*2 + l**3 = 0.
0, 1
Suppose -5*c + 9*c + 2*b = 24, b = c. Suppose 32*a**3 + 22*a - 3*a**4 + 4 + 16*a**c + 42*a**2 - 5*a**4 = 0. What is a?
-2, -1, -1/2
Let a = -46697/170 - -4872/17. Let z = -37/5 + a. Factor -2 - 4*d + z*d**3 + 3/2*d**2.
(d - 1)*(3*d + 2)**2/2
Let u be (-62)/(-340) + 52/442. Let f(n) be the second derivative of -2/15*n**6 - n + 0 + 0*n**2 + 1/6*n**3 - 1/3*n**4 + u*n**5 + 1/42*n**7. Factor f(o).
o*(o - 1)**4
Let v(m) be the second derivative of -m**7/126 + 2*m**6/15 - 13*m**5/15 + 8*m**4/3 - 32*m**3/9 - 148*m - 1. Factor v(s).
-s*(s - 4)**2*(s - 2)**2/3
Let n(q) be the first derivative of q**4/4 - 7*q**3/3 + 7*q**2 - 8*q + 192. Factor n(j).
(j - 4)*(j - 2)*(j - 1)
Let w(v) be the first derivative of -v**6/195 + v**5/65 - v**4/78 - 11*v + 6. Let o(y) be the first derivative of w(y). Find t, given that o(t) = 0.
0, 1
Suppose -4*x - q = -0*q - 53, 0 = -5*x + 4*q + 40. Factor -14*r + 2*r + 4*r**3 - 20 + 0*r + x.
4*(r - 2)*(r + 1)**2
Let a(s) be the third derivative of -s**5/150 - s**4/60 + 2*s**3/5 + 106*s**2. Let a(m) = 0. What is m?
-3, 2
Let k = -103 + 107. Let z(j) be the second derivative of 5/3*j**k - 2/3*j**6 + 0*j**2 - 4/3*j**3 + 0 + 2/5*j**5 - 6*j. Find t, given that z(t) = 0.
-1, 0, 2/5, 1
Let b(d) be the third derivative of -d**5/60 - d**3/6 + 43*d**2. Let n(f) = 18*f**2 + 3*f - 3. Let i = -4 - 2. Let p(u) = i*b(u) - n(u). Factor p(o).
-3*(o + 1)*(4*o - 3)
Let c = 103 + -102. Let r(n) be the first derivative of -n**2 + 1/4*n**3 - c + n. Factor r(f).
(f - 2)*(3*f - 2)/4
Let u(o) be the first derivative of o**7/1365 - o**6/390 + o**4/78 - o**3/39 - 5*o**2 - 12. Let i(r) be the second derivative of u(r). Factor i(n).
2*(n - 1)**3*(n + 1)/13
Let k(z) be the third derivative of z**6/840 + 19*z**5/210 + 5*z**4/24 - 37*z**3/21 + 440*z**2. Factor k(u).
(u - 1)*(u + 2)*(u + 37)/7
Let y = 82 - 163/2. Let b = 49 - 97/2. Find k such that -b*k + y*k**3 - 1/2 - k**4 + 3/2*k**2 = 0.
-1, -1/2, 1
Let q(t) = t**3 + 9*t**2 + 12*t - 10. Let s be q(-7). Suppose 0*x + 2*x**5 + x - x + s*x**4 = 0. Calculate x.
-2, 0
Suppose -3*g - 11 = -2*l, -7 = -3*l - g - 4*g. Let -2*m**l - 6*m**3 - 5*m + 2*m**2 + 17*m - 8*m + 2*m**5 = 0. Calculate m.
-1, 0, 1, 2
Let f(b) = -3*b**2 + 4*b + 87. Let g be f(6). Factor 0*d**g + 0*d - 6/5*d**2 + 3/5*d**4 + 3/5.
3*(d - 1)**2*(d + 1)**2/5
Let f = -2736 - -2738. Determine n, given that f*n - 2*n**3 + 6/5*n**4 - 2/5*n**2 - 4/5 = 0.
-1, 2/3, 1
Let j be (-2)/(-12) + (-1 - (-58)/12). Suppose j*x = p + 12, 2*x = p + 2*p + 16. Determine c so that 1/2*c + 1/2*c**x + 0 = 0.
-1, 0
Let k(v) = -v**3 + 4*v**2 + 12*v - 4. Let q(f) = f**2 - f - 1. Let h(o) = -k(o) + 4*q(o). Factor h(x).
x*(x - 4)*(x + 4)
Let c(n) be the first derivative of n**4/6 - n**2 - 4*n/3 - 190. Factor c(z).
