**3/3 - 7*c**2 + 6*c - 1077. Suppose r(p) = 0. Calculate p.
-1, 1, 3
Let z(l) be the second derivative of -l**6/2160 - l**5/90 - l**4/9 - 14*l**3/3 + 4*l. Let w(r) be the second derivative of z(r). Factor w(n).
-(n + 4)**2/6
Let n = 152/15 - 563/60. Solve -n*c**3 - 3/4*c**5 + 0*c**2 + 0 + 0*c + 3/2*c**4 = 0.
0, 1
Let n(d) be the second derivative of d**7/42 - 23*d**6/30 + 163*d**5/20 - 361*d**4/12 + 160*d**3/3 - 50*d**2 - 88*d. Find f, given that n(f) = 0.
1, 10
Let l(q) be the first derivative of 22 - 20*q - 5/3*q**3 + 25/2*q**2. Factor l(x).
-5*(x - 4)*(x - 1)
Let v be (56/6)/(10/195). Let d = v + -106. Suppose -78*c**2 + d*c**2 - 2 + 6*c - 2 = 0. What is c?
1, 2
Let c(m) = 3*m**3 + 30*m**2 + 57*m - 78. Let w(d) = -3*d**3 - 29*d**2 - 58*d + 76. Let s(k) = -7*c(k) - 6*w(k). Suppose s(u) = 0. Calculate u.
-10, -3, 1
Let h(i) be the second derivative of i**7/140 - i**6/90 - i**5/60 + 5*i**3/3 - 18*i. Let g(w) be the second derivative of h(w). Find q such that g(q) = 0.
-1/3, 0, 1
Let a(t) = -67*t + 4. Let h be a(0). Let k(j) be the second derivative of -2*j - 1/15*j**h + 2/5*j**2 + 3/25*j**5 - 2/5*j**3 + 0. Factor k(z).
4*(z - 1)*(z + 1)*(3*z - 1)/5
Let y(n) = -4*n**2 + 27*n - 29. Let x(z) = -z - 1. Let h(j) = -3*x(j) - y(j). Determine o, given that h(o) = 0.
2, 4
Let v = 335 - 335. Let d(p) be the second derivative of 0 + 0*p**2 + 1/14*p**7 - 1/4*p**4 - 8*p + 9/20*p**5 - 3/10*p**6 + v*p**3. Let d(j) = 0. What is j?
0, 1
Factor 4*v + 0 - 4/5*v**2.
-4*v*(v - 5)/5
Let v(q) be the second derivative of -4/21*q**3 - 4/7*q**2 + 0 + 10*q - 1/42*q**4. Solve v(g) = 0 for g.
-2
Let w(b) be the second derivative of 0 + 0*b**2 - 1/40*b**5 + 31*b + 0*b**3 - 1/12*b**4. Factor w(a).
-a**2*(a + 2)/2
Suppose 5*l + 3*t - 32 = -0*l, 0 = 2*l + 4*t - 24. Let f(a) = a**3 - 3*a**2 - 2*a - 6. Let k be f(l). Factor -4/7 + 4/7*y - 4/7*y**3 + 4/7*y**k.
-4*(y - 1)**2*(y + 1)/7
Let p = 1171 - 1171. Let k(x) be the third derivative of p*x**3 + 2*x**2 + 0 - 1/16*x**4 + 1/120*x**5 + 0*x. Solve k(i) = 0 for i.
0, 3
Let f = -1284/7 + 184. Let l = 97/21 + -13/3. Factor -f + 2/7*s**2 - l*s.
2*(s - 2)*(s + 1)/7
Factor 25*y**2 + 12*y**3 - 22*y**3 - 5*y - 25*y**4 + 15*y**3.
-5*y*(y - 1)*(y + 1)*(5*y - 1)
Let j(h) be the third derivative of -3*h**6/200 - h**5/10 - h**4/10 + 7*h**3 - 6*h**2. Let r(i) be the first derivative of j(i). Factor r(l).
-3*(l + 2)*(9*l + 2)/5
Let t(d) = 3*d**2 - 9*d + 12. Suppose -2*m - 3*a = -a - 12, 0 = -m + 2*a - 9. Let w(z) = z. Let i(l) = m*t(l) - 3*w(l). Determine q so that i(q) = 0.
2
Let t = 528 - 522. Let z(s) be the first derivative of s**3 - 7 - 3/2*s**2 - t*s. Factor z(j).
3*(j - 2)*(j + 1)
Determine t, given that 228/7 - 56*t + 20/7*t**2 = 0.
3/5, 19
Let q(k) be the first derivative of k**3 + 15/14*k**2 - 6/7*k + 5. What is j in q(j) = 0?
