2/3*v**4 - 16/15*v - 56/15*v**2 + 0 + 4/5*v**3 - 10/3*v**n = 0.
-2/5, 0, 1, 2
Let f(r) be the second derivative of r**5/10 - 25*r**4/6 - 4*r**3/3 + 100*r**2 - 9*r + 1. Factor f(y).
2*(y - 25)*(y - 2)*(y + 2)
Suppose 0 + 0*j + 2/3*j**4 + 68/9*j**3 + 22/9*j**2 = 0. What is j?
-11, -1/3, 0
Let o(i) be the first derivative of 25*i**4/4 - 10*i**3 - 25*i**2/2 + 30*i + 13. Factor o(j).
5*(j - 1)*(j + 1)*(5*j - 6)
Let x(g) be the second derivative of -g**5/90 - g**4/9 - 4*g**3/9 - g**2 + 3*g. Let l(k) be the first derivative of x(k). Factor l(y).
-2*(y + 2)**2/3
Let d = 116 + -113. Let f(q) be the first derivative of 1 + 4*q + 4/3*q**d + 4*q**2. Solve f(g) = 0.
-1
Let q(n) = n**5 - n**4 + n**2 + 1. Let u(a) = -a**5 + 9*a**4 + 17*a**3 + 15*a**2 + 6*a - 2. Let m(i) = 10*q(i) + 5*u(i). Let m(t) = 0. What is t?
-3, -2, -1, 0
Suppose -9*l + 281 = -1375. Let n = l - 1099/6. Factor -5/6*k**2 + n + 0*k.
-5*(k - 1)*(k + 1)/6
Let q(m) be the second derivative of m**4/3 + 4*m**3 - 182*m**2 - m - 286. Factor q(s).
4*(s - 7)*(s + 13)
Let i(h) be the second derivative of -h**5/60 - h**4/3 - 7*h**3/6 - 39*h**2/2 + 11*h. Let q(l) be the first derivative of i(l). Factor q(a).
-(a + 1)*(a + 7)
Factor -320*j**2 + 50*j**4 - 104528*j + 40*j**3 + 5*j**5 + 104528*j.
5*j**2*(j - 2)*(j + 4)*(j + 8)
Let i = -5 - -7. Let y be 3/(i + -1) - 0. Find r, given that 0*r + 2*r + 8*r**y + 64*r**2 - 74*r**2 = 0.
0, 1/4, 1
Let -211*q + 2*q**2 + 267*q - q**2 - 132 - 4*q**2 - q**2 = 0. What is q?
3, 11
Let y(k) be the second derivative of -13*k**5/5 + 2*k**4/3 + 104*k**3/3 - 16*k**2 + 5*k - 14. Find s, given that y(s) = 0.
-2, 2/13, 2
Let l(n) be the second derivative of -1/33*n**3 + 2*n + 2/11*n**2 - 1/66*n**4 + 0. Suppose l(z) = 0. Calculate z.
-2, 1
Let a = 609 + -1217/2. Let l(h) be the first derivative of a*h**2 + 0*h - 1/3*h**3 - 1/4*h**4 - 7 + 1/5*h**5. Factor l(d).
d*(d - 1)**2*(d + 1)
Let j(y) be the first derivative of y**5/40 - 5*y**4/32 + 5*y**3/24 + 5*y**2/16 - 3*y/4 + 200. Suppose j(o) = 0. Calculate o.
-1, 1, 2, 3
Suppose m - 4 = -0, -21 = -3*h - 3*m. Suppose -7 - 2 = -h*s. Factor -g + 5*g**3 - 4*g**s + 4*g**3 - 4*g**3.
g*(g - 1)*(g + 1)
Let t be 12/8*(-78)/(-9). Suppose -t - i**2 + 18*i - 1 - 2*i**2 - 1 = 0. Calculate i.
1, 5
Let y(b) be the third derivative of 1/180*b**5 + 0*b + 0 + 5/72*b**4 - 2*b**2 + 2/9*b**3. What is f in y(f) = 0?
-4, -1
Let c(i) be the first derivative of i**5/20 + i**4/4 + i**3/12 - 3*i**2/4 - 47. Find o, given that c(o) = 0.
-3, -2, 0, 1
Factor 19/7*i + 34/7 + 1/7*i**2.
(i + 2)*(i + 17)/7
Let 17/2*h**2 - 81/2 - 1/2*h**3 - 63/2*h = 0. Calculate h.
-1, 9
Let k(q) = q**4 + 20*q**3 - 5*q**2 - 33*q + 3. Let j(b) = 10*b**4 + 240*b**3 - 60*b**2 - 395*b + 35. Let m(s) = 3*j(s) - 35*k(s). Let m(r) = 0. Calculate r.
