4/6 + 21/9. Suppose -3*o = -2*o - 2*z + 7, -o + 23 = 4*z. Factor 5*w**4 - 4*w**o + 20*w - 15 - 13*w**i - 3*w**3 + 10*w**2.
5*(w - 3)*(w - 1)**2*(w + 1)
Let g = -1781690/11 - -161972. Factor 8/11*i**3 - 32/11*i + 32/11 - g*i**4 + 0*i**2.
-2*(i - 2)**3*(i + 2)/11
Let a(i) be the second derivative of 0 + 129*i + 1/6*i**4 + 20/3*i**3 - 44*i**2. Factor a(l).
2*(l - 2)*(l + 22)
Let v = 289999/42 - 41419/6. Factor -12/7*o - 1/7*o**2 - v.
-(o + 1)*(o + 11)/7
Let k(q) be the first derivative of q**5/5 - 17*q**4/4 + 32*q**3 - 104*q**2 + 128*q + 1735. Factor k(v).
(v - 8)*(v - 4)**2*(v - 1)
Let o = 5 + -41. Let j = o - -38. Factor 0*x + 14*x - 4*x**2 - 8 - j*x.
-4*(x - 2)*(x - 1)
Suppose 0 = -44*u - 476 + 476. Let r(x) be the second derivative of -1/8*x**3 - 1/4*x**2 + u - 35*x - 1/48*x**4. Factor r(z).
-(z + 1)*(z + 2)/4
Let q(t) be the second derivative of -t**6/2 - 20*t**5 + 45*t**4/4 - 2086*t. Factor q(i).
-5*i**2*(i + 27)*(3*i - 1)
Suppose 11*i + 3880 = -762. Let h = i - -425. Suppose 6*b - 8/3 + 2/3*b**h - 4*b**2 = 0. Calculate b.
1, 4
Let p(z) be the first derivative of -7*z**5 + 865*z**4/4 - 4055*z**3/3 + 4755*z**2/2 + 1710*z - 1525. Solve p(f) = 0 for f.
-2/7, 3, 19
Suppose -6006*w + 6096*w = 243 - 63. Factor -18/5*v**w - 28/5 + 46/5*v.
-2*(v - 1)*(9*v - 14)/5
Let n(d) = d**3 - 30*d**2 + 22*d - 205. Let u be n(29). Let t = u - -410. Factor -2/5*b + 2/5*b**3 - 2/5 + 2/5*b**t.
2*(b - 1)*(b + 1)**2/5
Let b = -3879 - -3883. Let d(a) be the first derivative of -23 + 0*a + 3*a**2 + 1/3*a**6 + 12/5*a**5 + 6*a**b + 20/3*a**3. Suppose d(s) = 0. Calculate s.
-3, -1, 0
Let k = 51137659/63420 + 1/63420. Let r = k - 805. Factor -2/3*v**2 + 2/3*v**4 + 4/3*v - r*v**3 + 0.
2*v*(v - 2)*(v - 1)*(v + 1)/3
Let s be 7/98 + (-2)/(224/(-248)). Suppose 4/7*u**4 + 0*u**2 - 2/7*u**5 + s*u**3 + 0 + 0*u = 0. Calculate u.
-2, 0, 4
Let x = 1906 - 1830. Suppose -28*h = -x*h. Determine o, given that 8/9*o**2 + h - 8/9*o**4 + 2/3*o - 2/3*o**3 = 0.
-1, -3/4, 0, 1
Suppose -58 = -b + 531. Let f = 589 - b. Factor f - 3/2*l**3 + 0*l - 1/3*l**2.
-l**2*(9*l + 2)/6
Let h = -5470 - -5465. Let w(x) = x - x**2 + 5*x - 5*x + 1. Let s(z) = -30*z**2 - 15*z - 5. Let q(k) = h*w(k) - s(k). Factor q(u).
5*u*(7*u + 2)
Let w be 64/18*3/4. Suppose 4*c = 4*r + 12, -1 = 383*r - 382*r. Factor 8/3*m - w - 2/3*m**c.
-2*(m - 2)**2/3
Let s be (-144)/(-120)*(-260)/6. Let i(z) = -18*z**2 - 260*z + 278. Let o(n) = 2*n**2 + 29*n - 31. Let v(x) = s*o(x) - 6*i(x). Factor v(a).
4*(a - 1)*(a + 14)
Solve 1728/7*x - 248832/7 - 3/7*x**2 = 0 for x.
288
Suppose 0 = 68*p - 55605 + 55333. Factor -10/3*x**3 - p - 1/3*x**4 - 29/3*x**2 - 32/3*x.
