 53*b - u. Suppose 0*n - 2/9*n**3 + 0 - 4/9*n**4 + 0*n**b - 2/9*n**5 = 0. Calculate n.
-1, 0
Let t be (10/(-30))/(3/(-45)). Let l(v) be the first derivative of 0*v - 2/15*v**3 - 6/25*v**5 + t - 2/5*v**4 + 0*v**2. Factor l(z).
-2*z**2*(z + 1)*(3*z + 1)/5
Suppose -81 + 34 - 79 - l + 9 - 3*l**2 + 49*l = 0. Calculate l.
3, 13
Factor 128/15*n + 2/15*n**2 + 42/5.
2*(n + 1)*(n + 63)/15
Let b(m) be the third derivative of m**5/180 - m**4/24 + m**3/9 - 3*m**2 - 11*m. Factor b(w).
(w - 2)*(w - 1)/3
Suppose -25*q - 17*q + 168 = 0. Let a(c) be the first derivative of -8*c**3 + 11/2*c**4 + 0*c + 4 - 25/3*c**6 - q*c**2 + 12*c**5. Determine k so that a(k) = 0.
-2/5, 0, 1
Let h(d) be the second derivative of -4/5*d**3 - 2/3*d**4 + 13*d + 0 - 4/15*d**6 + 41/50*d**5 + 1/35*d**7 + 0*d**2. Solve h(y) = 0.
-1/3, 0, 2, 3
Let x(d) be the first derivative of 2*d**3/15 + 32*d**2/5 - 66*d/5 + 86. Solve x(g) = 0.
-33, 1
Let x(m) be the second derivative of -3*m**5/20 + 3*m**4/4 + 9*m**3/2 - 81*m**2/2 - 89*m. Find t, given that x(t) = 0.
-3, 3
Let g(m) be the second derivative of -m**8/1260 + 17*m**7/2520 - m**6/54 + m**5/90 - 7*m**3/3 + m + 23. Let k(x) be the second derivative of g(x). Factor k(l).
-l*(l - 2)**2*(4*l - 1)/3
Let n(c) = c**2 - 48*c + 47. Let g be n(47). Let f(u) be the second derivative of 1/42*u**4 + g - 2/7*u**3 + 7*u + 9/7*u**2. Let f(k) = 0. What is k?
3
Suppose 4*k + 0 + 4 = 0. Let u be 1 - (-2 + 0 - k). What is d in 5 + 23*d - 5*d**u - 23*d = 0?
-1, 1
Let m(p) be the third derivative of -p**6/360 - 2*p**5/45 + 53*p**4/72 + 10*p**3/3 + 13*p**2 - 5. Determine b, given that m(b) = 0.
-12, -1, 5
Let x(g) be the third derivative of -g**6/60 - g**5/10 + 3*g**4/4 - 5*g**3/3 + 215*g**2. Let x(c) = 0. Calculate c.
-5, 1
Solve -33/2*m**3 - 3/2*m**5 - 2 + 17/2*m**4 + 0*m + 23/2*m**2 = 0 for m.
-1/3, 1, 2
Let c(t) be the second derivative of -t**9/83160 + t**8/36960 + t**7/6930 + t**4/4 - 7*t. Let y(i) be the third derivative of c(i). Factor y(a).
-2*a**2*(a - 2)*(a + 1)/11
Let z(p) be the first derivative of 125/4*p**2 + 0*p + 24 - 1/10*p**5 + 15/8*p**4 - 25/2*p**3. Let z(i) = 0. What is i?
0, 5
Let v(p) = 6*p**2 + p. Let n = -10 - -10. Let k = -1 - n. Let r(a) = -a**2. Let t(f) = k*v(f) - 5*r(f). Factor t(o).
-o*(o + 1)
Suppose -14*f + 22*f + 40 = 0. Let s be ((-8 - f)*(-2)/12)/1. Factor 2*x**4 + 2*x**2 + 0 - s*x**5 - 3*x**3 - 1/2*x.
-x*(x - 1)**4/2
Let f(u) be the first derivative of u**6/72 + 26*u**3/3 + 19. Let j(t) be the third derivative of f(t). Solve j(w) = 0.
0
Let h be -2 + 1 + -8*(-4)/8. Let z be (12/(-18))/((-1)/h). What is j in 8/3*j + 2/3*j**z + 8/3 = 0?
-2
Factor -17 - 163 + 88*r - 5*r**3 - 184*r + 239*r - 75*r**2 + 117*r.
-5*(r - 2)*(r - 1)*(r + 18)
Suppose 5 = 4*c + s + 1, -c + 18 = -4*s. Let f be 276/42 - -1 - 3. Solve f*u - 8/7 - 2*u**c = 0.
