et 1/4*r**5 + 0 - 1/4*r**4 - 3/4*r**3 + 1/4*r**2 + v*r = 0. What is r?
-1, 0, 1, 2
Solve -1/6*y**4 + 11/6*y**3 - 4*y + 0 + 7/3*y**2 = 0 for y.
-2, 0, 1, 12
Suppose -27*l**5 + 141*l**3 - 17*l**2 + 119*l**4 - 7*l**2 - 317*l**4 = 0. Calculate l.
-8, 0, 1/3
Suppose 2*p - 10 = -0*p. Factor -z**p - z**5 + 4*z**4 - z**3 - z**3.
-2*z**3*(z - 1)**2
Let u be -5 - -7 - (-2 + 1). Let n = u + 2. Determine c, given that -7*c**2 - 4*c**5 - 9*c**4 + 3*c**3 + 16*c**2 + 7*c**n - 6*c = 0.
-1, 0, 1, 2
Let v = -4126 - -4128. Find y such that 9/4 - 3/4*y**v + 3/2*y = 0.
-1, 3
Factor t**4 + 24*t**2 + 18*t**2 - 61*t + 32 - 3*t - 11*t**3 + 0*t**3.
(t - 4)**2*(t - 2)*(t - 1)
Factor -4/9 - 4/9*r + 4/9*r**2 + 4/9*r**3.
4*(r - 1)*(r + 1)**2/9
Let b be ((-6160)/(-300) + -20)*(-2 + 5). Find f such that -52/5*f**5 + 0 - b*f**3 + 12*f**4 + 0*f + 0*f**2 = 0.
0, 2/13, 1
Let o(m) = 3*m**3 - 10*m**2 + 35*m - 12. Let l be (-1)/2*(1 - 7). Let d(j) = -j**3 + 3*j**2 - 12*j + 4. Let x(q) = l*o(q) + 8*d(q). Factor x(v).
(v - 4)*(v - 1)**2
Let y(i) = -6*i**2 + 6*i + 21. Let n(l) = 5*l + 253 - 4*l - 249 - l**2. Let j(f) = -21*n(f) + 4*y(f). Determine t so that j(t) = 0.
0, 1
Suppose 5*t + m - 15 = 2*m, -m + 9 = 3*t. Factor 64*p**3 - 2*p**4 - 157*p**t - 3*p**4 - 10*p**2 + 78*p**3.
-5*p**2*(p + 1)*(p + 2)
Factor -54*r - 1/4*r**3 + 108 + 27/4*r**2.
-(r - 12)**2*(r - 3)/4
Let q(n) be the third derivative of n**7/105 - 3*n**6/20 + 13*n**5/30 + 3*n**4/4 - 14*n**3/3 - 2*n**2 - 66. What is r in q(r) = 0?
-1, 1, 2, 7
Let t(f) be the first derivative of 5*f**4/12 - 7*f**3/3 - 3*f**2/2 - 5*f - 2. Let p(g) be the first derivative of t(g). Solve p(c) = 0.
-1/5, 3
Suppose 1756*a = 1752*a. Factor -3/2*k**3 + 3/2*k**4 - 3/2*k**2 + 3/2*k + a.
3*k*(k - 1)**2*(k + 1)/2
Let g(c) be the second derivative of 28*c - c**3 + 0*c**4 + 2*c**2 + 1/10*c**5 + 0. Solve g(x) = 0.
-2, 1
Suppose 50 = -5*d + 65. Factor 18*u**2 + 14*u**4 - 13 - 11 - d*u**3 + 12*u + 6*u**4 - 23*u**4.
-3*(u - 2)*(u - 1)*(u + 2)**2
Let l(x) be the second derivative of 0 + 1/50*x**5 - 1/30*x**4 + 0*x**2 + 10*x + 0*x**3. Suppose l(h) = 0. Calculate h.
0, 1
Factor 420*t - 9*t**2 - 4*t**3 - 215*t - 213*t - 3*t**2.
-4*t*(t + 1)*(t + 2)
Let j be (-8)/30*(12 - (-489)/(-41)). Let s = j - -50/41. Determine a so that -6*a**4 + 0*a**2 - 3*a + s + 6*a**3 + 9/5*a**5 = 0.
-2/3, 1
Let c(f) = f**2 + f - 1. Let a(t) = 6*t**3 + 85*t**2 + 237*t - 197. Let z(l) = -a(l) + 5*c(l). Factor z(j).
-2*(j + 6)*(j + 8)*(3*j - 2)
Let k(q) be the second derivative of -q**5/160 - 5*q**4/96 - q**3/24 + q**2/2 - 119*q + 3. Factor k(x).
