)/3
Let k = 3449/2 - 1724. Suppose k*c**2 + 1/2*c**3 + 0 - c**4 + 0*c = 0. Calculate c.
-1/2, 0, 1
Let h(w) be the third derivative of w**8/2352 + w**7/294 + w**6/84 + w**5/42 + 5*w**4/168 + w**3/42 + 368*w**2. Factor h(l).
(l + 1)**5/7
Let b = 12 - 8. Suppose -4*w + f + 1 = -b*f, 2*f - 22 = -4*w. Factor -c**5 + 18*c**4 - 2 - w*c**3 - c**4 - 13*c**4 + 5*c - 2*c**2.
-(c - 2)*(c - 1)**3*(c + 1)
Let t(h) be the third derivative of h**8/112 + 12*h**7/35 + 24*h**6/5 + 128*h**5/5 + 11*h**2. Factor t(p).
3*p**2*(p + 8)**3
Let r = -1/336 + 2029/4368. What is o in r*o**2 - 6/13 - 16/13*o = 0?
-1/3, 3
Let r be (1*2)/((-8)/5 + 2). Suppose 19*h**2 + 7*h**4 - 3 + h**5 + 2 + 16*h + 19*h**3 + r + 6*h**2 = 0. What is h?
-2, -1
Suppose -s = s - 74. Let h = -35 + s. Determine q so that 0*q**3 + 0 - 1/2*q**4 + 3/2*q**h - q = 0.
-2, 0, 1
Find j such that 39/8*j**2 + 9/4*j + 1/8*j**5 + 0 + 9/8*j**4 + 29/8*j**3 = 0.
-3, -2, -1, 0
Let q be 0 + 2 - (-14)/56*128/(-17). Solve 22/17*r + q*r**3 - 18/17*r**2 + 2/17*r**4 - 8/17 = 0 for r.
-4, 1
Let v = 1 - 1. Let n = -856 + 3425/4. Factor v*p - 1/4 + n*p**2.
(p - 1)*(p + 1)/4
Let s = -4 - -6. Let k = 31 + -22. Factor 3*o**3 - 5*o**2 + 0*o - 3 - 4*o**s + k*o.
3*(o - 1)**3
Let p(h) = -h - 8. Let b be p(-10). Solve 20*o - 5*o**b + 10*o**2 - 2*o**2 - 5*o**2 - 50 = 0 for o.
5
Let l = 68/3 + -67/3. Let j(i) be the first derivative of 4*i**2 + 16*i - 6 + l*i**3. Factor j(b).
(b + 4)**2
Let w(o) be the first derivative of -o**6/15 + 18*o**5/25 + 21*o**4/10 + 22*o**3/15 + 377. Factor w(h).
-2*h**2*(h - 11)*(h + 1)**2/5
Suppose -3*l + 2*c = -c + 18, -2*l = 3*c - 3. Let f(q) = q**3 + 3*q**2 + 4. Let a be f(l). Factor 2*u**4 + u**a - 3*u**3 - 6*u**4.
-3*u**3*(u + 1)
Suppose 2*l + 11 = 17. Factor -8*s**2 - 169*s**3 + 84*s**3 + 89*s**l.
4*s**2*(s - 2)
Let r(v) be the second derivative of 21/20*v**5 + 0 - 24*v**2 + 3*v**4 + 2*v + 1/10*v**6 - 2*v**3. Let r(a) = 0. Calculate a.
-4, -2, 1
Let k be 4/((-6)/(-10) + -6 + (-1026)/(-90)). Factor 0*t - k*t**2 + 0.
-2*t**2/3
Let x(w) be the first derivative of w**5/10 - 7*w**3/2 - 5*w**2 + 317. Let x(a) = 0. Calculate a.
-4, -1, 0, 5
Let u(o) be the second derivative of -1/72*o**4 - 1/3*o**2 - 1/9*o**3 + 0 - 32*o. Determine j, given that u(j) = 0.
-2
Let z(j) = j**3 + j**2 + 3*j. Let f(r) = 23*r**3 - 529*r**2 + 365*r - 58. Let o(h) = f(h) - 5*z(h). Solve o(p) = 0 for p.
1/3, 29
Let n(p) be the first derivative of -p**4/32 + p**3/12 + p**2/4 - p + 63. Let n(s) = 0. What is s?
-2, 2
Suppose 16*o - 24*o = -160. Suppose -8*y**4 - o*y**3 + 0 - 3/2*y + 23/2*y**2 = 0. Calculate y.
-3, 0, 1/4
Let b = 9 - 8. Let i(p) = 2*p**2 - 6. Let o be i(-3). Let -b - o*w - w**2 + 25*w - 15*w = 0. What is w?
-1
Suppose 0 = 3*g - 0 - 12. Let -16 - 104*x**2 - 43*x**3 - 11*x**g - 23*x - 33*x - x**5 + 31*x**2 = 0. What is x?
