tive of -a**4 - 4*a**3/3 + 40*a**2 - 661. Factor k(v).
-4*v*(v - 4)*(v + 5)
Let l be 1 + (-2)/(-4) + 10/4. Factor -7*y - 1 + 2*y**3 - 10*y**2 - 134*y**5 + 139*y**5 + 11*y**l + 0*y**4.
(y - 1)*(y + 1)**3*(5*y + 1)
Let a(l) be the first derivative of -2 + 2/9*l**3 - 1/12*l**4 + 0*l + 0*l**2. Solve a(r) = 0 for r.
0, 2
Let s(y) = y**3 - 22*y**2 + 109*y - 78. Let r be s(6). What is v in 0 + r*v - 1/2*v**3 - 2*v**2 = 0?
-4, 0
Let u(x) be the third derivative of 9*x**2 + 5/24*x**4 + 0*x + 0*x**7 + 0*x**5 + 5/336*x**8 + 0 + 0*x**3 - 1/12*x**6. Factor u(s).
5*s*(s - 1)**2*(s + 1)**2
Solve -8/7 - 10/7*m**2 - 2/7*m**3 - 16/7*m = 0.
-2, -1
Let r = -257 - -265. Let k = r - 8. Let -3/4*t**3 + k*t + 0 - 3/4*t**2 = 0. What is t?
-1, 0
Let y(c) = c + 1. Let t be y(9). Factor -6 - 3*z**3 - 10 + t - 12*z**2 - 5*z - 10*z.
-3*(z + 1)**2*(z + 2)
Factor 11 + 73 + 3*g + 8 + 2*g**3 - 32*g**2 - 185*g + 120*g**2.
2*(g - 1)**2*(g + 46)
Let i(o) = 2*o + 1. Let n be i(1). Solve -10*c**4 + 12*c**3 - 6*c**3 - 3 + 18*c**2 + n + 2*c**5 = 0 for c.
-1, 0, 3
Let o(y) be the first derivative of 12 + 1/4*y + 1/4*y**3 - 3/8*y**2 - 1/16*y**4. Find n, given that o(n) = 0.
1
Let w(q) be the second derivative of -q**5/30 + q**4/12 + 7*q**2 + 14*q. Let d(i) be the first derivative of w(i). Factor d(k).
-2*k*(k - 1)
Suppose 0 = -74*z + 232 + 138. Factor 2/3*o**3 - 1/3*o**4 - 1/3*o**z + 2/3*o**2 - 1/3*o - 1/3.
-(o - 1)**2*(o + 1)**3/3
Let t(z) = z**3 - 13*z**2 - 208*z + 2645. Let h be t(12). Find g such that -4*g**2 - 1/4*g**h + 0 + 4*g + g**4 + 0*g**3 = 0.
-2, 0, 2
What is l in 0 + 1/2*l**5 - 3/2*l**3 + l**4 + 0*l**2 + 0*l = 0?
-3, 0, 1
Let m = 3839/560 - 51/112. Suppose 26*v**2 - 10*v**3 - 112/5*v + m = 0. Calculate v.
4/5, 1
Let h(s) be the third derivative of s**6/30 + 2*s**5/5 - 7*s**4/6 + 87*s**2. Factor h(i).
4*i*(i - 1)*(i + 7)
Determine d so that 3/2*d**2 + 0*d - 1/2*d**3 - 2 = 0.
-1, 2
Factor -2/9*l**3 - 22/9*l - 14/9*l**2 - 10/9.
-2*(l + 1)**2*(l + 5)/9
Let v = -102 + 105. Let r(c) be the second derivative of 1/6*c**v + 0 + 1/15*c**4 + 1/10*c**2 + 5*c. Factor r(u).
(u + 1)*(4*u + 1)/5
Let h(v) be the second derivative of v**4/42 + 6*v**3/7 + 17*v**2/7 + 65*v. Suppose h(j) = 0. Calculate j.
-17, -1
Let d(p) be the third derivative of -2*p**7/105 + p**6/6 - 3*p**5/5 + 7*p**4/6 - 4*p**3/3 + 2*p**2 + 25. Factor d(j).
-4*(j - 2)*(j - 1)**3
Suppose 6*o = 15*o - 54. Let s(d) be the third derivative of -1/120*d**5 - 1/24*d**4 + 0*d + 0*d**3 + 3*d**2 + 0 + 1/240*d**o. Find v such that s(v) = 0.
-1, 0, 2
Let n be (2*(-9)/(-15))/(66/165). Let y(f) be the first derivative of 4/5*f + 1/15*f**n - 1/2*f**2 - 1. Let y(j) = 0. Calculate j.
1, 4
Let k = 13609 - 13605. Factor -12/7 - 12/7*s + 12/7*s**3 + 9/7*s**2 + 3/7*s**k.