-1, 0, 2, 3
Let l be 920/65 - (-4)/(-26). Let z = l + -5. Solve 6*s**4 - 6*s + z*s**4 + 10*s**5 - 27*s**3 - 13*s**5 + 21*s**2 = 0.
0, 1, 2
Suppose 5*q = 27 - 17. Factor -6 - 7*c**2 + q*c**2 + 15*c**3 - 39*c**2 - 12*c**2 + 35*c.
(c - 3)*(3*c - 1)*(5*c - 2)
Let v be ((-5)/6)/((-15)/9). Let d be -6*(-1)/3 - (-1)/(-2). Factor v*c**3 + d - 5/2*c + 1/2*c**2.
(c - 1)**2*(c + 3)/2
Suppose -4*j = -6*j + 20. Let d = 13 - j. Determine p so that -3*p**3 + 3*p**4 - 6*p**2 + 0*p**2 + 3*p + d*p**2 = 0.
-1, 0, 1
Let x(t) = -13*t**4 + t**3 - 8*t**2 - 5*t + 5. Let o(y) = 11*y**4 - 2*y**3 + 7*y**2 + 4*y - 4. Let a(p) = 5*o(p) + 4*x(p). Factor a(h).
3*h**2*(h - 1)**2
Let f = -43 - -54. Suppose -f = -c - 7. Factor 0*u - 2/9*u**c + 0*u**2 - 4/9*u**3 + 0.
-2*u**3*(u + 2)/9
Let s be 2/(-3) + (-4)/(-6). Suppose -5*z - a + 57 = 0, s = -3*z + 3*a + 15 + 12. Determine b so that 0*b**4 + 9*b**4 - 12*b - 13*b**2 - 3*b**3 - z*b**2 = 0.
-1, -2/3, 0, 2
Let s(y) be the first derivative of -2*y**3/15 - 7*y**2/5 - 12*y/5 - 2. Factor s(q).
-2*(q + 1)*(q + 6)/5
Let m be 459/54*44/187. Let x be (-4)/(-3)*18/16. Let 3/4 - 3/4*r - x*r**m = 0. Calculate r.
-1, 1/2
What is o in -6*o**5 + 105*o**4 + 84*o - 27*o**5 - 59*o**2 - 51*o**3 + 41 - 34*o**2 - 53 = 0?
-1, 2/11, 1, 2
Let k(l) = -4*l + 47. Let w be k(11). Factor 5 + 21*j - 18*j**2 + 6*j**4 + 19 - 3*j**4 - w*j**3 - 9*j.
3*(j - 2)**2*(j + 1)*(j + 2)
Let p = 6373 - 6370. Factor 2/23*f**p + 2/23*f**2 - 2/23 - 2/23*f.
2*(f - 1)*(f + 1)**2/23
Let c(w) be the third derivative of -w**10/201600 + w**9/40320 - w**5/30 + 10*w**2. Let f(n) be the third derivative of c(n). Factor f(i).
-3*i**3*(i - 2)/4
Let y(b) be the first derivative of -b**6/18 + 2*b**5/15 + b**4/6 - 4*b**3/9 - b**2/6 + 2*b/3 + 18. Determine j, given that y(j) = 0.
-1, 1, 2
Let h(x) be the first derivative of x**4/8 - 8*x**3/3 + 29*x**2/4 - 7*x - 627. Let h(r) = 0. What is r?
1, 14
Let t(j) be the third derivative of -j**5/210 - 23*j**4/6 - 3703*j**3/3 + 18*j**2 + 4*j. Determine h, given that t(h) = 0.
-161
Let h = 99 - 84. Let t = 17 - h. Factor 3/7*b**t - 6/7 + 3/7*b.
3*(b - 1)*(b + 2)/7
Suppose 0 = -0*d + 5*d + 2*w - 45, 0 = 3*d - 4*w - 27. Let z be (d/10)/(54/45). Solve 3/2*u - z*u**2 + 0 = 0.
0, 2
Let t be 5/(90/21)*1/70. Let b(q) be the third derivative of 0 + t*q**6 - 4*q**2 + 0*q**3 + 1/30*q**5 + 0*q + 0*q**4. Factor b(y).
2*y**2*(y + 1)
Let m(z) = -169*z + 20*z**2 + 185*z - 25 - 19. Let v(q) = -13*q**2 - 11*q + 29. Let a(t) = 5*m(t) + 8*v(t). Let a(s) = 0. What is s?
-3, 1
Let u be ((-66)/11 - (-3 + 75/(-10))) + -3. What is w in u*w - 9/8 - 3/8*w**2 = 0?
1, 3
Let f(z) be the third derivative of 0*z + 0 + 1/390*z**5 + 5*z**2 - 1/39*z**3 + 0*z**4. Factor f(u).
2*(u - 1)*(u + 1)/13
Let c = 1656 - 1653. Factor -c*v**2 - 2/3 + 11/3*v.