2*(z - 2)*(z + 1)**2/3
Let j be -12*2/(-3 - 3). Let p(x) be the second derivative of 0*x**2 - 4*x + 0*x**3 + 0 + 3/20*x**5 + 1/4*x**j. Factor p(r).
3*r**2*(r + 1)
Factor -23*o**4 - 30*o**4 + 4*o**3 + 76*o**4 + 24 - 25*o**4 + 56*o + 38*o**2.
-2*(o - 6)*(o + 1)**2*(o + 2)
Let n(a) be the third derivative of a**6/120 - 3*a**5/10 - 13*a**4/8 - 10*a**3/3 + 45*a**2. Determine d, given that n(d) = 0.
-1, 20
Factor 30*o + 42 - 67 - 9*o**2 + 70 + 14*o**2.
5*(o + 3)**2
Let r = 8997 + -98965/11. Factor -2/11*k**2 + 4/11*k - r.
-2*(k - 1)**2/11
Determine d, given that 5*d**2 - 1/2*d**3 + 18 - 33/2*d = 0.
3, 4
Let w(x) be the third derivative of x**9/756 - x**7/105 + x**5/30 + x**3/6 + 14*x**2. Let m(n) be the first derivative of w(n). Factor m(v).
4*v*(v - 1)**2*(v + 1)**2
Let a(i) = -4*i**2. Let c(t) = 17*t**2 + 5*t - 14. Let d(g) = -4*a(g) - c(g). Factor d(y).
-(y - 2)*(y + 7)
Suppose 20 = -565*k + 561*k, k = -4*d + 7. What is p in 5/2*p**2 - 2*p**d + 0 - p + 1/2*p**4 = 0?
0, 1, 2
Let g(t) be the third derivative of 1/4*t**6 - 55/294*t**7 + 0 + 125/2352*t**8 - 17/105*t**5 - 13*t**2 + 0*t + 0*t**3 + 1/21*t**4. Let g(s) = 0. What is s?
0, 2/5, 1
Let a(z) be the third derivative of z**7/280 + z**6/30 + 17*z**5/240 + z**4/24 - z**2 - 29. Factor a(g).
g*(g + 1)*(g + 4)*(3*g + 1)/4
Factor -22*u**2 + 60*u + 2*u**3 - 46*u + 46*u.
2*u*(u - 6)*(u - 5)
Suppose 0 = -5*o - 3*o + 40. Let p(i) = -i**5 - 5*i**4 - 4*i**3 - 5. Let r(b) = -b**5 - 7*b**4 - 6*b**3 - 7. Let g(z) = o*r(z) - 7*p(z). Factor g(k).
2*k**3*(k - 1)*(k + 1)
Let m(a) be the first derivative of a**6/4 - 9*a**5/4 + 111*a**4/16 - 41*a**3/4 + 63*a**2/8 - 3*a - 416. Suppose m(b) = 0. Calculate b.
1/2, 1, 4
Determine y, given that -4/3*y**2 + 20/3*y + 56/3 = 0.
-2, 7
Let f be -3 + (-126)/(-49) - 31/(-7). Factor 14*i**3 - 18*i**3 + 4*i**f - 15*i**2 - 12*i - 5*i**2.
4*i*(i - 3)*(i + 1)**2
Let y(h) = 12*h**2 + 63*h + 10. Let o(s) = 15 - s - 60*s**2 - 37 - 29 - 314*s. Let z(c) = -5*o(c) - 24*y(c). Suppose z(t) = 0. Calculate t.
-5, -1/4
Let p(z) be the first derivative of -1/8*z**4 - 14 + 0*z**2 + 0*z - 1/3*z**3. Let p(y) = 0. What is y?
-2, 0
Let u(t) = t**3 + 11*t**2 - 2*t - 22. Suppose 4*p = 4 - 48. Let w be u(p). Solve -2/5*c + 2/5*c**2 + w = 0.
0, 1
Suppose -36 - 3 = -13*p. Let j(c) be the second derivative of 3*c**2 + 3/20*c**5 + 0 - 1/2*c**4 - 4*c - 1/2*c**p. Factor j(v).
3*(v - 2)*(v - 1)*(v + 1)
Let z(x) be the second derivative of -1/60*x**5 + 0 - 13*x + 5/12*x**4 + 125/6*x**2 - 25/6*x**3. Let z(p) = 0. Calculate p.
5
Let o = -5525/4 + 1390. Factor o*g - 5 - 5/2*g**2 - 5/4*g**3.
-5*(g - 1)**2*(g + 4)/4
Let f(b) be the second derivative of -b**4/30 + 52*b**3/5 - 6084*b**2/5 - 203*b. Factor f(v).
-2*(v - 78)**2/5
Let d(z) be the second derivative of -2*z**7/21 + 4*z**6/5 + 2*z**5 - 16*z**4/3 - 22*z**3 - 28*z**2 - 237*z. Factor d(i).