3*(s - 1)*(s + 1)*(s + 2)**2/7
Determine f, given that 289/4 + 1/4*f**2 + 17/2*f = 0.
-17
Let p(u) be the second derivative of 0*u**4 + 1/27*u**6 + 0 + 0*u**2 + 0*u**3 + 19*u - 1/45*u**5. What is g in p(g) = 0?
0, 2/5
Let h(w) be the second derivative of -w**5/10 - 4*w**4/3 - 5*w**3 - 45*w. What is r in h(r) = 0?
-5, -3, 0
Let m(y) be the third derivative of y**6/600 - y**5/60 + y**4/40 + 3*y**3/10 + 11*y**2. Let m(k) = 0. What is k?
-1, 3
Let m be 1/12*(-4 - (-1 + -7)). Suppose -1/3 + m*d**2 + 0*d = 0. Calculate d.
-1, 1
Let r = -2051 + 4561/2. Factor -759/2*o**2 - 204*o - 24 + r*o**3 - 243/8*o**4.
-3*(o - 4)**2*(9*o + 2)**2/8
Let y(c) be the second derivative of -5*c**4/12 + 175*c**3/3 - 6125*c**2/2 - 2*c - 22. Let y(x) = 0. What is x?
35
Suppose 746*u = 753*u - 21. Find w, given that -6/7*w**2 + 0 - 4/7*w - 2/7*w**u = 0.
-2, -1, 0
Let n(r) be the second derivative of -r**8/13440 - r**7/2520 + r**6/360 + r**5/30 - r**4/3 + 18*r. Let f(j) be the third derivative of n(j). Factor f(b).
-(b - 2)*(b + 2)**2/2
Suppose -173*p + 37 + 370 = -285. Solve -4*a**3 - 64*a - 24*a**2 - 1/4*a**p - 64 = 0 for a.
-4
Let r = 235 + -235. Let h(s) be the second derivative of 1/40*s**5 - 1/4*s**2 - 1/8*s**4 - 8*s + 1/4*s**3 + r. Determine w, given that h(w) = 0.
1
Let s(n) = n**3 + n. Let p(g) = -3*g**4 - 9*g**3 - 6*g**2 + 15*g + 9. Let u(j) = p(j) - 3*s(j). Factor u(c).
-3*(c - 1)*(c + 1)**2*(c + 3)
Let n = 20 - 15. Solve 6*t**3 - 19*t**4 + 4*t**5 - 8*t**4 + 3 - 18*t + 24*t**2 + 8*t**n = 0.
-1, 1/4, 1
Let q(h) be the first derivative of 2*h**5/45 - 2*h**4/9 - 2*h**3/27 + 4*h**2/9 - 266. Factor q(u).
2*u*(u - 4)*(u - 1)*(u + 1)/9
Suppose 0*m - 3 = m, -3*m - 9 = -2*q. Let k be -1*((2 - q) + -6). Factor -6*d**3 - 6*d**k - 7*d**4 - 8*d**4.
-3*d**3*(7*d + 2)
Let q be (5720/20)/26 - 9. Let -4/7*c**q - 5/7*c - 1/7*c**3 - 2/7 = 0. Calculate c.
-2, -1
Factor 0*v**2 + 65*v - 19 - 191 + 0*v - 5*v**2.
-5*(v - 7)*(v - 6)
Let -7*d**5 - 3*d**4 - 445*d**3 + 66*d**2 + 81*d**4 - 8*d**5 - 9*d + 325*d**3 = 0. What is d?
0, 1/5, 1, 3
Let c(j) be the first derivative of -5 - 1/2*j**2 + 0*j + 1/9*j**3. Factor c(m).
m*(m - 3)/3
Let t be (16*6)/(8/12). Factor 3*y**5 - 48 + 10*y**3 - 10*y**4 + 86*y**3 - 168*y**2 - 17*y**4 + t*y.
3*(y - 2)**4*(y - 1)
Let o(f) be the first derivative of f**4/32 - f**3/12 + f**2/16 + 77. Factor o(z).
z*(z - 1)**2/8
Let k(h) = -2*h**3 - 24*h**2 - 48*h + 59. Let z(f) = -2*f**3 - 36*f**2 - 72*f + 89. Let g(c) = 7*k(c) - 5*z(c). Factor g(o).
-4*(o - 4)*(o - 1)*(o + 2)
Let q(d) = d**3 + 3*d - 1. Let p(k) = 4*k**3 - 17*k**2 + 40*k - 18. Let m(l) = -2*p(l) + 6*q(l). Solve m(n) = 0.
1, 15
Let c = -6678 - -6681. Solve -3/7*u**c + 0 - 12/7*u - 12/7*u**2 = 0.
-2, 0
Let g = -3/226 - 1634/339. Let m = 11/2 + g. Factor -8/3*d**3 + 14/3*d**2 - m - 4/3*d.
