 = -4*g - 18. Let v be (d + -4 - -6) + 0. Factor -3*i**3 + i**v - i**3 + 0*i**3 + 3*i**2.
-3*i**2*(i - 1)
Determine b, given that -126/5*b + 3/5*b**2 + 123/5 = 0.
1, 41
Let c be (-2)/11 + (-26)/(-22). Let v(g) = g**2 + g + 1. Let h(x) = -9*x**2 - 9*x + 12. Let a(w) = c*h(w) + 6*v(w). Let a(f) = 0. What is f?
-3, 2
Let x be (-32)/(-12) + 203/(-84). Let z(c) be the second derivative of 5/6*c**4 + 25/6*c**3 + 0 - 29*c - x*c**5 - 15*c**2. Find g, given that z(g) = 0.
-2, 1, 3
Factor -3500658*u**2 + 2646*u**3 + 0*u - 1/2*u**4 + 0.
-u**2*(u - 2646)**2/2
Let d = -28 - -32. Suppose 0 = 3*p + 5*t - 12, -d = -p - 3*t + t. Let -2*r**3 - p*r**3 + 7*r**3 - 3*r**3 = 0. Calculate r.
0
Let n(v) be the third derivative of 13/6*v**4 - 2*v**2 - 1/30*v**6 + 0*v - 2/3*v**5 + 44/3*v**3 + 13. Factor n(q).
-4*(q - 2)*(q + 1)*(q + 11)
Let f(v) be the second derivative of -v**6/6 + 5*v**5/2 + 5*v**4/4 - 70*v**3/3 - 50*v**2 - 409*v. Determine s so that f(s) = 0.
-1, 2, 10
Let z(l) be the first derivative of -l**5/12 - 25*l**4/12 - 35*l**3/2 - l**2/2 - 3*l - 65. Let c(a) be the second derivative of z(a). Factor c(x).
-5*(x + 3)*(x + 7)
Let n = -1/2919 - -3337/2919. Factor -8/7*z**3 - 8/7 + 6/7*z**2 + 2/7*z**4 + n*z.
2*(z - 2)**2*(z - 1)*(z + 1)/7
Factor 70*o**2 - 63 + 11*o**3 + 34*o**2 + 227 + 250*o - 9*o**3 - 16*o**2.
2*(o + 1)*(o + 2)*(o + 41)
Let i(m) = 32*m - m**2 - 31*m - 4218*m**3 + 4219*m**3. Let a(v) = -4*v**2 + 7*v - 4. Let u be (1/((-1)/4))/(-2). Let j(t) = u*a(t) + 2*i(t). Factor j(k).
2*(k - 2)**2*(k - 1)
Let c(h) = h**3 - 35*h**2 - 5*h + 163. Let k be c(35). Let w be 1*-7 - (k - (-510)/105). Suppose -w*u**2 - 1/7*u + 2/7 = 0. Calculate u.
-2, 1
Let d(s) be the second derivative of s**5/20 + 35*s**4/12 - 77*s**3/6 - 111*s**2/2 + 1026*s. Factor d(a).
(a - 3)*(a + 1)*(a + 37)
Let o(w) = -122*w**2 - 297*w - 183. Let m = 50 - 55. Let t = 8 + m. Let r(y) = 1585*y**2 + 3860*y + 2380. Let d(g) = t*r(g) + 40*o(g). Factor d(v).
-5*(5*v + 6)**2
Let i = 96 + -94. Suppose -7*k**3 - 14*k**4 - 614*k - 34*k**2 + 602*k - i*k**5 - 27*k**3 = 0. What is k?
-3, -2, -1, 0
Let b(g) = g**4 - g**3 - g + 1. Let o(f) be the first derivative of f**5/5 - 19*f**4/2 - 8*f**3/3 - 5*f**2/2 + 5*f - 47. Let q(a) = 5*b(a) - o(a). Factor q(s).
s**2*(s + 8)*(4*s + 1)
Let x(g) be the second derivative of -11*g**3/6 - 70*g**2 + 2*g + 46. Let u be x(-13). Factor -21/4*s**3 - u*s + 0 + 12*s**2.
-3*s*(s - 2)*(7*s - 2)/4
Let t(b) be the second derivative of 7*b**5/4 + 265*b**4/4 + 1460*b**3/3 - 450*b**2 + b - 103. Determine u, given that t(u) = 0.
-18, -5, 2/7
Suppose -21*w**2 + 21/4*w**4 - 3/2*w**3 + 6*w + 0 = 0. What is w?
-2, 0, 2/7, 2
Suppose 4*u = -16*o + 11*o + 126, o = -3*u + 23. Suppose 3*m - o = 4*q, -4 = q + 1. Determine i so that -9/7*i**m + 3/7*i**3 + 9/7 - 3/7*i = 0.
