i(o) be the third derivative of -1/1050*o**7 - 1/100*o**5 - 1/200*o**6 + 0 + 0*o**3 - 11*o**2 + 0*o - 1/120*o**4. Factor i(l).
-l*(l + 1)**3/5
Suppose 4*n + 1 = 4*l - 3, -4*n = -5*l + 7. Factor n*r - 11*r + 5*r**2 + 5 - r.
5*(r - 1)**2
Let b(i) = -12*i**2 + 240*i + 272. Let j(x) = 2*x**2 - 34*x - 39. Let y(h) = -3*b(h) - 20*j(h). Suppose y(w) = 0. Calculate w.
-9, -1
Let x(i) be the third derivative of 61*i**5/28 + 33*i**4/14 + 2*i**3/7 - 122*i**2. Solve x(j) = 0.
-2/5, -2/61
Let h be 60/33 + 2/11. Factor 3*v**4 - 217*v**h - 9 - 18*v**3 + 2*v + 13*v + 223*v**2 + 3*v**5.
3*(v - 1)**3*(v + 1)*(v + 3)
Let x(y) be the third derivative of 2*y**7/105 + 4*y**6/15 - y**5/15 - 4*y**4/3 + 117*y**2. Factor x(k).
4*k*(k - 1)*(k + 1)*(k + 8)
Let a(b) = -b + 7. Let h be a(3). Let -3*p**2 - p + h*p**2 - 6*p + 6*p = 0. Calculate p.
0, 1
Let p = 33 + -32. Let r be ((-36)/(-20) - 2/p)*-2. What is k in -1/5*k**2 + r - 1/5*k = 0?
-2, 1
Let h(k) be the second derivative of -3*k**5/8 + 4*k**4 + 23*k**3/4 - 21*k**2/2 + 38*k. Let h(t) = 0. Calculate t.
-1, 2/5, 7
Let q(x) be the third derivative of -x**7/1470 - x**6/210 - x**5/140 + x**4/42 + 2*x**3/21 + 20*x**2. Determine k, given that q(k) = 0.
-2, -1, 1
Let d(m) be the third derivative of 0 + 0*m - 1/70*m**7 + 1/8*m**4 - 7*m**2 - 1/40*m**6 - m**3 + 3/20*m**5. Factor d(a).
-3*(a - 1)**2*(a + 1)*(a + 2)
Let v(k) be the second derivative of -k**3/6 + 9*k**2 + 31*k. Let s be v(18). What is f in 7/2*f**4 + s + 2*f + 4*f**2 - 19/2*f**3 = 0?
-2/7, 0, 1, 2
Suppose 8 = n + 6. Suppose 0*l**4 + 42*l**3 + 36 + 8*l**n - 84*l + 5*l**2 + 9*l**4 = 0. What is l?
-3, 2/3
Let j(b) = 27*b**2 + 564*b + 567. Let l(k) = -7*k**2 - 141*k - 142. Let d(u) = -4*j(u) - 15*l(u). Determine r so that d(r) = 0.
-46, -1
Let h(y) be the first derivative of 0*y**2 - 2/15*y**3 + 0*y**4 + 3/100*y**5 - 1/150*y**6 - 6*y - 2. Let m(n) be the first derivative of h(n). Factor m(f).
-f*(f - 2)**2*(f + 1)/5
Suppose 192*r - u = 196*r - 17, 23 = r + 4*u. Factor -12*o**2 + 12/5 - 32/5*o - 16/5*o**r.
-4*(o + 1)*(o + 3)*(4*o - 1)/5
Let 1/4 - 1/2*y + 1/4*y**2 = 0. What is y?
1
Let w = -4426810/13 - -340172. Let m = 352 + w. Factor 2/13*d**2 - 4/13 - m*d.
2*(d - 2)*(d + 1)/13
Let b(q) be the second derivative of -q**6/1020 + q**5/34 - 25*q**4/68 + 125*q**3/51 + 16*q**2 - 28*q. Let p(v) be the first derivative of b(v). Factor p(d).
-2*(d - 5)**3/17
Find o, given that 5/4*o**2 + 0*o - 45/4 = 0.
-3, 3
Let f be (-1)/(-5) - (-930)/600. Let x(l) be the first derivative of 2/3*l**3 + 0*l**2 + f*l**4 + l**5 + 0*l - 2. Suppose x(j) = 0. Calculate j.
-1, -2/5, 0
Suppose -79*j = -69*j. Let s(z) be the first derivative of 7 + j*z + 4/7*z**2 + 25/14*z**4 + 40/21*z**3. Suppose s(w) = 0. What is w?
