 -1, 1/3, 1
Let x = 272362 + -272353. Factor 0*w + x*w**2 + 0 + 1/2*w**3.
w**2*(w + 18)/2
Let v(n) be the third derivative of -n**5/20 + 13*n**4/4 - 84*n**3 + 3*n**2. Solve v(w) = 0.
12, 14
Suppose 0 = 3*x + 42*l - 513, 311*x - 21 = 312*x - 2*l. Solve -3/7*c**4 + 0 + 27/7*c**x + 0*c**2 + 0*c = 0 for c.
0, 9
Let z = -196 - -188. Let w(i) = -2*i**4 + 2*i**3 + 3*i**2 - 7*i - 11. Let n(t) = 5*t**4 - 7*t**3 - 10*t**2 + 20*t + 32. Let m(h) = z*w(h) - 3*n(h). Factor m(s).
(s - 1)*(s + 2)**3
Let s be (-164)/(-14) + 8/28. Let o be (s/(-3) - -4) + 3. Determine m so that -8*m**4 + 22*m**4 - m**3 + 5*m**3 + 0*m**o = 0.
-2/7, 0
Let i be 76/13 - (-2)/13 - 2. Let m(v) = 8*v**3 + 4*v**2 - 6*v - 9. Let h(c) = c**3 - c + 1. Let o(q) = i*m(q) - 36*h(q). Factor o(f).
-4*(f - 3)**2*(f + 2)
Suppose -5*f - 5*p - 5 = 0, -2*f + 7 = 8*p - 9*p. Solve -2*t**4 - 2*t**4 - 153*t**f - t**4 + 55*t - 100 + 53*t**3 + 150 = 0.
-2/5, 1, 5
Let j(r) be the third derivative of -r**7/1155 + 7*r**6/165 + r**5/110 - 41*r**4/66 - 56*r**3/33 - 402*r**2 - 3*r + 2. Suppose j(b) = 0. What is b?
-1, 2, 28
Let u(v) = -v**2 - v + 6. Let z be u(-3). Suppose z*t - t - 292 = -4*m, -3*t + 86 = m. Find x such that 3*x**3 + m - 74 - 7*x**3 = 0.
0
Factor 5*u**4 - 170*u**3 + 1980*u**2 - 1195 - 8470*u + 1148 + 6702.
5*(u - 11)**3*(u - 1)
Let b(y) be the second derivative of 2*y**6/15 + 4*y**5 + 134*y**4/3 + 680*y**3/3 + 450*y**2 - 3*y + 83. Factor b(h).
4*(h + 1)*(h + 5)**2*(h + 9)
Let d(k) be the second derivative of -32/9*k**3 - 8*k + 256/3*k**2 + 1/18*k**4 - 1. Solve d(z) = 0.
16
Suppose 6*k = -2737 + 13021. Let m = k + -8559/5. Factor -m - 57/10*x - 1/2*x**2.
-(x + 11)*(5*x + 2)/10
Determine d, given that -2/7*d**3 - 4333440368/7 - 10046616/7*d - 7764/7*d**2 = 0.
-1294
Let k(a) = 3*a - 12. Let u be k(0). Let p be ((-2)/(-3))/(u/(-360)). Factor 3 + 23*m**3 - 11 + p*m - 19*m**3 - 16*m**2.
4*(m - 2)*(m - 1)**2
Let a = -7 + 10. Let g be (4257/(-483))/(-11) + (-5)/(345/6). Factor 3/7*r**2 + g*r - 9/7*r**a + 4/7*r**4 - 3/7.
(r - 1)**3*(4*r + 3)/7
Let h be ((-1)/4)/(249/(-664)) + 94/21. Let s(x) be the first derivative of -4/21*x**3 + 26 + 16/7*x**2 + h*x. Suppose s(c) = 0. Calculate c.
-1, 9
Let d(h) be the first derivative of -44*h**5/5 - 16*h**4 - 20*h**3/3 + 11393. Factor d(z).
-4*z**2*(z + 1)*(11*z + 5)
Suppose 0 = h + h - 2*o - 4, -4 = -2*o. Suppose -s + h*s = m + 4, 4 = 2*s. Solve 0 + 1/5*w**m + 3/5*w = 0 for w.
-3, 0
Suppose 4136*p**3 + 868*p**2 + 11245*p**3 + 9042*p - 59*p**5 + 11*p**5 - 24787*p**2 - 1470 + 552*p**4 + 462 = 0. What is p?
-14, 1/4, 1, 24
Let z(i) = -i**4 - i**2. Let k(h) = -28*h**4 - 488*h**3 - 2756*h**2 - 484*h. Let n(d) = k(d) - 6*z(d). Find m such that n(m) = 0.