-1, 1, 3
Let h be 888/96 - 55/55. Let 3/2 - h*n + 57/4*n**2 + 9/4*n**4 - 39/4*n**3 = 0. Calculate n.
1/3, 1, 2
Let t(m) be the second derivative of -m**6/30 + 7*m**5/10 - 16*m**4/3 + 19*m**3 - 63*m**2/2 - 1208*m. Solve t(s) = 0 for s.
1, 3, 7
Let u(c) = -4*c - 7*c - 2*c**2 - 4 + 5*c. Let t(s) = 2*s**2 + 6*s + 4. Suppose 5*n + 10 = p, -27*n + p = -24*n + 4. Let v(k) = n*u(k) - 4*t(k). Factor v(q).
-2*(q + 1)*(q + 2)
Suppose 2*d - 397 = -187. Let v be ((-490)/d)/(-1 - 1). Suppose 0 + h - v*h**2 = 0. Calculate h.
0, 3/7
Solve 55*m + 2*m**4 - 2*m + 48*m**3 - 30*m**2 - 63*m**2 - 3*m**4 - 7*m = 0.
0, 1, 46
Let f(n) = -n**3 + 9*n**2 - 54*n + 642. Let i be f(10). Suppose 20/13*x**i - 58/13*x - 2/13*x**3 + 40/13 = 0. Calculate x.
1, 4, 5
Suppose -9*z**3 - 850*z**2 - 194*z**2 + 3123*z - 3119*z + 464 = 0. What is z?
-116, -2/3, 2/3
Let k(g) be the second derivative of -1/60*g**6 + 0*g**2 - 44*g + g**3 + 1 + 1/5*g**5 - 19/24*g**4. Factor k(c).
-c*(c - 4)*(c - 3)*(c - 1)/2
Let u(m) be the second derivative of m**7/16380 - m**6/1170 - m**5/156 - 43*m**4/12 + 78*m. Let p(l) be the third derivative of u(l). Factor p(c).
2*(c - 5)*(c + 1)/13
Find p, given that 2*p + 4 + p**4 + p**5 + 2*p - 5*p**3 + 69278*p**2 - 69283*p**2 = 0.
-2, -1, 1, 2
Let v be (-7 - 405/(-30))*-2 - -15. Factor 0*x - 1/4*x**v + 1/4.
-(x - 1)*(x + 1)/4
Suppose -i = -k - 138 + 1306, 3500 = 3*k - 2*i. Let h = k + -1145. Solve 10/3*z**4 - 38/3*z**3 - h*z - 1/3*z**5 + 68/3*z**2 + 6 = 0 for z.
1, 2, 3
Let p(u) be the first derivative of -u**5/20 - 15*u**4/16 + 73*u**3/12 - 57*u**2/8 + 523. Factor p(m).
-m*(m - 3)*(m - 1)*(m + 19)/4
Let j(f) be the third derivative of f**6/480 + f**5/24 - 53*f**4/96 + 7*f**3/4 - 128*f**2 + 2*f. What is s in j(s) = 0?
-14, 1, 3
Let z be 5/15 - 116/(-3). Let k = -87 + 90. Let z - k*s**2 - 39 + 3*s = 0. Calculate s.
0, 1
Suppose -25*y**4 - 234*y**3 - 238*y - 45*y**4 + 32*y**4 + 36*y**4 + 474*y**2 = 0. Calculate y.
-119, 0, 1
Factor -3/2*c**3 + 228 + 42*c**2 - 537/2*c.
-3*(c - 19)*(c - 8)*(c - 1)/2
Let y(i) be the second derivative of i**9/2016 + i**8/560 - i**6/120 - i**5/80 - 95*i**3/6 + 11*i - 2. Let m(a) be the second derivative of y(a). Factor m(z).
3*z*(z - 1)*(z + 1)**3/2
Let i(b) be the second derivative of -4*b + 0 + 7/15*b**3 + 8/5*b**2 - 1/30*b**4. Suppose i(y) = 0. What is y?
-1, 8
Let q(f) = f**2 - 14*f - 2062. Let c be q(53). Let m(x) be the third derivative of 0 + 2/5*x**4 + 16/5*x**3 - 14*x**2 + 0*x + 1/50*x**c. Factor m(a).
6*(a + 4)**2/5
Let p(k) be the first derivative of 16*k**3/27 + 65*k**2/9 + 16*k/9 + 874. Factor p(q).
2*(q + 8)*(8*q + 1)/9
Let r = 391530 - 1566119/4. Find m, given that r*m**2 - 9/4 + 2*m = 0.