-1, 2/7
Let m(z) be the second derivative of z**6/30 - 3*z**5/20 - 3*z**4/4 - 5*z**3/6 - z - 49. Factor m(v).
v*(v - 5)*(v + 1)**2
Let y(v) = -v**3 + v**2 - v - 1. Let l(r) = -r + 9 - 2*r**2 - 8 + 3*r. Let c(h) = l(h) - y(h). Let s(m) be the first derivative of c(m). Factor s(t).
3*(t - 1)**2
Let c be 1 - (-4)/1*1. Factor -c + 1 + 1 - 9*h - 3 - 3*h**2.
-3*(h + 1)*(h + 2)
Let l(b) be the second derivative of 1/300*b**5 + 8/15*b**3 + 0 - 3*b**2 + 7*b + 1/15*b**4. Let y(q) be the first derivative of l(q). Solve y(o) = 0 for o.
-4
Let i = 87/94 - 1483/1598. Let y = i + 1620/8789. Factor -2/11*v**3 + 2/11*v + 2/11*v**2 - y.
-2*(v - 1)**2*(v + 1)/11
Let l(w) be the second derivative of -w**4/42 - w**3/3 + 8*w**2/7 + w - 14. Factor l(y).
-2*(y - 1)*(y + 8)/7
Solve 36 + 25*w**3 - 3*w**5 + 13*w**3 - 55*w**3 + 16*w**3 + 43*w**3 - 39*w - 36*w**2 = 0 for w.
-4, -1, 1, 3
What is r in -2/3*r - 1/9*r**3 + 0 - 5/9*r**2 = 0?
-3, -2, 0
Let z = -328 - -328. Let b(p) be the third derivative of 6*p**2 + 0*p - 1/180*p**6 + z*p**3 + 2/135*p**7 + 0 + 0*p**4 - 1/135*p**5. Factor b(g).
2*g**2*(2*g - 1)*(7*g + 2)/9
Let g(z) be the first derivative of 92*z**3/21 - 12*z**2/7 - 125. Factor g(r).
4*r*(23*r - 6)/7
Suppose 0 = 2*c + 1 - 9. Suppose j**4 - 2*j**2 - c*j**3 - j + j**2 + 4*j**3 + j**3 = 0. Calculate j.
-1, 0, 1
Let i(s) be the first derivative of 2*s**6/3 + 8*s**5 + 33*s**4 + 176*s**3/3 + 40*s**2 - 65. Find r, given that i(r) = 0.
-5, -2, -1, 0
Let z(m) be the second derivative of 6*m - m**4 + 0 + 9/2*m**3 - 3*m**2. Factor z(t).
-3*(t - 2)*(4*t - 1)
Let a be 0 - (-6 + 0 - -6). Let t be ((-4)/(-3))/(8/18). Factor 0*j + 2/9*j**4 + 2/9*j**2 - 4/9*j**t + a.
2*j**2*(j - 1)**2/9
Suppose 5*p = 5*h, 2*p = -0*p + 4*h - 8. Let u be (27 - 27)*2*(-1)/p. Let 1/2*f - 1/2*f**2 + u = 0. Calculate f.
0, 1
Let y(a) be the first derivative of 5/4*a**4 + 3 + 10/3*a**3 + 0*a + 5/2*a**2. Factor y(w).
5*w*(w + 1)**2
Factor -10299*k**4 - 76*k**2 - 36*k**3 - 6*k**3 + 10297*k**4.
-2*k**2*(k + 2)*(k + 19)
Let s(g) be the first derivative of g**6/6 + 7*g**5/5 + 15*g**4/4 + 13*g**3/3 + 2*g**2 - 352. What is b in s(b) = 0?
-4, -1, 0
Let s(u) be the second derivative of 5*u**4/4 - 121*u**3/48 + u**2/16 + 3*u + 18. Factor s(i).
(i - 1)*(120*i - 1)/8
Let m(d) be the first derivative of -16/3*d**3 - 16/5*d**2 - 14/5*d**4 + 0*d - 12/25*d**5 - 1. Factor m(y).
-4*y*(y + 2)**2*(3*y + 2)/5
Suppose 66 = 3*l + 18. Factor 10*q**5 - 13*q**3 - 4*q**2 - q**3 + l*q**5 - 16*q**4 - 32*q**5.
-2*q**2*(q + 1)**2*(3*q + 2)
Let j(z) be the first derivative of 4/39*z**3 + 10 + 3/13*z**2 + 2/13*z. Let j(o) = 0. Calculate o.