-11, -2/11, 0
Let k = 119 - 243. Let o be (k/56 + 2)*-8. Suppose -4/7*u**3 + 0*u**2 + o*u + 8/7 = 0. What is u?
-1, 2
Let b(r) be the second derivative of -5*r**7/273 - 6*r**6/65 - 7*r**5/130 + r**4/3 + 4*r**3/13 - 8*r**2/13 + 970*r. Let b(g) = 0. Calculate g.
-2, -1, 2/5, 1
Let t(w) be the first derivative of 1/2*w**3 + 13 + 3*w + 1/5*w**4 + 3/5*w**2 + 3/100*w**5. Let q(j) be the first derivative of t(j). Factor q(c).
3*(c + 1)**2*(c + 2)/5
Let n(m) be the first derivative of m**3/15 + 149*m**2/5 - 1208*m/5 - 3362. Let n(y) = 0. What is y?
-302, 4
Determine v, given that 543/5*v - 276/5*v**2 + 3/5*v**3 - 54 = 0.
1, 90
Let w = -3142/45 + 632/9. Let g(n) be the first derivative of -w*n**5 + 1/6*n**6 + 2*n**2 + 0*n - 7 - 3/4*n**4 + 4/3*n**3. Factor g(c).
c*(c - 2)**2*(c + 1)**2
Suppose -12*k + 67*k = -95*k + 450. Let u(r) be the first derivative of 0*r + 0*r**2 + 42 - 16/55*r**5 + 5/22*r**4 + 4/33*r**6 - 2/33*r**k. Factor u(v).
2*v**2*(v - 1)*(2*v - 1)**2/11
Let p(n) be the third derivative of n**5/30 - 59*n**4/6 - 2*n**2 - 1729. Factor p(i).
2*i*(i - 118)
Let f(v) be the first derivative of 2/3*v**3 - 18*v - 58 + 8*v**2. Solve f(b) = 0.
-9, 1
Let l(y) = 26*y**5 - 22*y**4 + 14*y**3 + 6*y**2 + 8. Let m(d) = -d**5 - d**4 - d**2 - 1. Let z(x) = -l(x) - 8*m(x). Solve z(c) = 0.
0, 1/3, 1
Let q(t) be the second derivative of -5*t**4/48 - 155*t**3/12 + 315*t**2/8 + 808*t. Suppose q(f) = 0. Calculate f.
-63, 1
Suppose -29*m + 135 = -2*m. Suppose -5*j + m*j + 18*j = 0. Find o, given that -2/11*o**2 + j + 2/11*o = 0.
0, 1
Suppose -20 = 4*p + 189*c - 185*c, 3*p - 20 = 2*c. Let v(k) be the first derivative of 12*k + 23*k**p + 40 + 5/2*k**4 + 44/3*k**3. Factor v(z).
2*(z + 1)*(z + 3)*(5*z + 2)
Let a(x) be the third derivative of -x**8/784 + x**7/245 + 13*x**6/280 + x**5/14 + 428*x**2. Determine u, given that a(u) = 0.
-2, -1, 0, 5
Let h(z) be the second derivative of -2/33*z**3 + 6/11*z**2 + 0 - 1/132*z**4 + 9*z. Solve h(a) = 0 for a.
-6, 2
Let z(p) be the third derivative of 4*p**6/15 + 11*p**5/15 - 31*p**4/2 - 24*p**3 + 4*p**2 - 20*p. Factor z(r).
4*(r - 3)*(r + 4)*(8*r + 3)
Suppose -2*c = k - 80, 11*c + 27 = 12*c - 6*k. Let a be (-29)/(-9) - (18 - 689/c). Solve 2/9*z**3 - 4/3 + a*z - 16/9*z**2 = 0 for z.
1, 6
Let x(k) = -55*k**2 + 632*k - 96. Let z be 10/55 + 155/55. Let d(r) = 54*r**2 - 632*r + 96. Let u(q) = z*d(q) + 2*x(q). Factor u(f).
4*(f - 12)*(13*f - 2)
Let c = -320461/4 - -80522. Let n = 407 - c. Factor -n*a**2 + 7/4*a - 3/2.
-(a - 6)*(a - 1)/4
What is s in 8/7*s + 2/7*s**4 - 236/7*s**2 - 8/7*s**3 + 234/7 = 0?
-9, -1, 1, 13
Let b(a) be the second derivative of a**4/3 + 2336*a**3 + 6139008*a**2 - 2454*a. Let b(l) = 0. What is l?
-1752
Let p(t) be the third derivative of -t**8/108 - 4*t**7/63 - 4*t**6/135 + 112*t**5/135 + 8*t**4/3 + 64*t**3/27 - 34*t**2 - t. What is j in p(j) = 0?
