2*n(y). Factor o(s).
s**2*(s + 1)*(5*s - 2)
Let o be (-32)/40 + 26/20. Let k(z) be the first derivative of -o*z**2 + 1/3*z**3 - 1 - 2*z. Determine f, given that k(f) = 0.
-1, 2
What is t in -3*t**3 + 4 - 4 - t**2 + 4*t**2 = 0?
0, 1
Let t(s) = -2*s. Let r be t(-6). Suppose 3*j = 7*j + 3*p + 9, 4*j = -4*p - r. What is c in 1/5*c**5 + 0 + j*c**3 + 3/5*c**4 + 0*c - 4/5*c**2 = 0?
-2, 0, 1
Let f(t) be the first derivative of -t**3/8 - 21*t**2/8 - 39*t/8 - 51. Factor f(s).
-3*(s + 1)*(s + 13)/8
Let d be 18/15*(-5)/(-2). Suppose -d*o + r = -3, 2*o + 5 = 2*r + r. Factor -2*b**3 - b**5 - 1/2*b**o - 5/2*b**4 + 0 + 0*b.
-b**2*(b + 1)**2*(2*b + 1)/2
Let b(n) be the first derivative of -2 + 2/3*n**3 + 0*n + n**2. Factor b(m).
2*m*(m + 1)
Let b(p) = -1. Let v(f) = -2*f**2 + 14*f + 11. Let d(z) = -10*b(z) + 2*v(z). Factor d(r).
-4*(r - 8)*(r + 1)
Let g = 7 - 4. Suppose 4*a - 25 = -4*u + g*a, a = 3*u - 24. Factor -2*q + 7 - 5*q**2 - u.
-q*(5*q + 2)
Let u = 36 - 32. Factor -1/3*w**u - 2/3*w - 5/3*w**2 - 4/3*w**3 + 0.
-w*(w + 1)**2*(w + 2)/3
Let m(d) = 3*d**4 + d**3 + 11*d**2 - d - 6. Let o(x) = x**4 + 4*x**2 - 2. Let r(b) = -3*m(b) + 8*o(b). Determine z, given that r(z) = 0.
-2, -1, 1
Factor -6*v**2 - 9*v**4 - 2*v**3 + 7*v**3 + 8*v**4.
-v**2*(v - 3)*(v - 2)
Let k = -485 + 488. Find v, given that -2*v**k - 2/3*v + 8/3*v**2 + 0 = 0.
0, 1/3, 1
Find s such that s**3 - 7/3*s - 2/3*s**2 - 2/3 = 0.
-1, -1/3, 2
Suppose 4*p + p + 5 = 0. Let z be 0/((2 - 2) + p). Factor 2*i**3 + z + 0*i - 4/3*i**4 - 2/3*i**2.
-2*i**2*(i - 1)*(2*i - 1)/3
Suppose 3*m = 6, 3*u - 2*m - 4 = 5*u. Let g be u/(-6)*11/33. Let -2/9 + g*s**4 + 0*s**2 - 4/9*s**3 + 4/9*s = 0. What is s?
-1, 1
Suppose -4*c + 3*c + 4 = 0. Let q(o) be the first derivative of 4 - 1/20*o**5 + 1/12*o**3 + 0*o - 1/16*o**c + 1/8*o**2. Factor q(i).
-i*(i - 1)*(i + 1)**2/4
Let a(y) be the second derivative of -1/3*y**3 + 0 + 0*y**2 + 1/720*y**6 + 0*y**4 + 2*y + 0*y**5. Let h(r) be the second derivative of a(r). Solve h(k) = 0.
0
Let p = 1169 - 2337/2. Factor p + 0*i - i**2 + 0*i**3 + 1/2*i**4.
(i - 1)**2*(i + 1)**2/2
Determine f, given that -9*f**2 + 20*f**4 + 4*f**2 - 25*f**3 + 10*f**2 = 0.
0, 1/4, 1
Let n be 2*(25/(-30) - 9/(-6)). Find j such that n + 2/3*j - 2/3*j**2 = 0.
-1, 2
Let o(r) = 2*r**5 - 37*r**4 + 27*r**3 + r**2 + 7. Let h(k) = -k**5 + 12*k**4 - 9*k**3 - 2. Let u(a) = -7*h(a) - 2*o(a). Find l, given that u(l) = 0.
0, 1/3, 1, 2
Let n(c) be the second derivative of c**8/2240 - c**7/420 + c**4/6 - 6*c. Let i(u) be the third derivative of n(u). Factor i(z).
3*z**2*(z - 2)
Suppose -11*y + 0*y = 0. Factor -1/3*h**2 + y - 1/3*h**3 + 0*h.
-h**2*(h + 1)/3
Suppose 0 = -4*q - 0*q + 108. Let k = q + -25. Factor 0*c + 0 - 16/3*c**4 + 2*c**5 - 4/3*c**k + 14/3*c**3.