-1, -1/2
Let p(k) = 11*k**2 + 694*k + 24500. Let b(y) = 9*y**2 + 696*y + 24500. Let s(x) = 3*b(x) - 2*p(x). Factor s(v).
5*(v + 70)**2
Let k(d) be the first derivative of -d**6/6 + d**5/5 + 3*d**4/4 - d**3/3 - d**2 + 60. Factor k(m).
-m*(m - 2)*(m - 1)*(m + 1)**2
Let -20*c**5 + 39 + 142 - 264*c**4 + 53 + 31*c**5 - 978*c**2 + 21*c + 4*c**5 + 972*c**3 = 0. Calculate c.
-2/5, 1, 3, 13
Let n(x) be the first derivative of x**5/35 - x**4/28 + 200. Factor n(g).
g**3*(g - 1)/7
Let t(w) be the third derivative of -w**5/15 + 8*w**4 - 384*w**3 - w**2 + 44*w. Determine l so that t(l) = 0.
24
Let p be -15*1*(-28)/(-21). Let k be 174/10 + (-12)/p. Factor -j + j**5 + 2*j - 20*j**3 + k*j**3.
j*(j - 1)**2*(j + 1)**2
Let z(r) be the second derivative of 0*r**2 - 1/20*r**4 + 34*r + 0*r**3 + 3/100*r**5 + 0. Factor z(x).
3*x**2*(x - 1)/5
Let m be 5 + 4/(-4) - -1. Suppose m*z - 11*z + 24 = 0. Factor 0*n**2 + 1/2*n**5 + 1/2*n**3 - n**z + 0*n + 0.
n**3*(n - 1)**2/2
Let b(o) be the second derivative of o**4/18 + 34*o**3/3 + 867*o**2 - 3*o + 197. Solve b(d) = 0 for d.
-51
Let z(a) be the third derivative of -a**7/735 + a**6/84 - a**5/210 - a**4/4 + 6*a**3/7 + 26*a**2 + 1. Solve z(b) = 0 for b.
-2, 1, 3
Let w(l) be the first derivative of 0*l - 2/35*l**5 + 1/14*l**4 - 4 + 2/21*l**3 - 1/7*l**2. Let w(u) = 0. What is u?
-1, 0, 1
Let d = 97 - 2715/28. Let u(o) be the second derivative of -3/40*o**5 + d*o**7 + 0 - 1/8*o**4 + 0*o**3 + 1/20*o**6 - 6*o + 0*o**2. Factor u(c).
3*c**2*(c - 1)*(c + 1)**2/2
Suppose -14 = 4*q - 142. Factor -6*j - 20*j**3 - 8*j - 3*j + 5*j - q*j**2.
-4*j*(j + 1)*(5*j + 3)
Suppose 10*o = -o + 110. Let h(w) = w**3 - 10*w**2. Let l be h(o). Find m such that 0 + l*m + 3/5*m**2 = 0.
0
Let n = 61 - 63. Let b be (-4 - (n - 3/(-3)))*-1. Factor 8*g**2 + 1 + b*g**4 + 1/2*g**5 + 7*g**3 + 9/2*g.
(g + 1)**4*(g + 2)/2
Let g(m) be the first derivative of -128/3*m**2 + 256/3*m + 32/3*m**3 + 1/15*m**5 - 4/3*m**4 + 3. Let g(n) = 0. Calculate n.
4
Let t(j) be the third derivative of -8*j**7/945 + 62*j**6/135 - 1021*j**5/135 + 155*j**4/9 - 50*j**3/3 + 79*j**2. Factor t(g).
-4*(g - 15)**2*(2*g - 1)**2/9
Let l(r) be the third derivative of -r**6/660 - 4*r**5/55 - 7*r**4/11 + 784*r**3/33 + r**2 + 66. Suppose l(j) = 0. What is j?
-14, 4
Let u(z) be the first derivative of 3*z**4/20 - 18*z**2/5 + 48*z/5 - 110. Factor u(c).
3*(c - 2)**2*(c + 4)/5
Let v(d) be the first derivative of 2*d**3/45 - 16*d**2/15 - 379. Find z such that v(z) = 0.
0, 16
Let r(s) be the first derivative of -5/3*s**3 - 5 - 125*s + 25*s**2. Factor r(w).
-5*(w - 5)**2
Let m(u) be the second derivative of -u**7/462 + 3*u**6/110 - 3*u**5/44 + 7*u**4/132 + 47*u - 1. Suppose m(v) = 0. What is v?
0, 1, 7
Let l be (-36)/8*16/(-18). Factor -435/2*s**2 - 225/2*s**3 - 180*s - 54 - 45/2*s**l - 3/2*s**5.
-3*(s + 1)**3*(s + 6)**2/2
Let 