100. Let k(c) be the second derivative of -33*c + 1/10*c**3 + d*c**5 + 1/5*c**4 - 9/5*c**2 + 0. Factor k(v).
3*(v - 1)*(v + 2)*(v + 3)/5
Let w(d) be the first derivative of -d**5/10 - 5*d**4/8 + 29*d**3/6 + 105*d**2/4 + 4568. Suppose w(s) = 0. What is s?
-7, -3, 0, 5
Let k(j) be the second derivative of j**4/21 + 232*j**3/7 + 60552*j**2/7 - 155*j. Let k(a) = 0. Calculate a.
-174
Let g(y) be the second derivative of -y**6/30 - 49*y**5/10 + 25*y**4/3 + 49*y**3/3 - 99*y**2/2 - 694*y. Factor g(i).
-(i - 1)**2*(i + 1)*(i + 99)
Let f = -1639 - -1641. Let n(o) be the first derivative of 0*o**f - 2/5*o**3 + 0*o - 9 + 3/20*o**4 + 3/25*o**5. Find v such that n(v) = 0.
-2, 0, 1
Factor -129/8*z + 1/8*z**2 - 99/2.
(z - 132)*(z + 3)/8
Suppose 865/4*y - 343/2*y**2 - 383/4*y**3 - 21/2*y**4 - 75/2 = 0. What is y?
-5, 3/14, 2/3
Let c(s) be the third derivative of s**8/2184 + 4*s**7/273 - 43*s**6/195 + 17*s**5/15 - 151*s**4/52 + 54*s**3/13 - 9*s**2 + 78. What is r in c(r) = 0?
-27, 1, 2, 3
Let o = -125 - -128. Factor 20*z**4 - 281 + 41*z**2 - 1152*z - 359 - 148*z**o - 104*z**3 + 561*z**2 + 414*z**2.
4*(z - 5)*(z - 4)**2*(5*z + 2)
Let u(s) = 11*s**5 - 283*s**4 + 846*s**3 - 12*s - 6. Let y(j) = -21*j**5 + 568*j**4 - 1691*j**3 + 22*j + 11. Let k(v) = 11*u(v) + 6*y(v). Factor k(x).
-5*x**3*(x - 56)*(x - 3)
Let h be 41/((4 + -1)/3). Let r = 44 - h. Factor -13*m + 13*m - 3*m**3 + 8*m**r.
5*m**3
Let g = -15437 - -15474. Let v(d) be the second derivative of -g*d + 0*d**2 + 0 + 1/12*d**3 + 1/24*d**4. Factor v(o).
o*(o + 1)/2
Suppose -51 = 49*m - 68*m - 3*y, 5*y - 85 = 0. Find t such that -1/4*t**2 + m + 3/2*t = 0.
0, 6
Let f(r) be the third derivative of -1/2856*r**8 + 1/102*r**4 + 1/340*r**6 + 7*r**2 + 0 + 5*r - 1/102*r**5 + 0*r**3 + 1/1785*r**7. Factor f(c).
-2*c*(c - 1)**3*(c + 2)/17
Let x(p) be the second derivative of -85/9*p**3 - 2/15*p**5 + 16/9*p**4 - p + 7 + 25*p**2. Let x(w) = 0. What is w?
5/2, 3
Let p be 2*17/(-8)*(-1 + -3). Let u(d) = -5*d**3 - 7*d**2 - 12*d. Let c(k) = 14*k**3 + 20*k**2 + 34*k. Let n(h) = p*u(h) + 6*c(h). Factor n(l).
-l**2*(l - 1)
Let g = 65/6441 + -6/791. Let o(a) be the second derivative of 1/57*a**6 + 0*a**2 + 7/114*a**4 + 2*a + 0 - 2/57*a**3 - g*a**7 - 9/190*a**5. Factor o(x).
-2*x*(x - 2)*(x - 1)**3/19
Let j(r) = -r**2 + 6*r - 3. Let f be j(1). Suppose -368*k - 2*k**3 - 104*k**f - 229 - 123 - 2*k**3 = 0. Calculate k.
-22, -2
Suppose -12 = 4*o - 2*g, 0 = -201*g + 202*g - 6. Let u(p) be the second derivative of -3/40*p**5 + o - 9*p + 1/4*p**4 - 3/2*p**2 + 1/4*p**3. Factor u(y).
-3*(y - 2)*(y - 1)*(y + 1)/2
Suppose -405*y + 9075*y**5 - 230*y**3 - 18157*y**5 - 80*y**4 + 720*y**2 + 9077*y**5 = 0. Calculate y.
-9, 0, 1
Let c(b) = 5*b**2 - 52 + 57*b + 34*b + 10*b. Let k(t) = -10*t**2 - 201*t + 100. Let a(j) = -10*c(j) - 6*k(j). Solve a(y) = 0.
