20
Let v(t) be the first derivative of -2*t**3/27 + 35*t**2/9 - 116*t/3 + 7100. Factor v(n).
-2*(n - 29)*(n - 6)/9
Let b = 88447 - 265339/3. Factor -1/6*h**3 + b*h**2 - 2/3*h + 0.
-h*(h - 2)**2/6
Suppose -5*q + 360 + 447 = -4*z, 3*z = -3*q + 495. Let m = q - 159. Find w, given that -m*w**4 + 0*w**2 - 4/3*w**3 + 0*w + 0 - 5/3*w**5 = 0.
-2, -2/5, 0
Let w be (1244/48 - (-24 - -14)) + (-27)/(-324). Factor -4/3*u**3 + w + 12*u**2 - 36*u.
-4*(u - 3)**3/3
Let c(l) be the third derivative of -l**5/120 - 547*l**4/48 - 91*l**3/2 - 423*l**2 - 2*l - 3. Let c(z) = 0. Calculate z.
-546, -1
Find r, given that 0 - 76/9*r**2 + 16*r + 2/9*r**3 = 0.
0, 2, 36
Let u = 76059/17 + -227837/51. Factor 5*x**2 + 2/3*x**3 - 1/3*x**4 + 4/3*x - u.
-(x - 5)*(x - 1)*(x + 2)**2/3
Let k(q) be the first derivative of 6*q**5/5 - 127*q**4 + 4816*q**3 - 70560*q**2 + 87808*q + 4299. Factor k(x).
2*(x - 28)**3*(3*x - 2)
Suppose 100 = 2*q + 8*q. Let v be (-36)/q*35/(-21). Factor 3*z**3 + 0 + 0 + v*z - 18*z.
3*z*(z - 2)*(z + 2)
Let o = 22968 + -22965. Let p(g) be the third derivative of 1/3*g**o - 28*g**2 + 0 - 1/24*g**4 + 1/480*g**6 + 0*g - 1/120*g**5. Let p(v) = 0. What is v?
-2, 2
Let v be (-2 - 4)*(-1372)/6174. Let 0 - 68/3*k**2 + 68/3*k**3 - 28/3*k**4 + 8*k + v*k**5 = 0. Calculate k.
0, 1, 2, 3
Let t(l) be the second derivative of -l**4/6 + 15*l**3 - 29*l - 18. Find r, given that t(r) = 0.
0, 45
Let u be (-4)/(-11) + (-39088)/(-77). Let y be 3*-1*u/(-1905). Factor 14/5*f - 6/5*f**2 - y.
-2*(f - 2)*(3*f - 1)/5
Let g(x) be the first derivative of -2*x**3/3 - 96*x**2 + 1890*x + 26. Factor g(m).
-2*(m - 9)*(m + 105)
Let f(w) be the third derivative of -w**7/420 - 19*w**6/48 - 31*w**5/40 + 95*w**4/48 + 47*w**3/6 + 831*w**2. Suppose f(n) = 0. What is n?
-94, -1, 1
Suppose 35 - 23 = 4*d. Suppose 0 = -d*r - 0 + 6. Find j, given that r*j**2 - 14 + 13*j - 25*j + 1 - 1 = 0.
-1, 7
Let h(r) be the first derivative of -r**4/2 - 40*r**3/9 + 12*r**2 + 64*r/3 - 6454. Suppose h(p) = 0. Calculate p.
-8, -2/3, 2
Let l(u) = 7*u - 148*u - 127 - 374 + 54*u + 15*u. Let n be l(-7). Factor 0 - 1/4*o**4 + 1/4*o**2 + 1/2*o**n - 1/2*o.
-o*(o - 2)*(o - 1)*(o + 1)/4
Suppose -63*c + 70 = -56*c. Factor -12*f + 2*f**2 + 13*f**2 - c*f**2 - 30 + 37*f.
5*(f - 1)*(f + 6)
Suppose -5*l - 5*l + 20 = 0. Factor 0*x**2 + 7*x - 5*x**2 + 0*x**2 + 3*x**l - 3.
-(x - 3)*(2*x - 1)
Suppose 5*j - 3840*f + 3839*f = 11, 3*j = 5*f - 33. Let w(p) be the first derivative of -1/3*p**3 - 1/4*p**2 - 1/8*p**j + 0*p + 13. Factor w(c).
-c*(c + 1)**2/2
Let w(p) = -29*p**5 - 4*p**4 + 16*p**3 - 9*p**2 + 9*p + 18. Let i(q) = -3*q**5 - q**2 + q + 2. Let k(b) = 18*i(b) - 2*w(b). Factor k(x).
