t r be (-2)/4 + (-225)/90. Let m be 4*(11 - 9) + 1*r. Find l such that 0 - 6*l**3 + 4*l**2 - 1/2*l**m + 0*l + 3*l**4 = 0.
0, 2
Let v(t) be the second derivative of -t**5/170 + 25*t**4/51 + 575*t**3/51 + 1500*t**2/17 + 226*t + 3. Factor v(m).
-2*(m - 60)*(m + 5)**2/17
Suppose 5*k - 2*k = f - 22, 5*k - 24 = -3*f. Suppose -h = 5*x - 6, -12*h = 2*x - f*h - 8. Factor x + r + 1/8*r**2.
(r + 4)**2/8
Factor -488072/7 - 2/7*t**2 - 1976/7*t.
-2*(t + 494)**2/7
Let i = 833255/602 - 194/301. Let h = i + -1380. Solve 4 + h*t - 1/2*t**2 = 0.
-1, 8
Let s be 14/2 + 20181/(-2821) + (-112)/(-52). Let -4/5*x**s + 12/5 + 8/5*x = 0. What is x?
-1, 3
Let g(k) = -k**2 + 1. Let z be (-1098)/(-144) + 3/8. Let m(o) = -3*o**2 + z + 0*o + 0*o**2 - 5*o. Let t(l) = 4*g(l) - m(l). Factor t(d).
-(d - 4)*(d - 1)
Let n be (16/6*141/4700)/((-2)/(-40)). Factor n + 108/5*a**2 + 116/5*a.
4*(a + 1)*(27*a + 2)/5
Suppose -3*o + 34 = -5*p, -o - 2 = -43*p + 44*p. Suppose -3/5*z**o - 82/5*z - 32/5 - 53/5*z**2 = 0. What is z?
-16, -1, -2/3
Let t be 4/14 + -24 + (-4114)/(-154). Let f(u) be the first derivative of 2/7*u**2 - 1/7*u**t - 1/28*u**4 + 0*u - 9. Determine l, given that f(l) = 0.
-4, 0, 1
Suppose -5*q - 63 = -73. Suppose 6*k + 2 = 7*k + l, -q*k = -2*l - 4. Factor -3*n + 38*n - 11*n + k*n**2.
2*n*(n + 12)
Let h = 130 - 137. Let i(a) = 67*a**3 + 96*a**2 + 5*a - 17. Let z(c) = 22*c**3 + 32*c**2 + 2*c - 6. Let y(d) = h*z(d) + 2*i(d). Factor y(r).
-4*(r + 1)**2*(5*r - 2)
Factor -171 + 33 + 100*g - g**2 + g**2 + 3*g**2 - 235*g.
3*(g - 46)*(g + 1)
Let -26*x**2 - 582*x - 195 + 69*x**2 - 389 - 41*x**2 = 0. What is x?
-1, 292
Factor -2*m + 2/5*m**4 - 18/5*m**2 - 6/5*m**3 + 0.
2*m*(m - 5)*(m + 1)**2/5
Solve 288*h - 21*h**4 + 96*h**3 + 930*h**2 - 6*h**3 + 72*h**3 + 126*h**2 = 0.
-4, -2/7, 0, 12
Suppose -5*k + 2*c = -28, -c - 1029 + 1030 = 5*k. Factor 6/5*i**k - 3/5*i**3 + 0 + 0*i.
-3*i**2*(i - 2)/5
Let l(x) be the second derivative of 4/3*x**3 + 0*x**2 - 1/4*x**5 + 1 - 1/6*x**4 + 6*x - 1/30*x**6. Factor l(j).
-j*(j - 1)*(j + 2)*(j + 4)
Suppose 5*k - 3*l = -8*l, -k = -l - 8. Let d(b) = -b**3 - b**2. Let y(h) = -6*h**2 + 4*h. Let i(q) = k*y(q) - 4*d(q). Determine u, given that i(u) = 0.
0, 1, 4
Suppose 2*x - 5*q = -5, -489*q + 2 = -x - 487*q. Let u(n) be the third derivative of x - 1/30*n**5 + 0*n + 4*n**2 + 5/12*n**4 + 0*n**3. Factor u(m).
-2*m*(m - 5)
Factor -91/9*c - 365/9*c**2 + 0 - 4/9*c**3.
-c*(c + 91)*(4*c + 1)/9
Suppose 45*m - 15 - 30 = 0. Factor -36*v**3 - 13*v**2 - 12*v**4 - 7*v**2 - m + 21132*v**5 - 21128*v**5 + 1.
4*v**2*(v - 5)*(v + 1)**2
Find b such that 72/7 + 106/7*b**2 - 20/7*b**3 + 216/7*b - 2*b**4 = 0.
