 the second derivative of 0 - 8/9*p**3 + 1/3*p**5 + 2/3*p**4 - 16/3*p**2 + 6*p + 2/45*p**6. Factor c(r).
4*(r - 1)*(r + 2)**3/3
Let x = -8 + 10. Let 15 - 4*d - 19 + 4*d**x + 0*d - 20 = 0. What is d?
-2, 3
Suppose 2*j = 3*j - 81. Let b = -79 + j. Find u, given that 0*u + 0*u**b + 9/5*u**4 + 3/5*u**5 + 6/5*u**3 + 0 = 0.
-2, -1, 0
Suppose -2*a = -x - 1 + 12, -4*a - 5*x = 57. Let w = -6 - a. Determine j so that -j - 8*j + 2*j**w - 8 - 4*j**2 + j = 0.
-2
Let h(k) be the third derivative of 2*k**7/735 + k**6/280 - k**5/420 + 79*k**2. Find a, given that h(a) = 0.
-1, 0, 1/4
Factor -27/4 - 21/4*l + 1/4*l**3 + 7/4*l**2.
(l - 3)*(l + 1)*(l + 9)/4
Let s(m) be the first derivative of m**6/42 + 13*m**5/35 + 3*m**4/4 - 13*m**3/21 - 11*m**2/7 + 168. What is n in s(n) = 0?
-11, -2, -1, 0, 1
Let r(d) be the first derivative of -d**5/20 + 3*d**4/4 - 9*d**3/2 + d**2/2 - 13. Let q(o) be the second derivative of r(o). Factor q(i).
-3*(i - 3)**2
Let z(b) be the third derivative of -b**5/60 + b**4/24 + b**3/6 - 9*b**2. Let k(v) = -10*v**2 + 13*v + 5. Let t(g) = -2*k(g) + 18*z(g). Factor t(p).
2*(p - 2)**2
Let a(q) be the first derivative of -q**3/3 - 84*q**2 - 7056*q - 177. Determine f so that a(f) = 0.
-84
Let p(b) be the second derivative of 0*b**2 - 1/54*b**4 + 1/135*b**6 + 1/90*b**5 - 1/189*b**7 + 0 - b + 0*b**3. Determine q so that p(q) = 0.
-1, 0, 1
Let y(s) be the second derivative of -s**7/63 - s**6/9 - s**5/10 + 17*s**4/18 + 28*s**3/9 + 4*s**2 - 443*s. Determine p, given that y(p) = 0.
-3, -2, -1, 2
Suppose -2*p - 2*p + 12 = 0. Suppose -k - b = 2*b - 9, -13 = -3*k - 2*b. Solve 10*n**3 + n**4 - 2*n**2 - n - 8*n**p + 1 + 0*n**k - n**5 = 0.
-1, 1
Let b(l) be the second derivative of -l**5/170 + 2*l**4/17 - 7*l**3/17 - 98*l**2/17 - 159*l. Factor b(i).
-2*(i - 7)**2*(i + 2)/17
Let p(s) be the first derivative of -9 - 2/15*s**3 - 1/10*s**4 + s**2 - 6/5*s. Factor p(w).
-2*(w - 1)**2*(w + 3)/5
Let w be -1*((-220)/136 + (-30)/(-255)). Suppose w*x**4 + 0 + 0*x**2 + 9/2*x**3 - 6*x = 0. Calculate x.
-2, 0, 1
Let z be 0 + -1*(-6)/2. Suppose 5 = r + 5*h + 2, 0 = 4*r + 2*h - 12. Factor o - 3*o**3 + 2*o**z + o**r - o**3 + o**2 - 1.
-(o - 1)**2*(o + 1)
Let l(a) be the first derivative of -1/36*a**4 - 1/27*a**3 + 0*a + 1 + 1/9*a**2. Solve l(p) = 0.
-2, 0, 1
Let f(i) be the first derivative of -i**7/4200 + i**6/225 - 2*i**5/75 + 32*i**3/3 - 29. Let h(a) be the third derivative of f(a). Solve h(p) = 0.
0, 4
Let v(t) be the third derivative of t**6/30 - 2*t**5/15 - 19*t**4/6 + 40*t**3/3 + 159*t**2. Suppose v(r) = 0. Calculate r.
-4, 1, 5
Let j(f) be the second derivative of -f**4/66 - 64*f**3/33 + 65*f**2/11 + 12*f + 3. Factor j(g).
-2*(g - 1)*(g + 65)/11
Let j be ((-4)/(-9))/((-8)/(-36)). Let i(a) be the first derivative of -14/3*a**3 + 6 - j*a**4 + 2*a - 2*a**2. Find h, given that i(h) = 0.
