erivative of d + 1/3*d**3 + 0 + 1/12*d**4 + f*d**2. Factor c(v).
(v + 1)**2
Let r be (-2 + 0)/(((-30)/(-4))/(-15)). Let o be 2 - 6/4*-2. Suppose 3*n**2 + n**2 + 2*n**4 - r*n**3 - n**4 + 4*n - o*n**4 = 0. Calculate n.
-1, 0, 1
Let m(i) be the first derivative of 2*i**3/39 + 146*i**2/13 + 10658*i/13 + 514. Find q such that m(q) = 0.
-73
Let m be (4 - (-17 + 24))*-1. Factor 0*p - 5*p**2 - 5/2*p**4 - 15/2*p**m + 0.
-5*p**2*(p + 1)*(p + 2)/2
Let w(s) be the third derivative of s**8/84 - 2*s**7/105 - s**6/15 - 2*s**2 + 54. Factor w(l).
4*l**3*(l - 2)*(l + 1)
Let a(d) be the second derivative of -d**6/75 + d**5/50 + 7*d**4/30 - 13*d**3/15 + 6*d**2/5 - 974*d. Suppose a(o) = 0. What is o?
-3, 1, 2
Factor 1/11*u + 1/11*u**2 - 1/11*u**3 - 1/11.
-(u - 1)**2*(u + 1)/11
Let g(m) = -2*m**2 - m - 1. Let c(n) = 5*n**2 - 315*n - 25278. Let f(b) = -c(b) - 3*g(b). Determine t so that f(t) = 0.
-159
Let t(s) be the first derivative of 3*s**4/4 + s**3/2 - 3*s**2 + 8*s + 24. Let z(l) be the first derivative of t(l). Factor z(d).
3*(d + 1)*(3*d - 2)
Let u = -44 + 47. Let h(d) be the second derivative of 0*d**2 - 1/14*d**4 + 0 - 4*d - 1/70*d**5 + 0*d**u. Solve h(k) = 0.
-3, 0
Suppose -48 = -93*h + 101*h. Let d be (3 - (-66)/(-18)) + (-8)/h. Factor -d*k**2 + 2/3*k**4 + 0 + 0*k + 0*k**3.
2*k**2*(k - 1)*(k + 1)/3
Suppose 22*j + 2794 = 2838. Factor -2/7 + 64/7*r**3 + 16/7*r - 32/7*r**4 - 48/7*r**j.
-2*(2*r - 1)**4/7
Let w be (-8 - -7)*(-3)/(-231). Let n = w - -236/385. Solve 0 - n*v + 18/5*v**2 = 0 for v.
0, 1/6
Let z(d) be the third derivative of 5*d**8/42 + 439*d**7/735 - 523*d**6/420 - 2*d**5/3 + 17*d**4/21 + 16*d**3/21 - 2*d**2 - 59*d. Let z(b) = 0. What is b?
-4, -2/7, -1/4, 2/5, 1
Let r be (2/(-6))/((-9)/162). Suppose -3 = 3*z - 4*t, 5*z + r*t - 30 = t. Factor -4*p + 8*p - 6 + 8*p - 12*p**2 + z*p**3 + 3*p.
3*(p - 2)*(p - 1)**2
Find f such that -3/8*f**2 - 3/2*f + 3/2 + 3/8*f**3 = 0.
-2, 1, 2
Let -6 + 3*f**3 + 9*f - 546*f**2 + 534*f**2 + 9*f - 3*f = 0. What is f?
1, 2
Let w(p) = -p**2 - 142*p - 4228. Let y(x) = -x**2 - 138*x - 4227. Let f(b) = 2*w(b) - 3*y(b). Solve f(d) = 0 for d.
-65
Suppose 23*i - 24*i = 0. Let m(u) be the third derivative of -8*u**2 - 1/39*u**4 - 1/390*u**6 + 0*u - 7/390*u**5 + i + 4/39*u**3. Factor m(w).
-2*(w + 2)**2*(2*w - 1)/13
Suppose -156/7 - 2/7*k**2 - 158/7*k = 0. Calculate k.
-78, -1
Let k(j) be the second derivative of -5*j**7/189 + 4*j**6/45 - j**5/10 + j**4/27 + 229*j. Suppose k(a) = 0. What is a?
0, 2/5, 1
Let u(v) = -v**3 + 3*v**2 + v. Let f be u(3). Solve -6 - 9*o - 9/2*o**2 - 3/4*o**f = 0 for o.
-2
Factor -18/7 - 12*i**2 + 75/7*i + 12/7*i**3.
3*(i - 6)*(2*i - 1)**2/7
Let x(b) be the first derivative of -7/2*b + 7/6*b**3 + 1/8*b**4 - 1/4*b**2 + 5. What is q in x(q) = 0?