-20, 2/5
Let c(u) be the first derivative of u**6/30 - 3*u**5/10 + u**4/4 + 5*u**3/3 - 15*u + 41. Let d(m) be the first derivative of c(m). Factor d(i).
i*(i - 5)*(i - 2)*(i + 1)
What is b in 84 + 39*b + 3/2*b**4 - 171/2*b**2 - 39*b**3 = 0?
-2, -1, 1, 28
Let b = 117 + -16. Let h be (-12)/4 + 1 + 5 + 29. Factor -27*r**2 + h*r**2 - 11*r + b*r + 405.
5*(r + 9)**2
Let w(l) be the third derivative of -l**7/70 + 107*l**6/40 + l**5/20 - 107*l**4/8 + 511*l**2 - 4*l. Factor w(s).
-3*s*(s - 107)*(s - 1)*(s + 1)
Let 36*t**2 - 2/11*t**4 + 58/11*t**3 + 560/11 + 824/11*t = 0. What is t?
-2, 35
Let g(c) be the third derivative of c**6/120 + 202*c**5/15 - c**4/24 - 404*c**3/3 + c**2 + 671*c + 3. Suppose g(t) = 0. What is t?
-808, -1, 1
Let a(g) be the third derivative of -33*g**2 + 7/90*g**5 + 0*g + 1/45*g**6 + 0*g**3 - 11/36*g**4 + 0. Suppose a(p) = 0. Calculate p.
-11/4, 0, 1
Let r(j) be the first derivative of j**4/30 - 2*j**3/3 - 24*j**2/5 - 152*j/15 - 936. Factor r(f).
2*(f - 19)*(f + 2)**2/15
Let 127*w**2 + 42*w**2 + w**3 - 202*w - 335*w**2 + 35*w = 0. Calculate w.
-1, 0, 167
Factor -21*x + 69/2*x**2 - 15*x**3 + 0 + 3/2*x**4.
3*x*(x - 7)*(x - 2)*(x - 1)/2
Let j(i) = -6*i - 15. Let x be j(-3). Factor 5*r**3 + 0*r**3 - 3*r**3 - 6*r**x.
-4*r**3
Suppose 3*g + c - 6 = -2, 4*g = 4*c + 32. Let p be (234/65 + -2)/(94/47). Factor 0 + 2/5*t**g + p*t**2 + 2/5*t.
2*t*(t + 1)**2/5
Let v be 20/25 - 4/5. Suppose v = x + 6 - 10. Find u, given that -2*u**3 + 0*u**2 - 4*u**5 + 6*u**5 - 1 + 4*u**2 - 3*u**x = 0.
-1, -1/2, 1
Let f(k) be the first derivative of 76*k**3/33 + 75*k**2/11 + 74*k/11 + 1984. Solve f(i) = 0 for i.
-1, -37/38
Let z(d) be the third derivative of -4*d**7/105 + 101*d**6/30 + 17*d**5/5 - 10*d**2 + 8. Factor z(q).
-4*q**2*(q - 51)*(2*q + 1)
Let w be (-10)/(2*(-3)/(-567)). Let u = w + 7581/8. Suppose -3/4*y + 15/8*y**4 - 3/8*y**5 + u*y**2 + 0 - 27/8*y**3 = 0. What is y?
0, 1, 2
Let w(a) = 2*a**2 + 4. Let b be -2 - 4 - (-14 - 14). Let r(l) = -8*l**2 + 2*l - 16. Let d(p) = b*w(p) + 6*r(p). Suppose d(m) = 0. Calculate m.
1, 2
Let p(f) be the second derivative of 0 + 1/60*f**6 - 85*f + 7/12*f**3 + 5/24*f**4 - 7/40*f**5 - 3/2*f**2. Solve p(s) = 0.
-1, 1, 6
Suppose 26*c = 11047 + 991. Let r = c + -2314/5. Solve -r*s**2 + 4/5 + 3/5*s = 0.
-1, 4
Suppose -v + 143 = 5*c - 4*v, 4*v - 24 = -c. Suppose 3*u + 4*u - c = 0. Factor 6*g**2 + 3*g**2 + 0*g**2 - g**u - 6*g - 2*g**4.
-3*g*(g - 1)**2*(g + 2)
Let x(s) be the third derivative of 0 - 1/40*s**5 + 0*s - 210*s**2 + 10*s**3 - 3/8*s**4. Factor x(b).
-3*(b - 4)*(b + 10)/2
Suppose 54 = 6*u - 9*u. Let q = 16 - u. Determine h so that 70*h**3 - h**2 - 7*h**2 - 22*h**4 - 6*h**4 - q*h**3 = 0.