-1, 1/4
Let p(n) be the first derivative of -4*n**3/3 - 52*n**2 + 108*n - 192. Factor p(c).
-4*(c - 1)*(c + 27)
Factor 45*j**4 + 44*j**4 - 16*j**3 + 8*j**2 - 107*j**4 - 16*j**3.
-2*j**2*(j + 2)*(9*j - 2)
Determine y so that -9/5*y - 1/5*y**2 - 8/5 = 0.
-8, -1
Let z = -42 + 24. Let s be (18/30)/3 + z/(-10). Solve 71/4*o**3 - 21/4*o**4 + 2 - 31/2*o**s + o = 0 for o.
-2/7, 2/3, 1, 2
Let s(w) be the first derivative of w**3/3 - 15*w**2/2 + 14*w + 59. Let n(l) = l - 1. Let m(y) = -28*n(y) - 4*s(y). Let m(r) = 0. Calculate r.
1, 7
Let l(j) be the first derivative of 4*j**5/45 + j**4/3 + 5*j**3/27 + 284. Suppose l(u) = 0. What is u?
-5/2, -1/2, 0
Determine k, given that -2/3*k**3 + 2/15*k**4 + 2/15*k**5 + 0*k + 0 + 2/5*k**2 = 0.
-3, 0, 1
Let g(c) = -47*c**4 - 511*c**3 - 600*c**2 - 192*c + 7. Let h(i) = -16*i**4 - 170*i**3 - 200*i**2 - 64*i + 2. Let o(l) = -2*g(l) + 7*h(l). Factor o(k).
-2*k*(k + 8)*(3*k + 2)**2
Let f = 29 - 65. Let n = 36 + f. Factor 1/2 + n*d - 1/2*d**2.
-(d - 1)*(d + 1)/2
Let h(w) be the second derivative of -9*w**7/14 + 3*w**6 - 33*w**5/10 - 2*w**4 + 7*w**3/2 + 3*w**2 + 260*w. Solve h(k) = 0.
-1/3, 1, 2
Let u = 14 - -37. Let r = -48 + u. Let 27*m**2 - 27/2*m**3 + 3/2*m - r = 0. Calculate m.
-1/3, 1/3, 2
Let t(f) = f**3 - 7*f**2 - 6*f - 1. Let g be t(8). Let c = -13 + g. Factor -2*r**c + 0 - 1 + 18*r**3 + r - 19*r**3 + 3*r**2.
-(r - 1)**2*(r + 1)
Factor -18*i**2 - 8 + 4*i**2 - 23*i**3 + 22*i - 2 + 25*i**3.
2*(i - 5)*(i - 1)**2
Let r = 19931/21 - 949. Let z(d) be the second derivative of -r*d**3 + 0*d**2 - 1/35*d**5 + 0 - 2/21*d**4 - 6*d. Factor z(k).
-4*k*(k + 1)**2/7
Let m(q) = 3*q**4 + 8*q**3 - 6*q**2 + 4*q - 5. Let r(n) = -5*n**4 - 14*n**3 + 10*n**2 - 7*n + 9. Let a(x) = -7*m(x) - 4*r(x). Find v, given that a(v) = 0.
-1, 1
Factor 15*s - 225/2 - 1/2*s**2.
-(s - 15)**2/2
Let q(k) be the first derivative of -1/9*k**6 + 2/3*k**4 + 4/9*k**3 + 0*k**5 - 4/3*k - k**2 + 37. Find r, given that q(r) = 0.
-1, 1, 2
Let f be ((-2)/(-8))/((-78)/24 + 4). Let o(y) be the second derivative of 7*y + 0*y**2 - 1/3*y**4 + 0 + 1/10*y**5 + f*y**3. Factor o(p).
2*p*(p - 1)**2
Let p(y) = -23*y + 51. Let f be p(3). Let i be -2*1/10 - f/40. Factor -i*w**2 - 4 - 2*w.
-(w + 4)**2/4
Let y(j) be the third derivative of -j**6/60 - 2*j**5/15 - 629*j**2. Suppose y(d) = 0. Calculate d.
-4, 0
Let k(h) be the third derivative of h**9/45360 - h**7/7560 + 7*h**4/12 + 16*h**2. Let c(w) be the second derivative of k(w). Determine q, given that c(q) = 0.
-1, 0, 1
Let t be (-11)/3 + (-48)/(-72). Let a be 5*((-44)/20 - t). Solve 16/5*p**3 - 16/5 + 4/5*p**a - 16/5*p + 12/5*p**2 = 0 for p.
-2, -1, 1
Factor -12*k**2 + 3*k**3 + 4*k**3 - 12*k**3 + 12 + 2*k + 3*k**3.