-2, -2/7, 2
Let s = 2311/308 + -205/28. Factor 0 - 8/11*c**2 + s*c**4 - 4/11*c**3 + 16/11*c.
2*c*(c - 2)**2*(c + 2)/11
Let l(c) = -8*c**3 - 8*c**2 - 12*c. Let r(y) = -y**3 - y. Let i = 46 - 55. Let n be 14/(-49) + i/(-7) + -2. Let s(v) = n*l(v) + 6*r(v). Factor s(w).
2*w*(w + 1)*(w + 3)
Let v(w) = w**4 + w**2. Let m = -9 + 14. Let u(i) be the second derivative of i**6/10 + 7*i**4/12 + 21*i. Let k(o) = m*v(o) - u(o). Factor k(h).
2*h**2*(h - 1)*(h + 1)
Let c(y) be the first derivative of 3*y**6/7 - 26*y**5/7 - 499*y**4/14 + 2614*y**3/7 - 954*y**2 + 2592*y/7 - 5478. Let c(v) = 0. What is v?
-8, 2/9, 3, 9
Let a(m) be the first derivative of -m**3/6 + 143*m**2 + 1060. Factor a(w).
-w*(w - 572)/2
Suppose 21*i + 2970 = 27*i. Let x = -493 + i. Find a such that -1/8 - 3/8*a - 1/8*a**3 - 3/8*a**x = 0.
-1
Let w = 102 + -304/3. Suppose 158*n - 176*n = -36. Factor 0 - 1/3*o**n - w*o.
-o*(o + 2)/3
Let c(f) be the first derivative of 15 + 1/2*f**3 + 7/240*f**6 + 4*f**2 - 2/15*f**5 + 0*f - 17/48*f**4. Let o(p) be the second derivative of c(p). Factor o(g).
(g - 3)*(g + 1)*(7*g - 2)/2
Suppose -8 = -3*h + 25. Suppose -8*z + 11 = h. Factor -1/5*c**3 - 1/5*c + z - 2/5*c**2.
-c*(c + 1)**2/5
Let l(i) be the first derivative of 67 - 1/2*i**3 - 9*i**2 - 54*i. Let l(p) = 0. Calculate p.
-6
Let u(c) = -4*c**2 + 27*c + 12. Suppose 13*r = -46 + 137. Let a be u(r). Solve 5/2*m**a + 15/2*m + 0*m**4 - 5*m**2 + 5 - 10*m**3 = 0 for m.
-1, 1, 2
Let y be 40/140 - 19/(-7). Solve -u**y - 10*u - 33*u**2 + 70*u**2 + 5*u - 33*u**2 + 1 + 1 = 0 for u.
1, 2
Suppose 1487*d - 6842 = 1176*d. Let z(j) be the second derivative of -52/5*j**3 - 4/5*j**2 - d - 507/10*j**4 - j. Find p such that z(p) = 0.
-2/39
Let b(y) = 27*y + 354. Let n be b(-13). Let m be (n - -3)/(70/56). What is w in m*w - 9/5*w**4 - 7/5*w**2 - 1/5*w**5 + 16/5 - 23/5*w**3 = 0?
-4, -1, 1
Let p(s) be the third derivative of 0 + 0*s - 1/240*s**5 - 69*s**2 - 7/32*s**4 - 5/6*s**3. Find h, given that p(h) = 0.
-20, -1
Let m be ((-6)/4 - -1)/(12/(-96)). Let z(y) be the second derivative of 0*y**2 + 1/60*y**5 + 1/36*y**m + 12*y - 1/18*y**3 + 0 - 1/90*y**6. Factor z(w).
-w*(w - 1)**2*(w + 1)/3
Suppose -q - 2 + 1 = 2*i, q = 4*i - 13. Factor -71*l**2 - 13*l + l**4 + i*l**4 - 33*l**3 + 152*l**2 + 24 - 62*l.
3*(l - 8)*(l - 1)**3
Suppose 23*o**2 + 5193*o**4 + 20*o + 37*o**2 - 5178*o**4 + 55*o**3 = 0. What is o?
-2, -1, -2/3, 0
Let d(a) = 73*a - 290. Let r be d(4). Let z(s) be the second derivative of -1/6*s**3 - 16*s - 1/16*s**4 + 0 - 3/16*s**r + 1/240*s**6 + 0*s**5. Factor z(c).
(c - 3)*(c + 1)**3/8
Suppose -t = -18*t - 2*t. Suppose -100 = 85*u - 135*u. Factor 8/7*y - 10/7*y**u + 2/7*y**3 + t.
2*y*(y - 4)*(y - 1)/7
Let d = 6469 - 6469