4*x**3*(x - 2)*(x + 4)
Let o be 10*(-3)/(-6)*51/(-255)*0. Let x(k) be the third derivative of 0*k - 1/42*k**3 - 1/140*k**5 + 1/840*k**6 - 17*k**2 + o + 1/56*k**4. Factor x(w).
(w - 1)**3/7
Let d be (-15)/(-10) + 21/6. Suppose p + d*z = -p - 16, -4 = z. Determine q so that 3*q + 2*q**3 - 76*q**p + q**3 + 71*q**2 - q = 0.
0, 2/3, 1
Let n(g) be the third derivative of g**4/24 + g**3/3 - 2*g**2. Let k be n(3). Determine l so that 10 - k*l - 1 - l + 2*l**2 - 5*l**2 = 0.
-3, 1
Let v be 86/10 + 136/(-85) - 15/3. Suppose v*f**2 - 84/5 - 206/5*f = 0. Calculate f.
-2/5, 21
Let d(j) be the second derivative of -2*j**3/3 - 35*j**2/2 + 8*j. Let r be d(-10). Suppose -r*k**2 - 36 - 10*k**2 + 14*k**2 + 12*k = 0. What is k?
6
Let f = -184547 + 553649/3. Determine a, given that f*a + 0 + 2/3*a**3 - 8/3*a**2 = 0.
0, 2
Let u(a) be the second derivative of 5*a**4/12 + 1045*a**3/2 + 3125*a**2 - 8104*a. Let u(r) = 0. Calculate r.
-625, -2
Let d(y) = 4*y - 12. Let g be d(4). Let r be (6/9*-12)/(-2). Factor 4*s**2 + 4*s**g - 7*s**4 + r*s**3 + 4*s**4 - s**2.
s**2*(s + 1)*(s + 3)
Find d such that 22/3*d**2 + 0 + 16*d - 1/3*d**3 = 0.
-2, 0, 24
Let j = -377 - -322. Let c(i) = 7*i**2 - 235*i + 246. Let x(l) = -65*l**2 + 2115*l - 2215. Let o(k) = j*c(k) - 6*x(k). Factor o(u).
5*(u - 1)*(u + 48)
Suppose 325*o - 61*o - 792 = 0. Factor 0*p + 0*p**2 + 0 + 0*p**o - 1/7*p**4.
-p**4/7
Let r(k) be the first derivative of -k**4/4 - 6*k**3 - 24*k**2 - 42*k - 149. Let g be r(-15). Suppose -12/7 - 9*f**2 + 21*f**g - 72/7*f = 0. What is f?
-2/7, 1
Let q(m) = 3*m**2 + 7*m - 14. Let y(g) = -6*g**2 - 13*g + 29. Suppose -3*r + 51 = 93. Let f = 19 + r. Let a(c) = f*q(c) + 2*y(c). Find d, given that a(d) = 0.
-4, 1
Let 12 + 5 + 177*x**3 - 5*x**3 - 60*x**2 + 16*x**4 - 172*x + 11 + 16 = 0. What is x?
-11, -1, 1/4, 1
Let c(j) = 3*j**2 + 10*j. Let i(w) = -w**2 + 39*w - 195. Let x be i(33). Let p(h) = h**2 + 3*h - 1. Let f(v) = x*c(v) - 8*p(v). Factor f(m).
(m + 2)*(m + 4)
Let l = -6916/3 + 2307. Let u(h) be the first derivative of -l*h**3 - 80*h + 10 - 20*h**2. Factor u(c).
-5*(c + 4)**2
Factor -142 + 31*p + 2 + 50*p**3 + 5*p**4 - 82*p + 105*p**2 + 31*p.
5*(p - 1)*(p + 2)**2*(p + 7)
Let -1/5*c**2 + 143/5 - 142/5*c = 0. Calculate c.
-143, 1
Let u(k) be the second derivative of -19/42*k**4 - 175 + 1/70*k**5 + 17/3*k**3 - 2*k - 35*k**2. Determine g, given that u(g) = 0.
5, 7
Let o(n) = -34*n**2 - 292*n + 130. Let t be o(-9). Factor 7/2*b**2 + 1/2 + t*b.
(b + 1)*(7*b + 1)/2
Let p(t) be the first derivative of t**6/27 - 2*t**5/9 + 7*t**4/18 - 2*t**3/9 + 613. Find w, given that p(w) = 0.
0, 1, 3
Let p = -69 - -57. Let c(l) = -9*l**2 - 33*l + 60. Let t(q) = q**2 + q - 2. Let m(k) = p*t(k) - c(k). Factor m(r).
-3*(r - 4)*(r - 3)
Let d(i) be the first derivative of i**4/12 + 22*i**3/3 + 459*i**2/2 + 9248*i/3 + 4362. Factor d(l).