-2*(d - 1)**2*(4*d + 1)/3
Let q be 164/(-48) - -3 - 60/(-80). Let u be (-34)/12 - (-2 + -1). What is z in -u*z**2 - q*z - 1/6 = 0?
-1
Let d(q) be the first derivative of -3*q**5/40 - 45*q**4/32 - 61*q**3/8 - 63*q**2/16 + 147*q/4 + 85. Determine o so that d(o) = 0.
-7, -2, 1
Factor 2/5*h**2 + 64/5*h - 66/5.
2*(h - 1)*(h + 33)/5
Let u(c) = 7*c**4 - 9*c**3 + 5*c**2 + 4*c + 3. Let k(l) = -8*l**4 + 10*l**3 - 6*l**2 - 4*l - 4. Suppose 10 = 6*j - 4*j. Let z(g) = j*k(g) + 6*u(g). Factor z(a).
2*(a - 1)**3*(a + 1)
Let h(g) be the third derivative of g**10/831600 + g**9/332640 - g**8/55440 + g**5/3 + 3*g**2 + 2*g. Let i(s) be the third derivative of h(s). Factor i(x).
2*x**2*(x - 1)*(x + 2)/11
Suppose 4*b - 3*r = 9, 0*r - 3*r = -b. Let -433*w + b*w**5 - 3*w**4 - 6*w**3 + 433*w = 0. Calculate w.
-1, 0, 2
Let p(f) be the second derivative of -24*f + 2/5*f**2 + 1/50*f**5 + 1/3*f**3 + 2/15*f**4 + 0. What is c in p(c) = 0?
-2, -1
Let g = -16 - 7. Let k = g - -27. Factor 39*y**5 + y**2 - 38*y**5 + y**k - y**3 - 2*y**4.
y**2*(y - 1)**2*(y + 1)
Let p(k) = -2*k - 6. Let a be p(-6). Suppose 2*w - 3 = -5*l, 2*w + l - a*l - 13 = 0. Factor -x**3 + 1/2*x - 1/2 + 1/2*x**5 + x**2 - 1/2*x**w.
(x - 1)**3*(x + 1)**2/2
Let n(f) be the first derivative of -3/16*f**4 - 1/12*f**3 - 30 + 0*f + 1/20*f**5 + 1/24*f**6 + 1/4*f**2. Suppose n(u) = 0. What is u?
-2, -1, 0, 1
Let a(g) be the first derivative of 2/5*g**5 + 0*g - g**2 + 4 + 1/2*g**4 - 2/3*g**3. Factor a(f).
2*f*(f - 1)*(f + 1)**2
Let a(t) be the first derivative of 1/14*t**4 + 15 + 0*t**2 + 0*t - 2/21*t**3. Factor a(s).
2*s**2*(s - 1)/7
Let g(f) = 2*f**4 - 2*f**3 + 12*f**2 + 12*f - 12. Suppose d = -w + 12, -3*w = -5*d + 2*w + 60. Let b(a) = -a**2 - a + 1. Let t(v) = d*b(v) + g(v). Factor t(o).
2*o**3*(o - 1)
Let f(z) be the second derivative of -z**4/66 - 32*z**3/11 - 2304*z**2/11 - 20*z. Determine r so that f(r) = 0.
-48
Let x(z) be the second derivative of -z**6/255 - 3*z**5/170 + 2*z**4/51 - 3*z + 9. Suppose x(n) = 0. What is n?
-4, 0, 1
Let w(a) be the second derivative of a**4/24 - 11*a**3/12 + 5*a**2/2 - 3*a + 44. Factor w(f).
(f - 10)*(f - 1)/2
Suppose -4*s + 13 = -y, 9 = 2*s - 5*y - 2. Factor -1 - 7/4*w - 1/2*w**2 + 1/4*w**s.
(w - 4)*(w + 1)**2/4
Factor -6*k - 2*k**3 + 5*k**2 - 13*k**2 + 0 - 1 + 1.
-2*k*(k + 1)*(k + 3)
Let n = 30 + -21. Let u(o) = 3*o**2 - 2*o + 1. Let s be u(1). Factor -10*x - x**2 + s*x**2 + n*x.
x*(x - 1)
Factor 5/4*g**3 + 0 + g**4 + 1/2*g**2 + 0*g + 1/4*g**5.
g**2*(g + 1)**2*(g + 2)/4
Let z(s) be the third derivative of -s**6/6 - 7*s**5/15 - s**4/3 - 17*s**2 + 1. Find g such that z(g) = 0.
-1, -2/5, 0
Suppose 2/5*q**4 + 0*q**2 + 0*q**3 - 2/5*q**5 + 0*q + 0 = 0. What is q?
0, 1
Let i(d) = 9*d - 35. 