-7, -1, 1
Let a(f) be the first derivative of f**4/24 + 4*f**3/3 + 190. Factor a(w).
w**2*(w + 24)/6
Let y(f) = -2*f**3 - 16*f**2 + 11*f + 89. Let i be y(-8). Factor 1/4*q**2 + i - 5/4*q.
(q - 4)*(q - 1)/4
Factor 0*d + d**3 + 0 - 3/2*d**2 + 1/2*d**4.
d**2*(d - 1)*(d + 3)/2
Let v(f) = 9*f**3 - 30*f**2 - 137*f - 98. Suppose 8 + 16 = -4*b. Let l(t) = -5*t**3 + 15*t**2 + 69*t + 49. Let u(d) = b*v(d) - 11*l(d). Factor u(g).
(g + 1)*(g + 7)**2
Factor 16/5*x**3 + 32/5*x + 0 - 2/5*x**4 - 8*x**2.
-2*x*(x - 4)*(x - 2)**2/5
Let q(t) = 40*t - 116. Let p be q(3). Factor 0*b**2 + 0 + 0*b + 28/5*b**5 + 4*b**p - 8/5*b**3.
4*b**3*(b + 1)*(7*b - 2)/5
Let t(a) be the third derivative of 0 + 1/40*a**5 + 0*a + 0*a**3 + 3/80*a**6 + 2*a**2 - 1/8*a**4. Determine k, given that t(k) = 0.
-1, 0, 2/3
Suppose -9*u = -10*u - 83. Let o be -2 - (u/30 - (-4)/24). Factor 1/5*r**5 + 0*r - 2/5*r**2 + 0*r**4 + 0 - o*r**3.
r**2*(r - 2)*(r + 1)**2/5
Suppose w + 2*o = -166, -3*w = 5*o + 672 - 173. Let l = 168 + w. Let l - 4/5*q**2 - 8/5*q**3 - 4/5*q**4 + 0*q = 0. What is q?
-1, 0
Let l(x) be the third derivative of x**5/270 + 7*x**4/36 + 4*x**2 + 90*x. Solve l(b) = 0 for b.
-21, 0
Suppose -7*j = -j - 12. Factor 2*q**2 + j - 2*q + q - q**2 - 2*q.
(q - 2)*(q - 1)
Let d(x) be the second derivative of -1/54*x**4 + 35*x + 8/9*x**2 - 7/27*x**3 + 0. Let d(k) = 0. What is k?
-8, 1
Let c = -89 - -92. Suppose -14*w**4 + 0*w**c + 16*w**4 - 2*w**2 - w + 0*w**3 + w**5 = 0. Calculate w.
-1, 0, 1
Let r(u) be the second derivative of 22*u + u**2 + 7/9*u**3 + 5/18*u**4 + 0 + 1/30*u**5. Solve r(k) = 0 for k.
-3, -1
Let p be (-12)/(-1) + 18/(-9). Factor p*t**2 + 32*t + 2*t**5 + 1 + 26*t**2 + 38*t**3 + 14*t**2 + 7 + 14*t**4.
2*(t + 1)**3*(t + 2)**2
Let v = 545/7 + -6533/84. Let x(k) be the first derivative of 8 - 1/18*k**3 + 1/3*k + v*k**2. Factor x(s).
-(s - 2)*(s + 1)/6
Solve 6*j**2 - 45/2*j + 25 - 1/2*j**3 = 0 for j.
2, 5
Suppose 5*v = 2*d - 3*d, 2*d + 4*v = 0. Let n(b) be the second derivative of -1/12*b**4 + 4*b + d - 2*b**2 + 2/3*b**3. Let n(o) = 0. Calculate o.
2
Suppose 0*r + 5*s = -2*r - 8, -3*s - 10 = -4*r. Let j = r + 3. Factor -4*q**5 - 3*q**4 + 5*q**5 + q**2 + 2*q**j - q**3.
q**2*(q - 1)**2*(q + 1)
Let q(h) be the first derivative of -h**6/66 - h**5/55 + h**4/44 + h**3/33 + 22. Let q(v) = 0. What is v?
-1, 0, 1
Let w(d) be the second derivative of -d**7/189 + 4*d**6/135 + d**5/45 - 4*d**4/27 - d**3/27 + 4*d**2/9 + 47*d. Suppose w(s) = 0. Calculate s.
-1, 1, 4
Let b(p) be the third derivative of p**8/80640 + p**5/6 + 5*p**2. Let j(w) be the third derivative of b(w). Factor j(v).
v**2/4
Let q(h) = 2*h**5 - h**3 - h**2 + h - 1. Let r(s) = -29*s**5 - 16*s**4 + 42*s**3 + 63*s**2 + s + 11. Let l(k) = -22*q(k) - 2*r(k). Find p, given that l(p) = 0.