2*c**2*(c - 1)**2*(3*c - 2)/3
Let m = 1 - 4. Let l(y) = 4*y**2 - 4*y - 2. Let h(f) = -5*f**2 + 5*f + 1. Let w(k) = m*l(k) - 2*h(k). Suppose w(t) = 0. Calculate t.
-1, 2
Suppose 5*d = 10*d. Factor -4*m**3 + m**4 + 7*m**3 - 4*m + d*m.
m*(m - 1)*(m + 2)**2
Let w(b) be the second derivative of 7/540*b**6 - b**2 - 1/30*b**5 + 1/54*b**4 + 0 + b + 0*b**3. Let x(o) be the first derivative of w(o). Factor x(i).
2*i*(i - 1)*(7*i - 2)/9
Let h = 0 + 2. Let r(m) = m**h + 2 + 4*m - 3*m - 1. Let d(i) = i**4 + 2*i**3 - 6*i**2 - 7*i + 1. Let t(q) = d(q) + 3*r(q). Factor t(l).
(l - 1)**2*(l + 2)**2
Let i(l) be the first derivative of l**8/280 - l**7/420 - l**6/90 - 5*l**3/3 + 4. Let o(m) be the third derivative of i(m). Factor o(z).
2*z**2*(z - 1)*(3*z + 2)
Let v(i) = 15*i**3 + 15*i**2 - 15*i + 7. Let k(q) = -62*q + 54*q + 5*q**2 + 6 + 8*q**3 - 2 + 3*q**2. Let l(b) = -11*k(b) + 6*v(b). Factor l(s).
2*(s - 1)*(s + 1)**2
Let z be (-148)/(-224) + (-9)/24. Factor -2/7 + 2/7*c - z*c**4 + 2/7*c**5 - 4/7*c**3 + 4/7*c**2.
2*(c - 1)**3*(c + 1)**2/7
Suppose -21 - p**2 + 6 + 6*p**2 - 4*p - 6*p = 0. Calculate p.
-1, 3
Suppose 2 + 2 = 2*r + l, -4*l = 0. Suppose -r*f + q = -3, -3*q = -2*f + q - 6. Factor -7*h**f + 0*h - 3*h**4 - 4*h + 4*h - 2*h**2.
-h**2*(h + 2)*(3*h + 1)
Solve 3*m**5 - 6*m**4 - m**5 + 5*m**3 + m**3 - 2*m**2 = 0.
0, 1
Let o(k) be the first derivative of -1/9*k**3 - 1/2*k**2 + 1/4*k**4 + 2/3*k - 2 - 1/15*k**5. Factor o(v).
-(v - 2)*(v - 1)**2*(v + 1)/3
Let p(n) be the third derivative of -n**7/490 + 3*n**6/140 - 13*n**5/140 + 3*n**4/14 - 2*n**3/7 + 22*n**2. Factor p(i).
-3*(i - 2)**2*(i - 1)**2/7
Let s(h) be the third derivative of 2*h**7/105 + h**6/15 - 13*h**5/15 + 5*h**4/3 + 12*h**2. Suppose s(a) = 0. Calculate a.
-5, 0, 1, 2
Let v(l) = -2*l + 5. Let p be v(-5). Suppose p = -0*s + 5*s. Factor 11/4*u + 7/4*u**s - 1/2 - 4*u**2.
(u - 1)**2*(7*u - 2)/4
Let u = -95 - -286/3. Let h(z) be the second derivative of 1/12*z**4 + u*z**3 - 1/2*z**2 - 3*z - 1/10*z**5 + 0. Solve h(g) = 0 for g.
-1, 1/2, 1
Let k(f) = -f**5 + f**4 + 2*f**3 + 3*f**2 - 3*f. Let g(b) = 2*b**5 + 0*b**3 - 4*b**2 + 4*b + 4*b**3 - 6*b**3. Let m(r) = -3*g(r) - 4*k(r). Factor m(i).
-2*i**3*(i + 1)**2
Let l(b) be the first derivative of 0*b - 2 - 1/12*b**4 + 1/6*b**2 + 0*b**3. Factor l(d).
-d*(d - 1)*(d + 1)/3
Let z(j) be the first derivative of 2/21*j**3 - 3/7*j**2 - 4/35*j**5 + 2/7*j + 3/14*j**4 + 2. Determine v, given that z(v) = 0.
-1, 1/2, 1
Solve -2*g**2 - 19*g**2 - 60 - 132*g + 24 = 0 for g.
-6, -2/7
Let l = 677 - 675. Factor -50/3*b**3 + 14*b**l + 6*b**4 - 4/3 - 2*b.