-2/5, 0
Let z(x) be the third derivative of x**9/211680 + x**8/35280 - x**7/4410 - x**6/315 + x**5/4 + 29*x**2. Let q(n) be the third derivative of z(n). Factor q(c).
2*(c - 2)*(c + 2)**2/7
Let -2/5*o**2 - 1/5*o + 1/5*o**4 - 1/5*o**5 + 2/5*o**3 + 1/5 = 0. Calculate o.
-1, 1
Let k(o) be the second derivative of o**5/5 + o**4/3 - 2*o**3/3 - 2*o**2 - 20*o - 2. Factor k(g).
4*(g - 1)*(g + 1)**2
Suppose 12 = 3*k - 24. Let n be (k/14)/((90/(-28))/(-5)). Factor -n*s**2 - 2/3*s**5 - 4/3*s**3 + 2*s - 2/3 + 2*s**4.
-2*(s - 1)**4*(s + 1)/3
Let w(k) be the second derivative of -24*k + 0 + 1/26*k**4 - 4/13*k**2 + 4/39*k**3. Determine u, given that w(u) = 0.
-2, 2/3
Let g(i) be the first derivative of -3*i**5/80 + i**4/8 - i**3/8 + 18*i - 2. Let p(f) be the first derivative of g(f). Suppose p(a) = 0. Calculate a.
0, 1
Let g = -6/79 - -403/4266. Let y = g + 853/594. Factor -8/11 - y*r - 6/11*r**2.
-2*(r + 2)*(3*r + 2)/11
Let u = 458/2305 - -3/2305. Determine y so that -u*y**3 + 2/5*y**2 - 2/5*y**4 + 1/5*y**5 + 0*y + 0 = 0.
-1, 0, 1, 2
Let a(l) be the second derivative of l**5/150 - 29*l**4/10 + 2523*l**3/5 - 219501*l**2/5 + 27*l - 1. Suppose a(c) = 0. What is c?
87
Let u be 62/168 + ((-1830)/360)/61. Factor 0*w - 2/7*w**3 + 0*w**4 + 0*w**2 + 0 + u*w**5.
2*w**3*(w - 1)*(w + 1)/7
Suppose 5*a**2 - 1088*a + 10978 + 13833 - 3686 + 438*a = 0. What is a?
65
Let p = 37087/5 + -7417. Suppose 28/15*m - 14/15*m**2 - p - 8/15*m**3 = 0. Calculate m.
-3, 1/4, 1
Let y(z) be the second derivative of -z**8/1120 - z**7/280 - z**6/240 + 9*z**3/2 - 28*z. Let q(i) be the second derivative of y(i). Factor q(f).
-3*f**2*(f + 1)**2/2
Let -38 + 2*w**2 - 4*w + 38 + 22*w**2 = 0. What is w?
0, 1/6
Let q(j) be the second derivative of -j**8/13440 - j**7/1680 - j**6/480 - j**5/240 + 19*j**4/12 + j. Let t(g) be the third derivative of q(g). Solve t(z) = 0.
-1
Let n(k) be the second derivative of 1/10*k**5 + 1/30*k**6 - 1/12*k**4 - 1/3*k**3 + 0 + 12*k + 0*k**2. Factor n(f).
f*(f - 1)*(f + 1)*(f + 2)
Let s be (-4)/(-2) - ((-6)/7)/((-90)/210). What is a in -2/13*a**2 + s*a + 2/13*a**3 + 0 = 0?
0, 1
Let m = 5992 - 5989. Suppose -v + 13 = 3*v + 5*w, 0 = -v + 4*w - 2. Factor 0 - 2/3*a**m + 4/3*a**v - 2/3*a.
-2*a*(a - 1)**2/3
Let g be (-800)/(-150)*25/20*(-4)/(-10). Factor g*s - 16/3 - 1/3*s**2.
-(s - 4)**2/3
Suppose 19*i = -208 + 246. Let u(r) be the second derivative of -4/3*r**3 + 0 - i*r**2 - 1/3*r**4 + 10*r. Factor u(o).
-4*(o + 1)**2
Let o be (-1860)/(-1705) - 36/33. Factor o + 20/3*u**3 + 16/3*u**2 - 4/3*u.
4*u*(u + 1)*(5*u - 1)/3
Determine u, given that -2/3*u**2 + 0 - 8*u**3 + 8*u + 2/3*u**4 = 0.
-1, 0, 1, 12
Let w(a) be the second derivative of 4*a - 1/3*a**3 + 1/18*a**4 - 2/3*a**2 + 1/45*a**6 + 0 + 1/10*a**5. Find g such that w(g) = 0.