-3, -1, -2/7, 0, 2
Let u = -761/4 - -2291/12. Factor 0*r + u*r**2 - 2/3*r**4 + 0 + 0*r**3.
-2*r**2*(r - 1)*(r + 1)/3
Suppose 0 = -3*v + 5*d + 31, -d = 15*v - 14*v + 3. Let m be 15 + -13 + v/4*2. Factor 0 + 0*t + 8/5*t**m - 4/5*t**4 + 12/5*t**2.
-4*t**2*(t - 3)*(t + 1)/5
Factor 0 + 2/5*m**3 + 4/5*m - 6/5*m**2.
2*m*(m - 2)*(m - 1)/5
Suppose 142 = -4*q + 250. Let x be 24/q*9/12. Solve -x*o**4 + 2/3*o**5 + 0*o + 0*o**2 - 4/3*o**3 + 0 = 0.
-1, 0, 2
Let y(g) = g**2 - 2*g - 6. Let n be y(5). Let x = n + -9. Factor 5*s + 9 + x + 4*s**2 + 3 - 21*s.
4*(s - 3)*(s - 1)
Let s(i) = -i**2 - 3*i. Let d(p) = 12*p**2 + 272*p + 3844. Let f(j) = -d(j) - 8*s(j). Factor f(r).
-4*(r + 31)**2
Solve 21/8*q**2 - 21/8*q**4 + 0 + 57/8*q**3 - 27/4*q - 3/8*q**5 = 0.
-9, -1, 0, 1, 2
Let v(z) be the second derivative of z**7/840 - z**6/240 - z**5/20 - 3*z**4/2 - 14*z. Let p(j) be the third derivative of v(j). Factor p(y).
3*(y - 2)*(y + 1)
Let n(c) be the second derivative of -c**7/42 + c**6 - 253*c**5/20 + 35*c**4 - 98*c**3/3 + 2*c + 406. Solve n(l) = 0 for l.
0, 1, 14
Factor -32 - 2/9*t**2 + 34/3*t.
-2*(t - 48)*(t - 3)/9
Let l = -8/263 + 743/15780. Let t(m) be the third derivative of 0 + 9*m**2 + 1/150*m**5 + 0*m**3 + l*m**4 - 1/525*m**7 + 0*m - 1/300*m**6. Factor t(j).
-2*j*(j - 1)*(j + 1)**2/5
Let a(n) be the first derivative of -n**4/14 - 2*n**3/7 + 9*n**2/7 + 54*n/7 - 125. Determine k so that a(k) = 0.
-3, 3
Let f(v) be the second derivative of -v**6/1980 + v**4/132 + v**3/6 - 9*v. Let h(p) be the second derivative of f(p). Suppose h(n) = 0. Calculate n.
-1, 1
Factor -52*s**4 - 20*s**5 - 136*s**3 + 58*s**3 + 34*s**3 - 12*s**2.
-4*s**2*(s + 1)**2*(5*s + 3)
Let n(i) be the first derivative of -i**7/14 - i**6/5 + i**4/2 + i**3/2 + 22*i + 24. Let d(x) be the first derivative of n(x). Solve d(z) = 0.
-1, 0, 1
Let b be (-87)/30 - (-7)/(21/9). Let j(l) be the first derivative of -1/25*l**5 - 1/5*l - 1/30*l**6 + 1/10*l**4 + 2/15*l**3 + 2 - b*l**2. Factor j(s).
-(s - 1)**2*(s + 1)**3/5
Suppose 0*k + 10 = 4*k + 2*b, k + 3*b = 0. Suppose 0 = -7*x - k*x + 12*x. Factor x - 1/2*s**3 - 1/4*s - 3/4*s**2.
-s*(s + 1)*(2*s + 1)/4
Let k(q) be the first derivative of 2*q**3/33 + 10*q**2/11 - 78*q/11 - 91. Factor k(g).
2*(g - 3)*(g + 13)/11
Suppose 5*u - 7 - 13 = 0. Let k be u - (-4)/(-4)*-5. Factor t - 32*t**2 + 10 + k*t + 15*t - 3*t**2.
-5*(t - 1)*(7*t + 2)
Let c = -30 - -35. Suppose -3*n = o + 1, 0 = -c*o - 4*n - n + 5. Factor -4/5 - 8/5*p - 1/5*p**3 - p**o.
-(p + 1)*(p + 2)**2/5
Suppose -8*j - 1/3*j**3 - 3*j**2 - 20/3 = 0. Calculate j.
-5, -2
Let f(x) be the second derivative of -x**8/26880 - x**7/3360 + x**6/720 + 5*x**4/4 + 43*x. Let d(o) be the third derivative of f(o). Factor d(u).
-u*(u - 1)*(u + 4)/4
Let o(