-2, -3/7, 3
Find m, given that 1/2*m**3 - 125*m + 0 - 45/2*m**2 = 0.
-5, 0, 50
Suppose 56 = -3*v + 275. Let d = v - 70. Factor -5*g**2 - 7*g**3 - 1 + 9 + 8*g**d + 17*g + 15*g**2.
(g + 1)**2*(g + 8)
Let t(v) be the third derivative of v**8/112 + 19*v**7/70 + 5*v**6/2 + 51*v**5/5 + 18*v**4 + v**2 + 1036. What is q in t(q) = 0?
-12, -3, -2, 0
Suppose 39/2*b**2 - 1/2*b**4 + 17/2*b**3 - 19 - 17/2*b = 0. Calculate b.
-2, -1, 1, 19
Let m(r) = -30*r**3 - 6*r**2 + 28*r + 92. Let k(d) = 53*d**3 + 12*d**2 - 57*d - 185. Let g(o) = -4*k(o) - 7*m(o). Factor g(b).
-2*(b - 4)*(b + 3)*(b + 4)
Determine a so that 5454*a + 76*a**2 + 52*a**3 - 5394*a - 15*a**4 + 40*a**2 + 11*a**4 = 0.
-1, 0, 15
Suppose -48*s - 17220 = -89*s. Let b be -1 - s/36*(-6)/63. Factor b*c**2 + 1 - 2/3*c.
(c - 3)**2/9
Let z(j) be the first derivative of -2/9*j**3 + 0*j - 14 + 2*j**2 + 1/90*j**5 - 1/36*j**4. Let d(l) be the second derivative of z(l). Find p such that d(p) = 0.
-1, 2
Let x(y) be the first derivative of y**6/4 + y**5/5 - 9*y**4/8 - 2*y**3 - y**2 - 2141. Determine k so that x(k) = 0.
-1, -2/3, 0, 2
Let t(k) be the second derivative of -k**5/140 - 3*k**4/28 + 2*k**3/7 + 10*k**2/7 - 13*k + 36. Factor t(a).
-(a - 2)*(a + 1)*(a + 10)/7
Let a(d) be the first derivative of 4/3*d**3 + 0*d - 22*d**2 - 35. Factor a(l).
4*l*(l - 11)
Factor 110/17*l**2 + 536/17 + 6/17*l**3 - 512/17*l.
2*(l - 2)**2*(3*l + 67)/17
Let w(o) be the third derivative of -17/216*o**4 + 0*o + 1/15*o**5 + 1/27*o**3 + 56*o**2 + 0. Find g, given that w(g) = 0.
2/9, 1/4
Factor -h**2 - 17*h - 9*h**3 - 14*h - 9*h + h**4 + 49*h.
h*(h - 9)*(h - 1)*(h + 1)
Let s(g) be the second derivative of 33/2*g**3 + 0 - 233*g + 0*g**2 - 1/4*g**4. Factor s(y).
-3*y*(y - 33)
Let n(w) be the first derivative of 2*w**5/85 + 26*w**4/17 - 72*w**3/17 + 4842. Factor n(b).
2*b**2*(b - 2)*(b + 54)/17
Factor 313965 - 313818 + b**2 - 2*b**2 + 0*b**2 - 46*b.
-(b - 3)*(b + 49)
Find q such that -72/5*q**2 - 144/5 - 48*q + 48/5*q**3 + 27/5*q**4 + 3/5*q**5 = 0.
-6, -2, -1, 2
Let r(p) = -670*p**2 + 3242*p - 3850. Let n(u) = -u**2 - 3*u + 1. Let h(q) = 6*n(q) + r(q). Factor h(d).
-4*(13*d - 31)**2
Let x(b) be the second derivative of b**5/40 - b**4/48 + 41*b**2/2 - 26*b. Let v(m) be the first derivative of x(m). Suppose v(i) = 0. Calculate i.
0, 1/3
Suppose 5*y = q, -8*y = 2*q - 3*y - 60. Let 25*h**3 - 20*h - 1278*h**4 - q*h + 1273*h**4 - 10*h**2 = 0. Calculate h.
-1, 0, 2, 4
Let h(k) be the third derivative of 0 - 6*k**3 + 1/5*k**6 + 0*k - 9*k**4 - 224*k**2 + 1/15*k**5. Let h(o) = 0. Calculate o.
-3, -1/6, 3
Let t(n) = -7*n**3 + 16*n**2 - 13*n + 26. Let x(j) = -j**3 + 3*j**2 - 2*j + 4. Let b(d) = -6*t(d) + 39*x(d). Find h, given that b(h) = 0.
-7, 0
Let b be -7 - (-1062)/81 - 5. Let m(a) be the second derivative of 7/36*a**6 - 16*a + 5/9*a**3 + 0 + 0*a**2 - b*a**4 + 5/24*a**5. Find h such that m(h) = 0.