-(x + 1)**2*(x + 2)*(x + 6)/3
Suppose -4*s - x + 5 = 0, 5*s - 4*s = -5*x - 13. Solve 6*t**3 + 19*t**s + 6*t**2 + 45*t - 9*t**3 + 17*t**2 = 0.
-1, 0, 15
Let h(p) be the first derivative of 3/4*p**4 + 3*p + 33 - p**3 - 3/2*p**2. Factor h(b).
3*(b - 1)**2*(b + 1)
Suppose -6972 = 30*i - 16*i. Let f = i - -500. Factor -1/3*d - 1/2 + 1/6*d**f.
(d - 3)*(d + 1)/6
Let l(o) be the second derivative of o**5/5 + 14*o**4/3 + 64*o**3/3 - 256*o**2 + 4363*o. Factor l(m).
4*(m - 2)*(m + 8)**2
Determine b so that 8/7*b**3 + 578/7*b + 584/7*b**2 + 144/7 = 0.
-72, -1/2
Let p(r) be the second derivative of 0 + 1/45*r**6 - 11/30*r**5 - 28/9*r**3 + 0*r**2 - 182*r + 16/9*r**4. Factor p(c).
2*c*(c - 7)*(c - 2)**2/3
Let h(p) be the third derivative of -p**6/240 - 25*p**5/24 - 61*p**4/6 - 121*p**3/3 + 558*p**2. Factor h(b).
-(b + 2)**2*(b + 121)/2
Let m = 141571/66 + -2145. Let b(q) be the third derivative of 1/11*q**3 - 1/330*q**5 + 14*q**2 + 0 + 0*q + m*q**4. Factor b(h).
-2*(h - 3)*(h + 1)/11
Let p(w) = -3*w - 6. Let r be p(-3). Suppose 6*t - 27 = r*t. Factor t*c - c**2 + 0*c + 21 - 15 + 4*c**2.
3*(c + 1)*(c + 2)
Let w(c) be the first derivative of c**6/90 - c**5/5 + 12*c**3 + 104. Let f(h) be the third derivative of w(h). Factor f(p).
4*p*(p - 6)
Let m(b) be the second derivative of b**6/15 - 13*b**5/10 + 11*b**4/3 + 2135*b. Find u such that m(u) = 0.
0, 2, 11
Let f be (-6765)/(-10) + (-2)/(-4). Let u = f + -674. Find d such that 4/5*d**2 + d**u + 1/5*d + 0 + 2/5*d**4 = 0.
-1, -1/2, 0
Let c = 47/225 + 9/50. Let h = 167/126 + c. Factor 3/7*n**2 + 9/7 + h*n.
3*(n + 1)*(n + 3)/7
Let o(n) = 7*n**2 - 1112*n - 304716. Let c(r) = -19*r**2 + 3334*r + 914145. Let u(t) = -4*c(t) - 11*o(t). Factor u(p).
-(p + 552)**2
Suppose 13 = 8*p - 11. Solve 140*u - 14 + 4*u**p + 4*u**3 - 76*u**2 - 4*u**3 - 54 = 0.
1, 17
Let l(v) = -v**4 - v**3 - 2*v + 1. Let w(h) = -28*h**4 - 313*h**3 - 96*h**2 + 22*h - 11. Let f(j) = -11*l(j) - w(j). Factor f(r).
3*r**2*(r + 8)*(13*r + 4)
Let h(i) be the second derivative of i**7/3780 - i**6/1080 - 3*i**4/2 + i**3/3 - i + 7. Let c(q) be the third derivative of h(q). Factor c(o).
2*o*(o - 1)/3
Let i(j) = -3*j**2 + 6582*j + 3544713. Let f(v) = v**2 - 10*v - 1. Let p(l) = -6*f(l) - i(l). Factor p(r).
-3*(r + 1087)**2
Find c, given that 1/9*c**2 - 44/9*c - 92/9 = 0.
-2, 46
Factor -143*c + 71 - 881*c**2 + 476*c**2 + 478*c**2 - c**3.
-(c - 71)*(c - 1)**2
Let z = 147053/35 - 29195/7. Factor z*k**3 + 98/5*k**4 + 64/5*k**2 + 0 + 8/5*k.
2*k*(k + 1)*(7*k + 2)**2/5
Let x = 3622 - 21707/6. Let k(r) be the second derivative of 5/12*r**4 - 4*r + 15/2*r**2 - 1/4*r**5 + 0 + x*r**3. Factor k(q).
-5*(q - 3)*(q + 1)**2
Let m(a) be the first derivative of 0*a - 3/32*a**4 + 0*a**2 + 56 + 7/4*a**3. Factor m(z).
-3*z**2*(z - 14)/8
Let n = -2447 - -2451. Let f(g) be the first derivative of -g**5 + 14 + 35/4*g**n + 270*g - 135/2*g**2 - 15*g**3. Factor f(o).