2/7, 2
Let r = 451 - 451. Let r*d + 2/5*d**2 + 0 = 0. Calculate d.
0
Let l(h) be the third derivative of 0*h + 1/70*h**6 - 1/392*h**8 + 1/21*h**3 + 1/735*h**7 + 3*h**2 - 1/28*h**4 + 0 - 1/105*h**5. Let l(r) = 0. Calculate r.
-1, 1/3, 1
Let b(g) be the third derivative of g**7/210 + g**6/12 + 5*g**5/12 + g**2 - 7*g. Factor b(j).
j**2*(j + 5)**2
Let x(h) be the second derivative of -h**4/48 + h**3/12 + h**2 + 3*h + 39. Suppose x(w) = 0. What is w?
-2, 4
Factor 208*a**2 + a**4 - 412*a**2 + 205*a**2 + 2*a**3.
a**2*(a + 1)**2
Let a = 2669/2 - 1334. Factor -a*g**3 - 1/4*g**4 + 1/2*g + 1/4*g**2 + 0.
-g*(g - 1)*(g + 1)*(g + 2)/4
Let z(o) be the second derivative of -2*o**5/15 + 34*o**4/9 + 71*o**3/9 + 6*o**2 - 6*o + 9. What is k in z(k) = 0?
-1/2, 18
Suppose 0 = 4*m + 6*v + 10, -12*m = -7*m - 4*v - 22. Let -8*n + 17/2*n**2 + m - 5/2*n**3 = 0. Calculate n.
2/5, 1, 2
Suppose 2*h - 5*r + 6 = -19, -5*r = h - 10. Let b(u) = 3*u**2 + 12*u - 27. Let j(c) = c**2 + 5*c - 11. Let i(n) = h*b(n) + 12*j(n). Factor i(m).
-3*(m - 1)*(m + 1)
Suppose -2*u = -5*u - 3*v, 0 = -3*u + 3*v + 18. Suppose -5*r + 15 = -0. Find h, given that -3*h**u + 6*h**3 + h**2 + h - h**4 - 4*h**r = 0.
-1, 0, 1
Let y(s) be the second derivative of s**4/4 - 2*s**3 - 90*s**2 + 398*s. Factor y(v).
3*(v - 10)*(v + 6)
Let n = 123 + -120. Suppose -q = -2*s + 11, -4*s = q - 4 - n. Factor 1/2 + 3/2*b**2 + 3/2*b + 1/2*b**s.
(b + 1)**3/2
Let d = -11918 - -59604/5. Factor -112/5*a - 64/5 + d*a**3 - 33/5*a**2 - 1/5*a**4.
-(a - 8)**2*(a + 1)**2/5
Let s(m) be the third derivative of m**6/32 - 19*m**5/24 + 5*m**4/4 - 2*m**2 - 96*m. Factor s(w).
5*w*(w - 12)*(3*w - 2)/4
Let o(l) be the third derivative of 5*l**2 + 1/21*l**3 + 1/28*l**4 + 0 + 0*l - 2/105*l**5. Suppose o(m) = 0. What is m?
-1/4, 1
Let j(h) = h**2 - 4*h - 6. Suppose 2*q - 4*q - 2 = 0. Let y(r) = r**2 - r - 1. Let t(a) = q*j(a) + 6*y(a). Determine f, given that t(f) = 0.
0, 2/5
Let l(h) = -h**4 + 13*h**3 - 26*h**2 + 29*h - 15. Let u(r) = r**3 + r**2 - r - 1. Let p(x) = -l(x) + 3*u(x). Factor p(z).
(z - 6)*(z - 2)*(z - 1)**2
Let v(q) be the third derivative of q**5/390 + q**4/52 - 10*q**3/39 + 22*q**2. Factor v(o).
2*(o - 2)*(o + 5)/13
Let f(t) = -20*t + 582. Let x be f(29). Let g(y) be the first derivative of -8/3*y**3 + 4*y**x - 1/2*y**4 + 2/5*y**5 + 5 + 0*y. Factor g(p).
2*p*(p - 2)*(p - 1)*(p + 2)
Let g(u) be the second derivative of 5/72*u**4 + 1/6*u**2 - 1/4*u**3 + 3/40*u**5 + 0 - 17*u - 7/180*u**6. What is f in g(f) = 0?
-1, 2/7, 1
Let b be 56/(-84) + 28/39. Let n(u) be the second derivative of b*u**3 - 1/26*u**5 + 0*u**2 + 2*u + 1/26*u**4 + 0. Factor n(s).
-2*s*(s - 1)*(5*s + 2)/13
Factor 3*y**2 + 8*y**2 + 60 - 25*y**2 - 42*y + 2*y**3 - 6.