0, 2/7, 1
Let b(v) be the first derivative of 155/2*v**2 - 187 + 16*v**5 + 15/2*v**6 - 30*v - 50*v**4 - 50/3*v**3. What is j in b(j) = 0?
-3, -1, 2/9, 1
Let y = -5 - -9. Factor -160*s**y - 161*s**4 - 2*s**5 + 327*s**4 - 4*s**3.
-2*s**3*(s - 2)*(s - 1)
What is j in 90/13*j**2 + 2/13*j**4 - 140/13 - 22/13*j - 2*j**3 = 0?
-1, 2, 5, 7
Let f(x) be the second derivative of x**6/180 + 7*x**5/60 - 2*x**4/3 - 122*x**3/3 + 174*x. Let h(v) be the second derivative of f(v). Factor h(o).
2*(o - 1)*(o + 8)
Let g(z) = -z**2 - 9*z + 8. Let w be g(-9). Let h(b) = -7*b**2 + 172*b + 900. Let c(m) = 3*m**2 - 57*m - 300. Let x(j) = w*c(j) + 3*h(j). Solve x(y) = 0 for y.
-10
Let q(o) be the third derivative of -o**5/60 + 157*o**4/24 - 155*o**3/3 - 290*o**2. Factor q(t).
-(t - 155)*(t - 2)
Solve 2/15*g**4 + 0 + 0*g + 153760/3*g**2 - 496/3*g**3 = 0 for g.
0, 620
Let v(i) be the third derivative of -i**5/330 - 3*i**4/22 - 56*i**3/33 - 60*i**2 - 7*i. Factor v(a).
-2*(a + 4)*(a + 14)/11
Suppose 4*l = 32 - 20. Suppose -5*a - 17 = l*x - 96, 2*a = -5*x + 43. Factor a*j - 4*j**3 - 2*j + 244 - 8*j**2 - 244.
-4*j*(j - 1)*(j + 3)
Let x be (0 - 303)/(3*7/(-7)). Let b = x + -101. Factor 0 + b*r + 1/5*r**2.
r**2/5
Let n be 12720/432 + 9 + -38. Suppose -2/9 + n*i**3 - 4/9*i + 2/9*i**2 = 0. What is i?
-1, -1/2, 1
Suppose 0 = -5*v - i + 14, 30 = 5*v + 5*i. Suppose 2*n = 3*n - v. Factor 2*m - 4*m**4 + 3*m**2 + m**n + 15*m**5 - 17*m**5.
-2*m*(m - 1)*(m + 1)**3
Let o = 207 + -197. Let n be (9 - 7)*(3 + -2). Let -21*z**n - o*z - 22*z**2 + 48*z**2 = 0. What is z?
0, 2
Determine n so that 59*n**2 + 340*n**3 + 28503*n - 25*n**4 + 80*n**2 - 28489*n = 0.
-1/5, 0, 14
Let s(c) be the first derivative of 5*c**4/4 + 35*c**3/6 - 5*c**2/2 - 35*c/2 - 264. Find z, given that s(z) = 0.
-7/2, -1, 1
Let o = 38 + -58. Let y = 32 + o. Determine n so that 6*n**3 - y*n**2 + 3*n**4 + 2*n + 21 - 8*n - 37 + 25 = 0.
-3, -1, 1
Suppose -361*k + 2*k - 9*k + 22*k - 90*k - 4*k**2 = 0. Calculate k.
-109, 0
Let x(a) be the first derivative of -6*a**2 + 279*a - 174. Let m be x(23). Find f, given that -3 - 3/4*f + 3/4*f**m + 3*f**2 = 0.
-4, -1, 1
Let b(g) be the first derivative of -g**4/2 + 10*g**3 + 34*g**2 + 9058. Factor b(p).
-2*p*(p - 17)*(p + 2)
Let j(v) = 39*v**3 - 2477*v**2 + 2487*v. Let o(y) = -140*y**3 + 8670*y**2 - 8705*y. Let u(b) = 25*j(b) + 7*o(b). Determine s, given that u(s) = 0.
-248, 0, 1
Let h(f) = 4*f**2 - 1407*f - 169918. Let n(o) = -3*o**2 + 1410*o + 169920. Let g(i) = 6*h(i) + 7*n(i). Solve g(k) = 0.
-238
Factor -3358/3*p - 2/9*p**3 - 32*p**2 + 21316/9.
-2*(p - 2)*(p + 73)**2/9
Find q such that -7*q**3 - 165*q**2 + 605 + 160 + 167*q + 4*q**3 - 35*q - 729*q = 0.
-51, -5, 1
Let k(a) be the second derivative of a**8/168 - a**7/21 - a**6/60 + a**5/