2*(b - 1)**3*(9*b + 2)/3
Let j(z) be the second derivative of z**4/12 + z**3/18 - 5*z. Factor j(g).
g*(3*g + 1)/3
Let n = 10 + -7. Let d = 8 - n. Factor -d + 0*m + 2*m + 4 - m**2.
-(m - 1)**2
Let i = 103 + -101. Factor 1/5*w**i - 1/5*w**4 - 1/5*w**3 + 0 + 1/5*w.
-w*(w - 1)*(w + 1)**2/5
Suppose -5*z - 2*f - 21 + 106 = 0, 5 = -f. Let j = z + -18. Let -15/2*a**3 + 9/2*a + 2*a**2 + j = 0. What is a?
-2/5, -1/3, 1
Let l(n) = -6 - 4 - n + 0*n. Let a be l(-12). Suppose 0*g + 1/4 - 1/4*g**a = 0. What is g?
-1, 1
Determine n, given that 6*n**2 + 3*n**2 - 5*n**2 + 0*n - 2 + 2*n = 0.
-1, 1/2
Let n(k) = -k**3 - k + 1. Let a(l) = 10*l**3 - 15*l**2 + 10. Let h(y) = a(y) + 5*n(y). Factor h(c).
5*(c - 3)*(c - 1)*(c + 1)
Suppose 0 = -3*j + j - 10, 4*d - 2*j - 698 = 0. Suppose 2*v = -2*k - 0*v + 72, -d = -5*k - 3*v. What is h in -18*h - k*h**3 + 18*h**2 - h**2 + 31*h**2 + 2 = 0?
1/4, 1
Let b(w) be the first derivative of -w**5/30 - w**4/12 + w**2/2 - 2. Let i(k) be the second derivative of b(k). Determine m so that i(m) = 0.
-1, 0
Let a = 50 - 45. Let u(b) be the first derivative of 2/5*b**a - 1/4*b**2 + 2/3*b**3 - 1/12*b**6 - 2 - 3/4*b**4 + 0*b. Factor u(y).
-y*(y - 1)**4/2
Let x(s) be the third derivative of s**7/840 - s**5/120 - s**3/6 + 2*s**2. Let t(u) be the first derivative of x(u). Factor t(c).
c*(c - 1)*(c + 1)
Let k be 10/(-4)*(-2)/5*4. Let n(a) be the second derivative of a - 1/18*a**k + 0*a**2 + 0 + 2/9*a**3. Factor n(v).
-2*v*(v - 2)/3
Find l, given that 4/23*l**2 - 2/23*l - 2/23 = 0.
-1/2, 1
Let i be 15/2*16/(-24). Let x = i - -9. Find t, given that -5/2*t**x + 1/2*t**3 + 5/2*t**2 - 3/2*t**5 + t + 0 = 0.
-1, -2/3, 0, 1
Let m(k) be the second derivative of -k**8/480 - k**7/140 - k**6/240 + k**5/120 - k**3/3 - k. Let c(j) be the second derivative of m(j). Factor c(f).
-f*(f + 1)**2*(7*f - 2)/2
Let o be (492/380 - 1) + (-6)/(-57). Factor -o*l + 0 + 2/5*l**2.
2*l*(l - 1)/5
What is n in 0*n**3 - 2*n**4 - 2*n**2 - 3*n**3 + 0*n**3 - n**3 = 0?
-1, 0
Let c(k) be the second derivative of -3*k**5/100 + 3*k**4/10 - 9*k**3/10 + 4*k. Determine l, given that c(l) = 0.
0, 3
Let s(u) = u - 10. Let m be s(9). Let b = 3 + m. Let 2*w**2 + 3*w**3 - 2*w - 2*w**3 + w**3 - b = 0. What is w?
-1, 1
Factor -13 + 9 + s**3 + 2*s**2 + s**2.
(s - 1)*(s + 2)**2
Let m(n) be the second derivative of n**6/6 - n**5/4 - 5*n**4/4 + 25*n**3/6 - 5*n**2 - n + 21. Factor m(i).
5*(i - 1)**3*(i + 2)
Let w = 7543/14 + -539. Let v = 12/7 + w. Find r such that v*r**3 + 0*r - 3/2*r**4 + 3/2*r**2 + 0 - 3/2*r**5 = 0.
-1, 0, 1
Let k(z) be the first derivative of -z**3/6 + z**2/4 + z - 21. Factor k(i).
-(i - 2)*(i + 1)/2
Let y(i) = -2*i**2 + 29*i - 56. Let r be y(12). Suppose -2/7*w**r - 4/7*w + 0 - 8/7*w**3 - 10/7*w**2 = 0. What is w?
-2, -1, 0
Let f = 77 - 74. Let u(b) be the third derivative of 1/210*b**5 - 1/42*b**4 + 0*b + 0*b**f - 3*b**2 + 1/420*b**6 + 0. Find j such that u(j) = 0.
-2, 0, 1
Facto