-5*(o - 3)**3*(o + 2)
Find t, given that 181/2*t**4 - 1/2*t**5 - 90128*t - 4484*t**3 + 35354*t**2 + 59168 = 0.
1, 4, 86
Factor 0 - 64*m + 10/9*m**3 - 104/9*m**2.
2*m*(m + 4)*(5*m - 72)/9
Let x(k) = -k**4 - k**3 - 2. Let w(o) = 60*o**3 + 4*o**2 + 0*o**2 - 3732*o**4 + 3664*o**4 - 4*o - 8. Let p(t) = w(t) - 4*x(t). Solve p(i) = 0 for i.
-1/4, 0, 1/4, 1
Factor -1/4*i**2 - 1/2*i + 323/4.
-(i - 17)*(i + 19)/4
Let m = 4824 + -173677/36. Let d = -1/4 - m. Find c, given that d*c**2 - 4/9*c + 1/3 = 0.
1, 3
Let l(t) be the first derivative of -t**3/3 - 19*t**2/2 + 68*t + 134. Let g be l(-22). Factor -9/2*u**g - 1/2*u**3 - 15/2*u + 25/2.
-(u - 1)*(u + 5)**2/2
Let r(l) be the third derivative of l**5/120 - 403*l**4/24 + 162409*l**3/12 - 2*l**2 - 578*l. Find o such that r(o) = 0.
403
Let x(p) be the second derivative of 13/30*p**4 - 1 - 4*p + 11/5*p**2 - 1/50*p**5 - 23/15*p**3. Find v, given that x(v) = 0.
1, 11
Let k(t) be the first derivative of -3*t**4/4 - t**3 + 6*t**2 + 12*t + 8207. Determine g, given that k(g) = 0.
-2, -1, 2
Let j(i) be the third derivative of i**8/336 + 47*i**7/1050 - i**6/20 - 480*i**2. Factor j(x).
x**3*(x + 10)*(5*x - 3)/5
Suppose -89 = 6*m - 113. Suppose -17*b + 226 = 209. Solve -2*d**m - 9/2*d + 9/2*d**3 + b + d**2 = 0 for d.
-1, 1/4, 1, 2
Let q(u) = -12*u**3 - 171*u**2 + 372*u + 1401. Let k(a) = 9*a**3 + 170*a**2 - 372*a - 1398. Let t(w) = 3*k(w) + 2*q(w). Let t(h) = 0. What is h?
-58, -2, 4
Let z(u) be the first derivative of 5*u**3 - 3/5*u**5 - 12*u + 0*u**2 + 66 + 0*u**4. What is n in z(n) = 0?
-2, -1, 1, 2
Let m(y) be the third derivative of -y**7/280 - 3*y**6/160 - y**5/40 - 3*y**2 + 84. Solve m(x) = 0.
-2, -1, 0
Let d(c) be the third derivative of -1/60*c**6 + 0*c + 1/630*c**7 - 1/6*c**3 + 1/1008*c**8 + 6 - 7/90*c**5 - 2*c**2 - 11/72*c**4. Factor d(f).
(f - 3)*(f + 1)**4/3
Let o be 12 + (56/30 - 10/(-75)). Suppose -4*t = -o - 6. Suppose -6*v + 25*v**4 - 6*v**3 - 10*v**3 - 10*v**4 + 21*v**2 - 3*v**t - 11*v**3 = 0. Calculate v.
0, 1, 2
Let h be ((-136)/30)/((-324)/(-540)) - -18. Factor 2209/9 + 1/9*i**2 + h*i.
(i + 47)**2/9
Let p = 95 - 101. Let i be 9/p*(-14)/105*20. What is k in -2/3*k**2 + 14/3*k - i = 0?
1, 6
Suppose n - 10 = -0. Suppose 0 = -n*g + 7*g + 12. Factor -x**3 - 6*x**4 + 0*x**4 + x**4 + x**5 + g*x**4 + x**2.
x**2*(x - 1)**2*(x + 1)
Let z be (0/4)/(1 + -9). Suppose 42*j - 52*j = z. Suppose -1/4*d**3 + 0 + j*d - 1/4*d**2 = 0. Calculate d.
-1, 0
Let g(u) = -5*u**2 - 10*u - 27. Let j be g(-9). Let a be (-1)/((-22)/(-4)) + j/(-66). Factor 3*h**5 - a*h**3 + 23*h**3 - 10*h**4 - 5*h**4.
3*h**3*(h - 3)*(h - 2)
Let y = -16118/3 - -5374. Factor -y + 1/3*z**2 + 4/3*z - 1/3*z**3.
-(z - 2)*(z - 1)*(z + 2)/3
Let b(t) be the second derivativ