-4, -1
Let o be 1/6 - (-4)/24*11. Factor -3*b**o - b**2 + 3*b**2 + 3*b**2 - 2.
2*(b - 1)*(b + 1)
Let v(j) be the second derivative of -1/12*j**4 + 1/6*j**3 + 0*j**2 + 0 - 22*j. Determine w so that v(w) = 0.
0, 1
Let r(j) = -j**2 + j. Let m(d) = -40*d**2 + 8*d + 19*d**2 + 13*d**2. Let f(b) = -2*m(b) + 14*r(b). Factor f(i).
2*i*(i - 1)
Let x(j) = -j - 10. Let p be x(-14). Factor -2 - 6*u**4 - 9*u**2 + 17*u**2 + 4 + 2*u**5 + p*u**3 - 6*u - 4*u**2.
2*(u - 1)**4*(u + 1)
Let z = 30869/3 + -10285. Suppose 0 + 2/3*p**5 + 10/3*p**4 + z*p**2 + 4/3*p + 6*p**3 = 0. Calculate p.
-2, -1, 0
Let b(i) be the third derivative of i**5/15 - 2*i**4 - 26*i**3/3 + 23*i**2 - 2. Factor b(n).
4*(n - 13)*(n + 1)
Let a be 6/(-10)*5 - 1*-5. Factor 4/7*w**5 + 32/7*w + 4/7*w**4 - 20/7*w**3 - 4/7*w**a - 16/7.
4*(w - 1)**3*(w + 2)**2/7
Let f(b) be the second derivative of b**7/441 - b**6/45 + 3*b**5/35 - 11*b**4/63 + 13*b**3/63 - b**2/7 - 329*b. Factor f(y).
2*(y - 3)*(y - 1)**4/21
Let s(h) be the second derivative of 2/15*h**6 - h**2 - 1/6*h**4 + 0 - 5/6*h**3 + 17*h + 1/5*h**5 + 1/42*h**7. Solve s(d) = 0 for d.
-2, -1, 1
Let s be (-7824)/(-3840) - (4 - (4 + -2)). Let z(o) be the second derivative of -1/8*o**4 + 0 + 3/4*o**2 - 1/8*o**3 + 4*o + s*o**5. Let z(w) = 0. What is w?
-1, 1, 2
Let d = 7946 + -7944. Factor -8/5*c + 2/5*c**d + 8/5.
2*(c - 2)**2/5
Factor -3/4*t - 1/8*t**2 - 1.
-(t + 2)*(t + 4)/8
Let h = -6074/5 - -1216. Let k(x) be the third derivative of h*x**5 - 10/3*x**4 + 0*x + 7*x**2 + 0 + 2/105*x**7 + 16/3*x**3 - 7/30*x**6. Factor k(l).
4*(l - 2)**3*(l - 1)
Let b be (10 + -3 - 2) + 3. Suppose -8 = 4*y - b*y. Solve -y - 3*q**4 - 1 + 5*q**3 - 6*q + q**3 + 6 = 0.
-1, 1
Let t(x) = 2 - 5*x**3 - 1 + 2 - 3*x + 5*x**2. Let o(i) = 5*i**2 + i - 6*i**2 + i**3 - 3 + 2. Let g(j) = 3*o(j) + t(j). Factor g(n).
-2*n**2*(n - 1)
Suppose -5*f + 10 = 5*q, 0 - 6 = 2*q + 4*f. Suppose y**2 + q*y**2 - 3*y**2 = 0. Calculate y.
0
Suppose 96 - 4*m**3 - 3*m**2 + 0*m**3 + 2*m**4 + 5*m**2 - 96 = 0. What is m?
0, 1
Let m(a) = 6*a**3 - 2*a**2 - a - 3. Suppose 5*t + 101 - 26 = 0. Let k(w) = -w**3 - w**2 + w + 1. Let d(y) = t*k(y) - 5*m(y). Factor d(p).
-5*p*(p - 1)*(3*p - 2)
Let -3/4*c**5 + 0 - 3/4*c**4 + 3/4*c**2 + 3/4*c**3 + 0*c = 0. What is c?
-1, 0, 1
Suppose 0*t - 83*t - 81 = -413. Factor -4/11*c**3 - 12/11*c**2 + 1/11*c**t + 64/11 + 32/11*c.
(c - 4)**2*(c + 2)**2/11
Let x(m) = -39*m + 195. Let r be x(5). Let i(p) be the first derivative of 0*p + r*p**2 + 3 - 4*p**3 - 4/5*p**5 + 4*p**4. Suppose i(o) = 0. Calculate o.
0, 1, 3
Factor -107/3*u - 36 + 1/3*u**2.
(u - 108)*(u + 1)/3
Suppose 4*d - 27*m + 25*m + 8 = 0, -4*d - 12 = -3*m. Factor 7/5*j**5 + d*j**3 + 0*j**2 + 0*j + 0 - 2/5*j**4.
j**4*(7*j - 2)/5
Let h be (-1)/((-8)/7 - -1). Suppose l - 5 = -3*c, -3*c + 3*l + 3 = -6. Factor -h*k**2 + k**3 + 11*k**c - k**4 - k - 3*k**2.