(l + 17)**2*(l + 32)/3
Let k = 0 + -25. Let n be (44/(-20))/(5/k). Factor 107 + p**2 - 107 - 4*p + n*p**2 + 4*p**4 - 12*p**3.
4*p*(p - 1)**3
Let u(r) be the third derivative of -r**6/60 - 5*r**5/6 - 11*r**4/2 + r**2 + 890. Factor u(d).
-2*d*(d + 3)*(d + 22)
Let u = 6 + -3. Suppose -3*y = m - 3*m + 13, -u*m + 12 = -2*y. Let -1/6*n**5 + 4/3 + 4/3*n**4 + 19/3*n**m - 14/3*n - 25/6*n**3 = 0. Calculate n.
1, 2
Let z(f) be the second derivative of 2*f**6/105 + 33*f**5/35 - f**4/21 - 22*f**3/7 + 284*f + 2. Factor z(w).
4*w*(w - 1)*(w + 1)*(w + 33)/7
Let u(b) be the second derivative of -20*b**3 + 57*b + 0 + 15/4*b**4 - 1/4*b**5 + 40*b**2. Find j, given that u(j) = 0.
1, 4
Let y be (2/(-3))/(7/(-21)). Suppose -12*n - 3*n**y + 3 - 3*n + 1 + 11*n = 0. Calculate n.
-2, 2/3
Let s be (-28578)/(-110) - 4*(-3)/(-15). Let u be (-1)/(-4) - s/(-148). Solve u*a + 5/3*a**2 + 0 - 1/3*a**3 = 0.
-1, 0, 6
Let s be -12*1 - (0 - (-61 + 83)). Solve 20/3*m**4 - s*m**2 + 35/3*m**3 + 10/3 - 35/3*m = 0 for m.
-2, -1, 1/4, 1
Let c(l) be the second derivative of l**4/12 + 331*l**3/12 - 210*l**2 - 3203*l. Factor c(k).
(k + 168)*(2*k - 5)/2
Let i(d) = -5*d**2 - 2484*d - 1493284. Let h(c) = -c**2 - 10*c. Let g(w) = -4*h(w) + i(w). Let g(z) = 0. What is z?
-1222
Let x(p) be the third derivative of 4/3*p**3 - 18*p**2 + 3/8*p**4 + 0 + 1/60*p**5 - 2*p. Suppose x(q) = 0. Calculate q.
-8, -1
Let k(q) = -q**3 - 37*q**2 - 68*q + 68. Let s be k(-35). Let m be 52/42 + s/14*4. Factor 0*f**4 + m*f - 16/9*f**2 + 4/3*f**3 + 0 - 2/9*f**5.
-2*f*(f - 1)**3*(f + 3)/9
Let j(f) be the second derivative of f**5/24 + 5*f**4/12 + 5*f**3/4 + 12*f**2 - f + 51. Let a(y) be the first derivative of j(y). Suppose a(l) = 0. What is l?
-3, -1
Let j(u) be the third derivative of 0*u - 23/60*u**5 - 17/48*u**4 - 1/35*u**7 + 62*u**2 + 0 - 43/240*u**6 - 1/6*u**3. Determine z, given that j(z) = 0.
-2, -1, -1/3, -1/4
Let c(u) = 10*u**2 + 1112*u - 157874. Let m(z) = 2*z**2 - 2*z + 8. Let n(f) = -c(f) + 6*m(f). Factor n(x).
2*(x - 281)**2
Let v(o) be the second derivative of -24/7*o**7 + o - 4*o**4 + 3/2*o**3 - 44 + 0*o**2 + 76/5*o**6 - 57/20*o**5. Let v(d) = 0. Calculate d.
-1/3, 0, 1/4, 3
Suppose -22/13*y**4 - 2/13*y**5 - 34/13*y**2 - 62/13*y**3 + 64/13*y + 56/13 = 0. Calculate y.
-7, -2, -1, 1
Let x be 138/(-23) + (1060/264 + -1 - -3). Let c(y) be the third derivative of 0 + 0*y + x*y**3 + 2*y**2 - 1/132*y**4 + 1/660*y**5. Factor c(s).
(s - 1)**2/11
Let q(p) be the second derivative of -2*p**6/195 - 19*p**5/130 - 25*p**4/78 - 8*p**3/39 - 69*p. Suppose q(o) = 0. What is o?
-8, -1, -1/2, 0
Let j(r) = r**2 + 21*r + 26. Let g be j(-20). Let p be ((-10)/(11 - g))/(3/(-2)). Factor -27*k**2 + 12*k - p.
-(9*k - 2)**2/3
Suppose -44*u - 2461654 = -2461742. Factor -60/13*i + 