-(v - 1)*(9*v - 2)/3
Let h(s) be the second derivative of s**4/3 - 8*s**3/3 - 24*s**2 + 19*s + 1. Let h(z) = 0. Calculate z.
-2, 6
Let h = -26057/3 + 8407. Let c = 279 + h. Determine o so that c*o**2 - o + 2/3 = 0.
1, 2
Find v such that -v**2 - 445 - 60*v + 309 + 8*v**2 - 3*v**2 = 0.
-2, 17
Solve 88/7*f**2 + 0 + 324/7*f**4 + 8/7*f + 306/7*f**3 = 0.
-1/2, -2/9, 0
Suppose 0 = m - 20 + 15. Let d(p) be the second derivative of 0 + 1/189*p**7 + 0*p**m + 0*p**2 + 2*p - 1/27*p**3 + 2/135*p**6 - 1/27*p**4. Factor d(h).
2*h*(h - 1)*(h + 1)**3/9
Suppose -3*q + 3 = -3. Let z be 3/(-189)*(-16 + -2). Factor 10/7*j + z*j**3 + 4/7 + 8/7*j**q.
2*(j + 1)**2*(j + 2)/7
Let l(w) = 30*w - 72. Let k be 2/6 + (-350)/(-30). Suppose s - k = -3*s. Let i(v) = v**2 + 1. Let f(p) = s*i(p) - l(p). Factor f(h).
3*(h - 5)**2
Let m be (-5)/3*(-42)/210. Let 0*q + 2/3*q**4 + 0 + 0*q**2 - 1/3*q**3 - m*q**5 = 0. What is q?
0, 1
Let h = 158 + -149. Let w(t) be the second derivative of 1/2*t**4 + h*t - 1/15*t**6 - 1/3*t**3 + 0 + 1/10*t**5 - 2*t**2. Factor w(a).
-2*(a - 2)*(a - 1)*(a + 1)**2
Let u(v) be the second derivative of v**6/30 + v**5/5 + v**4/4 - 2*v**3/3 - 2*v**2 + v. Solve u(s) = 0.
-2, -1, 1
Let t = 8788 - 4135. Let c be (t/135)/11 + 3*-1. Let 8/15*s**2 + 0 + 2/3*s**3 + c*s + 4/15*s**4 = 0. What is s?
-1, -1/2, 0
Let p(j) be the second derivative of 4*j**7/21 - 7*j**6/15 - 39*j**5/5 - 131*j**4/6 - 76*j**3/3 - 12*j**2 - 247*j. Find c, given that p(c) = 0.
-2, -1, -1/4, 6
Suppose 0*v = -2*n - 2*v + 16, -4*n = v - 23. Suppose 2*a = -c + 7*a - 17, -5*a + n = -5*c. Find u, given that -2/5*u**4 + 6/5*u**2 - 2*u + 4/5 + 2/5*u**c = 0.
-2, 1
Factor 11/4*u**3 + 1/2 + 15/4*u + 6*u**2.
(u + 1)**2*(11*u + 2)/4
Let d(k) be the third derivative of 1/70*k**7 - 29/360*k**6 + 0 + 9*k**2 + 11/60*k**5 + 0*k + 1/9*k**3 - 5/24*k**4. Suppose d(w) = 0. What is w?
2/9, 1
Suppose 2/21*t**4 + 0*t + 14/3*t**2 + 4/3*t**3 + 0 = 0. Calculate t.
-7, 0
Let -5/3*x**2 + 13/3*x + 6 = 0. What is x?
-1, 18/5
Let u(t) = -t + 7. Let k be u(4). Let w be (-3 + k)/((-4)/(-4)). Suppose w*j**4 - 3/5*j + 2/5 + 4/5*j**3 - 1/5*j**5 - 2/5*j**2 = 0. What is j?
-2, -1, 1
Let c(j) be the second derivative of 3/40*j**5 + 6*j + 0 - 1/3*j**3 + 1/168*j**7 + 1/24*j**6 - 1/12*j**4 + 0*j**2. Factor c(b).
b*(b - 1)*(b + 2)**3/4
Let f be (18 + -16)*(-45)/(-18). Suppose -98/11*a**3 + 30/11*a - 112/11*a**f + 4*a**2 + 4/11 - 228/11*a**4 = 0. What is a?
-1, -2/7, -1/4, 1/2
Let o(h) be the second derivative of -23*h + 1/315*h**7 + 1/90*h**4 + 8/45*h**3 + 4/15*h**2 + 0 - 1/225*h**6 - 1/30*h**5. Factor o(y).
2*(y - 2)**2*(y + 1)**3/15
Let y = -1105 - -1107. Determine n, given that -16/3*n + 0 - 4/3*n**y = 0.
-4, 0
Let d(r) be the fi