-9, 1
Let n(r) be the second derivative of -r**5/5 + 6*r**4 - 70*r**3/3 - 300*r**2 - 1880*r. Factor n(u).
-4*(u - 15)*(u - 5)*(u + 2)
Suppose -23 + 26 = p. Let x be ((-84)/(-77) + 4 - 5)/((-16)/(-88)). Suppose x*c**2 - 1/2*c**p + 0 + 0*c = 0. What is c?
0, 1
Let t(f) be the first derivative of -2*f**3/3 + 58*f**2 - 114*f + 3153. Determine d so that t(d) = 0.
1, 57
Let v(n) be the third derivative of -n**5/360 + 23*n**4/48 + 1196*n**2. What is d in v(d) = 0?
0, 69
Let w be ((-101)/(-1919))/(9/342). Suppose 2/5*m**w - 136/5*m + 2312/5 = 0. What is m?
34
Suppose -2*t = -2*m + 13 - 1, 10 = -3*t - 5*m. Let x be 2 + (0/4)/t. Factor 3*r**2 - 7*r**2 - r**x + 20.
-5*(r - 2)*(r + 2)
Factor 20*o**2 - 113239*o + 11*o**2 + 113189*o + 2*o**3 + 17.
(o - 1)*(o + 17)*(2*o - 1)
Let c(m) be the first derivative of 2*m**5 + 7*m**4/2 - 578*m**3/15 - 119*m**2/5 - 24*m/5 + 1183. Solve c(z) = 0.
-4, -1/5, 3
Let r(z) be the second derivative of z**6/10 + 291*z**5/20 - 49*z**4/2 - z + 1104. Factor r(f).
3*f**2*(f - 1)*(f + 98)
Suppose 5*w - 20 = 5*j, -w + 6*w - 24 = j. Suppose 17 = 4*a + 2*z + z, 0 = z + j. Factor -114 - 4*x**4 + 4*x**a + 114.
4*x**4*(x - 1)
Let f(m) = -m**3 - 17*m**2 + 970*m + 338. Let t be f(24). Factor -4/5 + n - 1/5*n**t.
-(n - 4)*(n - 1)/5
Factor 126*w + 26*w - w**2 - 409*w - 5 + 5.
-w*(w + 257)
Let t = 165 - 171. Let w(d) = -15*d**3 - 75*d**2 - 24*d - 6. Let a(i) = 15*i**3 + 74*i**2 + 23*i + 7. Let f(l) = t*a(l) - 7*w(l). Factor f(o).
3*o*(o + 5)*(5*o + 2)
Let f(s) = -624*s + 4995. Let q be f(8). Let b(i) be the first derivative of -2/17*i - 12 - 2/85*i**5 + 4/51*i**q + 0*i**4 + 0*i**2. Factor b(j).
-2*(j - 1)**2*(j + 1)**2/17
Let o(c) = -c**3 + 11*c**2 - 30*c + 5. Let z be o(5). Determine w, given that -18*w + 11*w - 5*w**2 + 9*w**2 - z*w = 0.
0, 3
Suppose 2*w = -277 - 231. Let b = w - -259. Solve 2/7*i**b + 0 + 2/7*i**4 + 0*i**2 + 0*i + 0*i**3 = 0 for i.
-1, 0
Let u(q) = -51*q - 200. Let i be u(-4). Solve -i + 2389*z - 2381*z + 4*z**5 - 12*z**3 + z**4 + 4*z**2 + 4 - 5*z**4 = 0.
-1, 0, 1, 2
Let z be -7 + (-13)/3380*-2180. Find y, given that 2/13 + 16/13*y**2 + z*y = 0.
-1, -1/8
Let p(y) be the first derivative of -36125*y**6/18 - 2295*y**5 + 140*y**4 - 20*y**3/9 - 1754. Find x such that p(x) = 0.
-1, 0, 2/85
Let w(x) be the second derivative of 6*x**6/5 - 69*x**5/10 + 481*x**4/48 + 23*x**3/6 + x**2/2 + 2*x - 382. Determine r so that w(r) = 0.
-1/12, 2
Let c(k) = -27*k + 8*k + 16*k + 29. Let q be c(9). Suppose 7*z**q + 177*z - 153*z - 26*z**3 - z**5 + 9*z**4 - 16 + 3*z**3 = 0. Calculate z.
-1, 1, 4
Let d(g) = -8*g**2 + 392*g - 820. Let f(z) = 15*z**2 - 788*z + 1635. Let b(w) = -7*d(w) - 4*f(w). Factor b(a).
-4*(a - 100)*(a - 2)
Let s be 4*6/3*(((-77)/44 - 10) + 12). Factor 0 + 0*l**2 + s*l - 1/2*l**3.
-l*(l - 2)*(l + 2