2*(y - 9)*(y - 1)*(y + 3)
Let y be ((2 - 3) + 480)/533*1. Let t = y - -1/41. Solve 4/13*g**5 + 2/13*g**2 + 2/13*g**4 + 0 + 4/13*g - t*g**3 = 0 for g.
-2, -1/2, 0, 1
Let f(z) = -z**3 - 7*z**2 + 11*z + 12. Let o be f(-8). Let s be 3 - -1 - (-39)/o. What is u in 0 + 1/4*u**4 + 0*u**3 + 1/2*u - s*u**2 = 0?
-2, 0, 1
Let y = -217 + 221. Let b(n) be the third derivative of -5/24*n**y - 7/60*n**5 + 3*n**2 + 0 + 0*n + 1/3*n**3. Let b(v) = 0. What is v?
-1, 2/7
Let s(l) be the second derivative of l**6/90 - 7*l**5/30 + 61*l**4/36 - 14*l**3/3 + 6*l**2 - 56*l. Let s(h) = 0. What is h?
1, 6
Let z(x) = -x**2 + 25*x + 4. Let n be z(0). Let w(u) be the first derivative of -1/4*u**n + u**3 - 3/2*u**2 - 3 + u. Suppose w(v) = 0. Calculate v.
1
Solve 40*z - 29*z**3 + 62*z**3 - 36 - 32*z**3 + 5*z**2 - 18*z**2 = 0.
2, 9
Let n be (-2)/(-12) - (-76)/(-24). Let c = 9 + n. What is l in -9*l**5 - 3 - 40*l**2 - 15*l - 39*l**4 - 66*l**3 - c*l - 14*l**2 = 0?
-1, -1/3
Let q(u) be the third derivative of u**7/210 - u**6/24 + 3*u**5/20 - 7*u**4/24 + u**3/3 + 24*u**2. Factor q(o).
(o - 2)*(o - 1)**3
Suppose -2*b**2 + 12 + 10 - b - 24 + 3*b**2 = 0. Calculate b.
-1, 2
Determine o, given that 154/5*o**2 - 94/5*o + 12/5 = 0.
2/11, 3/7
Let f be (-156)/(-3)*3/(-6). Let d = f + 28. Factor -g**3 - 4*g**2 + g**2 + d*g**2.
-g**2*(g + 1)
Let s(v) be the first derivative of -6*v**5/5 + 25*v**4 - 448*v**3/3 + 128*v**2 + 876. Factor s(y).
-2*y*(y - 8)**2*(3*y - 2)
Let j(z) be the second derivative of -z**6/30 - 3*z**5/20 + z**4/3 + 2*z**3 + z + 19. Determine r, given that j(r) = 0.
-3, -2, 0, 2
Suppose 19*i + 3*c - 2 = 15*i, -4*i + 2*c = -12. Let s(t) be the first derivative of 6 + 4/3*t**3 + 0*t**i + 0*t. Factor s(r).
4*r**2
Let n(w) = 9*w**2 - 3. Let k(a) = a**3 + a**2 - 1. Suppose -12 = -2*t - 2*t. Let y = -13 - -12. Let i(p) = t*k(p) + y*n(p). Let i(j) = 0. What is j?
0, 2
Suppose -2*s = -3*j + 11, 0 = j + 2 - 5. Let a be ((-4)/(3 + s))/(-1). Factor -4/5 + 2/5*y**a + 2/5*y.
2*(y - 1)*(y + 2)/5
Let h(z) be the second derivative of -z**5/50 - 17*z**4/6 - 328*z**3/15 - 324*z**2/5 - 205*z + 2. Suppose h(y) = 0. Calculate y.
-81, -2
Suppose -3*f - 60 = -8*f. Suppose x + 3*x = f. Factor 2*k + 0*k + x*k - 1 - 4*k**2.
-(k - 1)*(4*k - 1)
Let c(x) = -4*x**4 - 116*x**3 - 893*x**2 - 778*x - 3. Let z(u) = u**2 + 2*u - 1. Let f(v) = c(v) - 3*z(v). Factor f(i).
-4*i*(i + 1)*(i + 14)**2
Factor 19*y - 68*y + 111 - 17*y + 3*y**2 - 48*y.
3*(y - 37)*(y - 1)
Let p(f) be the first derivative of 2*f**3/3 + 7*f**2 + 24*f + 27. What is r in p(r) = 0?
-4, -3
Factor 11*m**3 + 26*m**2 - 24 + m**4 + 1 + 0*m**4 + 16*m + 23.
m*(m + 1)*(m + 2)*(m + 8)
Let t(b) be the first derivative of 5*b**4 - 5*b**3/3 - 7. Factor t(j).
5*j**2*(