-k*(k - 1)**2*(k + 1)
Let d(h) be the first derivative of -7*h**4/30 + 16*h**3/45 + h**2/3 - 4*h/5 - 122. Determine b, given that d(b) = 0.
-6/7, 1
Factor -1/5*b**2 - 14/5*b - 24/5.
-(b + 2)*(b + 12)/5
Find r, given that -3 + 4*r**2 + 0*r + 1 - 3*r + 1 = 0.
-1/4, 1
Let i be (-4 + (7 - 175/28)*6)*0. Find m, given that -6/5*m**4 + 6/5*m**2 + 0 - 2/5*m**3 + 2/5*m**5 + i*m = 0.
-1, 0, 1, 3
Let t(f) = f - 32 - 18 + f**2 + 50. Let o(w) = 6*w**2 + 5*w. Suppose -2 = -5*v - 7, 2*s = -2*v. Let j(i) = s*o(i) - 5*t(i). Solve j(m) = 0 for m.
0
Let n(p) = 4*p**4 + 10*p**3 + 5*p**2 - 25*p + 21. Let l(y) = -y**4 - y**3 - y**2 + y - 1. Let o(j) = 5*l(j) + n(j). Suppose o(t) = 0. Calculate t.
-2, 1, 2, 4
Let w(j) = j**3 - 10*j**2 - 6*j - 7. Let z be w(11). Suppose 0 = 2*t + t - z. Factor 3*c**4 - 3*c**2 - 16 - 3*c + t + 3*c**3.
3*c*(c - 1)*(c + 1)**2
Suppose 6*i - 4*c - 8 = i, 0 = 3*i + 3*c + 6. Let s(r) = -r + 6. Let l be s(3). Determine d, given that -4 + l*d + 8 + 14*d**2 - 21*d + i = 0.
2/7, 1
Let s(t) = 7*t**2 + 29*t - 30. Let a(j) = -95*j**2 - 405*j + 420. Let l(z) = 4*a(z) + 55*s(z). Factor l(f).
5*(f - 3)*(f - 2)
Factor 4/3 - 1/3*a - 1/6*a**2.
-(a - 2)*(a + 4)/6
Find z, given that 1/2*z + 13/3*z**3 + 0 - 8/3*z**2 + 1/2*z**5 - 8/3*z**4 = 0.
0, 1/3, 1, 3
Let a(o) = -7*o**2 + o - 4. Suppose 2*r - 21 = 21. Suppose 0 = 5*s - 5 - 15. Let y(q) = 36*q**2 - 6*q + 21. Let v(k) = r*a(k) + s*y(k). Factor v(f).
-3*f*(f + 1)
Suppose 0*l + 4 = l + 3*j, -5*l - 4*j - 24 = 0. Let w = -4 - l. Solve 2*c**2 - 4*c**4 + 3*c**3 + c**w + 6*c**3 - 8*c**2 = 0 for c.
0, 1, 2
Let a = -873/77 - -153/11. Factor 22/7*f + 8/7 + a*f**2 + 2/7*f**3 - 2/7*f**4.
-2*(f - 4)*(f + 1)**3/7
Let a(q) be the third derivative of 27*q**2 - 19/210*q**5 + 0 + 0*q**3 - 5/84*q**4 + 1/105*q**6 + 0*q. Factor a(m).
2*m*(m - 5)*(4*m + 1)/7
Let s be 372/52 + -7 + (-14)/(-78). Let i(b) be the second derivative of 0 - s*b**3 + 1/2*b**2 - 5*b + 1/12*b**4. Factor i(l).
(l - 1)**2
Suppose 13*u - 6*u = 23555. Factor -2*h**2 - u*h + 3365*h.
-2*h**2
Let p(l) = -17 - 13 + 4 + 4 + 4*l. Let w be p(6). Determine o so that -1/5*o - 2/5 + 1/5*o**3 + 2/5*o**w = 0.
-2, -1, 1
Let x be 183/(-9)*((-22)/16 - -1). Let w = x - 25/8. Factor 7/2*y**2 - 15/2*y + w - 1/2*y**3.
-(y - 3)**2*(y - 1)/2
Determine t, given that -81/2*t - 27 + 3/2*t**4 + 9/2*t**3 - 21/2*t**2 = 0.
-3, -2, -1, 3
Let -2/13*b**3 + 20/13*b - 32/13 + 14/13*b**2 = 0. Calculate b.
-2, 1, 8
Let p = 1116 - 1114. Let w(g) be the second derivative of -1/7*g**p - 7*g - 2/21*g**3 - 1/42*g**4 + 0. Factor w(a).
-2*(a + 1)**2/7
Suppose -1000 = z + 7*z. Let w