-2, -1, 1
Let c(d) = 5*d + 19. Let q be c(-4). Let y(z) = 4*z**4 + 8*z**3 - 8*z**2 - 16*z + 4. Let n(u) = -u**4 + u**2 + u. Let f(x) = q*y(x) - 8*n(x). Solve f(r) = 0.
-1, 1
Let s(f) be the second derivative of -f**8/1848 - f**7/1155 + f**2/2 + 11*f. Let c(j) be the first derivative of s(j). Find n, given that c(n) = 0.
-1, 0
Let h be 6/2*7/7. Let z(c) = 3*c**4 + 5*c**3 - 7*c**2 - 5*c. Let s(q) = 2*q**4 + 5*q**3 - 8*q**2 - 5*q. Let y(n) = h*z(n) - 2*s(n). Factor y(t).
5*t*(t - 1)*(t + 1)**2
Let t be 80*(-3 - 0 - 0)*-1. Determine n, given that -18*n**4 - t*n**2 - 70*n**3 + 8*n**3 - 33*n**3 - 17*n**3 - 32 - 192*n = 0.
-2, -2/9
Let x be (-3)/(-9)*(-6)/(-14 + 8). Suppose 3*o + 10 = -z, 3*z = 4*z - o - 6. What is v in 0*v + 0 + x*v**3 + 0*v**z = 0?
0
Let a(b) be the second derivative of -b**4/3 + 4*b**3/3 - 2*b**2 - 3*b - 6. Factor a(u).
-4*(u - 1)**2
Let z(r) be the second derivative of r**5/120 - r**4/24 - r**3/6 + 2*r**2/3 + 7*r - 14. What is w in z(w) = 0?
-2, 1, 4
Factor 1/4*u**2 - u**5 + 0 - 7/4*u**4 + 0*u - 1/2*u**3.
-u**2*(u + 1)**2*(4*u - 1)/4
Let i(h) be the second derivative of -h**6/210 - 4*h**5/35 - 2*h**4/7 + 160*h**3/21 - 200*h**2/7 - 164*h. Factor i(g).
-(g - 2)**2*(g + 10)**2/7
Let z(l) = l**2 - 4*l - 93. Let g be z(12). Let f(p) be the first derivative of -1 - 4/3*p**g + 4*p + p**4 - 2*p**2. Factor f(o).
4*(o - 1)**2*(o + 1)
Suppose -5 = -272*t + 224*t - 5. Suppose t*l**3 - 1/5*l**2 + 0 + 0*l + 1/5*l**4 = 0. What is l?
-1, 0, 1
Let l(f) = -f**2 - f - 4. Let r be l(7). Let h = 182/3 + r. Find g such that -4/9*g**3 - 2/9*g**2 + h*g**4 + 0*g + 0 = 0.
-1/3, 0, 1
Let j = 3 - -1. Suppose -j*w + 4*u = -8, -4*u = -2*w - 2 + 6. Let -8*h - 5*h + 17*h - 6 + 2*h**w = 0. What is h?
-3, 1
Let p(n) be the third derivative of 1/900*n**6 - 4/45*n**3 - 1/90*n**5 + 2/45*n**4 + 20*n**2 + 0*n + 0. Suppose p(q) = 0. What is q?
1, 2
Let -1/5*d**4 - 1/5*d + 1/5*d**3 + 7/5*d**2 - 6/5 = 0. Calculate d.
-2, -1, 1, 3
Let f(o) = 25*o**4 - 82*o**3 + 22*o**2 + 37*o + 13. Let i(y) = 26*y**4 - 81*y**3 + 23*y**2 + 36*y + 14. Let l(a) = 6*f(a) - 5*i(a). Let l(j) = 0. Calculate j.
-2/5, -1/4, 1, 4
Let s(d) = -3*d**3 - 39*d**2 + 8*d. Let g(f) = 15*f**3 + 195*f**2 - 42*f. Let u(k) = -4*g(k) - 21*s(k). Find a, given that u(a) = 0.
-13, 0
Let o(l) be the second derivative of -l**4/6 - l**3 + 4*l**2 - l + 31. Factor o(g).
-2*(g - 1)*(g + 4)
Let w = 103 + -112. Let z be ((-15)/w)/((-3)/18*-5). Find o, given that 0 - 3/2*o**3 + 3/2*o**z + 3*o = 0.
-1, 0, 2
Let t(h) = -3*h**3 + 9*h**2 + 9*h - 9. Let g(d) = d**2 + d - 1. Let o(b) = 6*g(b) - t(b). Let o(s) = 0. Calculate s.
-1, 1
Let q be (27/(-54))/((-12)/4*1). Let a(l) be the second derivative of -5*l + 1/80*l**5 + q*l**3 + 1/12*l**4 + 0 + 0*l**2. Factor a(h).
h*(h + 2)*