-2, 0, 2/7, 1
Suppose -6*c - 2*w - 2370 = -c, w = 4*c + 1883. Let i = -472 - c. Suppose 6/19*l**3 + 2/19*l**5 + 6/19*l**4 + 0*l + i + 2/19*l**2 = 0. Calculate l.
-1, 0
Let g(b) be the third derivative of -4*b**8/315 + 4*b**7/945 - b**6/1620 + b**5/10 + 5*b**4/8 + 25*b**2. Let d(v) be the third derivative of g(v). Factor d(a).
-4*(24*a - 1)**2/9
Let m = 30412 + -30375. Let y(u) be the second derivative of 1/12*u**6 - 1/84*u**7 - 1/6*u**3 - 9/40*u**5 + 0 + 0*u**2 - m*u + 7/24*u**4. Factor y(k).
-k*(k - 2)*(k - 1)**3/2
Let w(g) = 17*g**2 + 7*g - 66. Let i be w(6). Let b = -582 + i. Determine d, given that 27/2*d**2 + 18*d + b + 3*d**3 = 0.
-2, -1/2
Let b be 2*12/(((-35)/105)/((-1)/(-3))). Let z(n) = n**3 - n + 1. Let h(u) = -7*u**3 - u + 15*u + 9*u**2 + 9*u - 33. Let l(m) = b*z(m) - 3*h(m). Factor l(c).
-3*(c - 1)*(c + 5)**2
Let b(y) be the third derivative of -1/68*y**6 - 21/170*y**5 - 1/1785*y**7 - 49/204*y**4 - 38*y + 0 + 0*y**3 - 2*y**2. Factor b(x).
-2*x*(x + 1)*(x + 7)**2/17
Suppose 22*b + 2088 = 30*b. Let c = 263 - b. Find i such that 2/7*i**c - 12/7*i + 2/7*i**4 + 8/7*i**3 + 0 = 0.
-3, -2, 0, 1
Suppose -511*n + 56 = -507*n. Factor 14*f + 0*f**2 - 43*f + n*f - 3*f**2 + 12*f.
-3*f*(f + 1)
Let k(d) be the first derivative of 5*d**4/16 - 775*d**3/6 + 123165*d**2/8 - 117045*d + 1130. Factor k(l).
5*(l - 153)**2*(l - 4)/4
What is q in 488*q**2 - 1118*q**2 - 2*q**4 - 930*q**2 + 0*q**4 + 116*q**3 - 1872*q - 1728*q = 0?
-2, 0, 30
Let h(z) = -6*z**2 + 60*z + 98. Let a(m) = -35*m**2 + 353*m + 592. Let k(g) = -4*a(g) + 23*h(g). Let k(u) = 0. Calculate u.
-3, 19
Suppose -3*n = 28*n + 124. Let o be (-368)/(-230)*(-5)/n. Factor 0*m - 1/2*m**4 + 1/2*m**o - 1/2*m**5 + 1/2*m**3 + 0.
-m**2*(m - 1)*(m + 1)**2/2
Let y(w) be the first derivative of -4*w**3/9 - 224*w**2 - 1332*w - 5539. Factor y(g).
-4*(g + 3)*(g + 333)/3
Suppose 5*u + 2*m - 112 = 3*u, u - 71 = -4*m. Let x be u/15 - 5 - -2. Solve -14/5 + x*r**2 + 12/5*r = 0.
-7, 1
Let c(t) be the first derivative of -1282*t**6/3 + 10248*t**5/5 - 3838*t**4 + 10208*t**3/3 - 1266*t**2 - 8*t + 2882. Suppose c(d) = 0. Calculate d.
-2/641, 1
Suppose -48*l + 48329 = -23623. Let r = l - 1496. Solve 0*v**2 + r*v - 1/4*v**3 + 4 = 0.
-2, 4
Let r(f) = -7*f**2 - 366. Let u(j) = 2*j**2 - j + 122. Let a(h) = r(h) + 3*u(h). Factor a(v).
-v*(v + 3)
Let i(j) be the third derivative of j**6/1800 + j**5/300 - j**4/40 + 37*j**3/3 + 125*j**2. Let v(g) be the first derivative of i(g). What is d in v(d) = 0?
-3, 1
Suppose -205*h**4 + 95288419*h + 390*h**3 - 95288419*h + 5*h**5 = 0. Calculate h.
0, 2, 39
Let c(u) = 2*u**2 + 4*u + 4. Let z be c(-3). Suppose -6*s**5 - z*s - 12*s**2 - 148*s**3 + 6 + 8*s**4 + 164*s**3 - 2 = 0. Calculate s.
-1, 1/3, 1, 2
Suppose 2*z = -z + 105. 