o**3.
-5*o**2*(o + 54)
Let u be (10 - 1421/140)/(6/(-716)). Let k = -35/2 + u. Let 2*c + 6/5 - k*c**3 + 2/5*c**2 = 0. Calculate c.