-2*(k - 1)*(k + 1)*(k + 6)
Let a(q) be the first derivative of q**4/10 - 4*q**3/5 + 12*q**2/5 - 16*q/5 - 55. Let a(x) = 0. What is x?
2
Let k(r) = r**2 + 8*r + 18. Let c be k(-4). Let f(i) be the first derivative of 2/33*i**3 + 0*i + 1/22*i**4 + 4 + 0*i**c. Factor f(u).
2*u**2*(u + 1)/11
Let u = 23/12 - 5/3. Let l be (-2)/6*21/(-28). Factor u*b**4 + 0 + 0*b + 1/4*b**5 - 1/4*b**3 - l*b**2.
b**2*(b - 1)*(b + 1)**2/4
Let j = 11 + -2. Let y be (j/(-6))/((-5)/90). Suppose 449 - 449 - 48*o**3 - y*o**4 - 15*o**2 + 6*o = 0. Calculate o.
-1, 0, 2/9
Let t(d) = -6*d**2. Let c(f) = f**2 + 1. Suppose 0 = 3*j - 4*j + 4*u + 7, -2*j + 7 = -u. Let z(v) = j*c(v) + t(v). Factor z(w).
-3*(w - 1)*(w + 1)
Let s be (7/(-28))/((-1)/20). Factor -3*k**3 + 3*k**2 + 5*k**3 - s*k**3.
-3*k**2*(k - 1)
Let r(w) = w**2 + w - 1. Let a(i) be the second derivative of i**5/20 - i**4/4 - i**3 + 3*i**2/2 - 20*i. Let u(b) = a(b) + 5*r(b). Factor u(p).
(p - 1)*(p + 1)*(p + 2)
Let w(g) be the second derivative of -g**4/60 + 13*g**3/30 - 343*g. Suppose w(h) = 0. Calculate h.
0, 13
Find z such that -17*z**2 - 6*z**2 - 17*z**2 - 5*z**5 + 6*z**3 + 40*z**4 - z**3 = 0.
-1, 0, 1, 8
Let q(r) be the first derivative of -r**5/20 + r**3/2 - 7*r**2/2 - 4. Let b(x) be the second derivative of q(x). Find z such that b(z) = 0.
-1, 1
Let p(x) = x**3 - 53*x**2 + 2*x + 56. Let d(n) = -6*n**3 + 266*n**2 - 10*n - 282. Let t(b) = -3*d(b) - 16*p(b). Factor t(j).
2*(j - 1)*(j + 1)*(j + 25)
Suppose 15*h - 24*h**2 + 20062*h**3 + 7 + 35 - 20059*h**3 = 0. What is h?
-1, 2, 7
Let w(h) be the third derivative of h**7/105 + h**6/30 - 11*h**5/30 - h**4 - 183*h**2 + 1. Solve w(j) = 0.
-4, -1, 0, 3
Suppose 20*x - 28*x + 16 = 0. Suppose -4*c - 2*q + 32 = 0, -c + 2*c + 5*q = 17. Solve x*z**2 - 3*z**3 + c*z**3 + 8*z**5 + 11*z**3 + 18*z**4 - 3*z**3 = 0 for z.
-1, -1/4, 0
Let l(o) be the third derivative of 0*o**3 - 1/108*o**6 - 7/270*o**5 + 0 - 1/945*o**7 + 0*o - 1/36*o**4 + 28*o**2. Let l(m) = 0. What is m?
-3, -1, 0
Let m(a) be the second derivative of a**5/5 - 45*a**4 - 35*a + 5. Find t such that m(t) = 0.
0, 135
Factor 3/2*t**2 - 390*t + 25350.
3*(t - 130)**2/2
Let o(i) be the first derivative of i**4/6 - 2*i**3/9 - 2*i**2 + 316. Find k such that o(k) = 0.
-2, 0, 3
Let t(k) be the second derivative of k**7/42 - k**6/15 - k + 9. Find s, given that t(s) = 0.
0, 2
Let s(x) be the first derivative of -75/4*x**2 - 65/6*x**3 + 20 - 5*x. Factor s(f).
-5*(f + 1)*(13*f + 2)/2
Factor 1/2*z**2 + 1/2*z - 6.
(z - 3)*(z + 4)/2
Suppose -9 + 278*f**2 - 17 + 28*f**4 + 188*f**3 - 38 + 58*f**2 + 112*f = 0. What is f?
-4, -2, -1, 2/7
Let v(h) be the second derivative of -h**7/70 - h**6/50 + 3*h**5/50 + h**4/10 - h**3/10 - 3*h**2/10 - 251*h. Determine