-4*(i - 7)*(i - 2)*(i + 1)**3
Let j(b) be the first derivative of b**6/27 - 4*b**5/45 - b**4/6 - 105. Determine d so that j(d) = 0.
-1, 0, 3
Factor 85/3*m + 50/3 + 40/3*m**2 + 5/3*m**3.
5*(m + 1)*(m + 2)*(m + 5)/3
Let i(c) be the second derivative of c**5/80 + 11*c**4/48 + 3*c**3/2 + 9*c**2/2 - 298*c. Factor i(b).
(b + 2)*(b + 3)*(b + 6)/4
Let q(k) = 4*k**4 - 12*k**3 + k**2 + 15*k - 8. Let l(h) = -4*h**4 + 12*h**3 - 2*h**2 - 14*h + 8. Let u(w) = 3*l(w) + 2*q(w). Factor u(t).
-4*(t - 2)*(t - 1)**2*(t + 1)
Determine l, given that -4 + 3*l**2 + 119 + 51*l + 113 - 342 = 0.
-19, 2
Let y be (-5)/15 - ((-15)/9 - -1). Let q(m) be the third derivative of 1/6*m**4 + 0 + m**2 - y*m**3 + 0*m - 1/30*m**5. Factor q(w).
-2*(w - 1)**2
Suppose 0*k - 3*k + 15 = 0. Suppose -7 = -4*z + k. Factor 0*n**2 + 2*n + z*n**4 - n**3 + 0*n**2 - 3*n**2 - n**5.
-n*(n - 2)*(n - 1)**2*(n + 1)
Let z(s) be the third derivative of -1/200*s**6 + 15*s**2 - 1/5*s**3 + 0 + 0*s + 1/40*s**4 + 1/50*s**5. Factor z(g).
-3*(g - 2)*(g - 1)*(g + 1)/5
Factor -5/4*y**2 + 15*y + 0.
-5*y*(y - 12)/4
Let w be 142/(-22) + (-8 + 11 - -4). Determine s so that 8/11 - 2/11*s**2 + w*s = 0.
-1, 4
Suppose 2/9*p**3 - 4/9*p**2 + 0 - 16/9*p = 0. What is p?
-2, 0, 4
Let q(o) be the second derivative of 0 + 5/16*o**4 - 1/10*o**5 + 1/120*o**6 + 1/3*o**3 - 2*o**2 - 3*o. Solve q(f) = 0 for f.
-1, 1, 4
Solve -42 - 81/2*l**2 + 3*l**3 + 3/2*l**4 + 78*l = 0.
-7, 1, 2
Let g be 1/2*(8 - 64/8). Let w(a) be the third derivative of g*a - 4*a**2 + 1/2*a**4 - 3*a**3 - 1/30*a**5 + 0. Suppose w(p) = 0. What is p?
3
Let p(q) = -q**2 - q + 12. Let r be p(0). Let h(a) be the first derivative of -25*a**2 + 7 + 47*a**2 - r*a - 16*a**2 - a**3. Factor h(d).
-3*(d - 2)**2
Solve 2*k**3 + 138 - 42 + 51*k + 22*k**2 + 29*k = 0.
-4, -3
Suppose -21/2*o**3 + 0 + 21*o**2 + 3/2*o**4 - 12*o = 0. What is o?
0, 1, 2, 4
Let l(g) be the first derivative of g**5 + 20*g**4 + 150*g**3 + 500*g**2 + 625*g - 690. Factor l(v).
5*(v + 1)*(v + 5)**3
Let q(k) = -9*k**4 - 8*k**3 + k**2 - 5*k + 5. Let t(s) = -4*s**4 - 4*s**3 - 2*s + 2. Let j(o) = -4*q(o) + 10*t(o). Let j(f) = 0. Calculate f.
-1, 0
Suppose 4*d = 3*k - k - 108, 2*k - 143 = -3*d. Suppose 67*l - k*l - 9 = 0. What is h in -4/3*h**4 - 4/3*h**2 + 0 + 1/3*h**5 + 1/3*h + 2*h**l = 0?
0, 1
Let d(z) be the first derivative of -z**5/60 - 7*z**4/36 - 5*z**3/6 - 3*z**2/2 - 13*z + 11. Let t(m) be the first derivative of d(m). Factor t(l).
-(l + 1)*(l + 3)**2/3
Let r(x) = 28*x**2 + 148*x - 18. Let d(u) = 107*u**2 + 592*u - 73. Let s(a) = -4*d(a) + 18*r(a). What is b in s(b) = 0?
-4, 2/19
Let h be ((-7)/(-14))/((-1)/(-12)). Suppose h = -3*m - 0