-(x - 1)*(x + 2)*(x + 4)/8
Let u(w) be the third derivative of w**8/1680 + w**7/1050 - w**6/600 - w**5/300 + 3*w**2 - 24*w. Factor u(a).
a**2*(a - 1)*(a + 1)**2/5
Find s, given that -12/5 + s**3 - 27/5*s**2 + 8*s = 0.
2/5, 2, 3
Find x such that -9/4*x - 3/4*x**2 - 5/4 + 1/4*x**3 = 0.
-1, 5
Let j(c) be the third derivative of -1/840*c**7 + 0*c**3 + 0 + 0*c**4 + 1/240*c**6 + 0*c - 1/240*c**5 - 11*c**2. Solve j(a) = 0 for a.
0, 1
Let r be (27 - 24)*3/(9/(-5)). Let b be r/30 + 62/84. Find p such that 8/7*p - b*p**2 - 4/7 = 0.
1
Suppose -u + 3*i + 15 = 0, 4*u + 18 = 9*u + 4*i. Suppose -8 = -u*p + 10. Determine d so that -5*d - 2*d**2 + p*d - 4 - 6*d + 2*d = 0.
-2, -1
Suppose 19*q = 49*q. Let x(l) be the second derivative of 2/3*l**4 - 1/21*l**7 + 0*l**2 + q*l**3 - 1/5*l**6 + 0*l**5 - 3*l + 0. Factor x(c).
-2*c**2*(c - 1)*(c + 2)**2
Let s = 69 + -54. Determine h so that -12*h**2 + h**3 - 19*h**2 + 22*h**2 + 25 + s*h = 0.
-1, 5
Suppose 5*i - 8 = -2*x, -4*i = x - 5 + 1. Factor -2*r**3 + r**3 - 4*r**x - 6*r**2 - 7*r**3 + 2*r**4.
-2*r**2*(r + 1)*(r + 3)
Suppose -3*o = -4*l + 14, 0 = 4*l + 69 - 89. Factor 25/9*c**4 - 5*c**3 + 0 + 8/3*c**o - 4/9*c.
c*(c - 1)*(5*c - 2)**2/9
Suppose 0 - 2/9*n**4 + 10/9*n**2 + 0*n + 8/9*n**3 = 0. What is n?
-1, 0, 5
Let f = -1927/5 + 389. Let i(m) be the first derivative of -27/2*m**2 + 16*m**3 - 1/2*m**6 + f*m**5 - 4 + 6*m - 21/2*m**4. Factor i(y).
-3*(y - 2)*(y - 1)**4
Let v = -177 + 180. Let a(r) be the second derivative of -1/20*r**5 + 0*r**v + 0 - r + 0*r**2 + 1/42*r**7 + 1/12*r**4 - 1/30*r**6. Factor a(i).
i**2*(i - 1)**2*(i + 1)
Let w(t) be the second derivative of -1/4*t**3 + 0 + 1/16*t**4 + 9*t + 0*t**2. Factor w(p).
3*p*(p - 2)/4
Let n(d) be the third derivative of d**10/50400 - d**9/20160 - d**5/5 - 6*d**2. Let b(r) be the third derivative of n(r). Solve b(y) = 0 for y.
0, 1
Let x(g) be the second derivative of g**9/16632 - g**7/1540 + g**6/990 - 4*g**3/3 + 11*g. Let t(c) be the second derivative of x(c). Solve t(s) = 0 for s.
-2, 0, 1
Let y(q) be the third derivative of q**6/24 - 15*q**5/4 - 5*q**4/24 + 75*q**3/2 - q**2 + 11. Factor y(x).
5*(x - 45)*(x - 1)*(x + 1)
Let h(u) be the third derivative of u**8/840 + u**7/105 + u**6/36 + u**5/30 + u**3/3 - 4*u**2. Let o(v) be the first derivative of h(v). Factor o(a).
2*a*(a + 1)**2*(a + 2)
Let m(i) be the first derivative of -2*i**5/15 - i**4/4 + i**3/3 + i**2/3 - 86. Factor m(u).
-u*(u - 1)*(u + 2)*(2*u + 1)/3
Let 4/9*f**5 + 532/9*f - 268/9 + 8/9*f**2 - 536/9*f**3 + 260/9*f**4 = 0. What is f?
-67, -1, 1
Let n(o) = -19*o**3 + 3*o**2 + 77*o + 41. Let f(y) = 6*y**3 - 2*y**2 - 26*y - 14. Let u(j) = 7*f(j) + 2*n(j). Factor u(q).
4*(q - 4)*(q + 1)**2
Suppose 2*x + 4 = 5*j, 3*j - 9 = 9*x - 10*x. Find y such that 336/5*y**4 + 72/5*y - 52/5*y**j - 274/5*y**3 + 16/5 - 98/5*y**5 = 0.
-2/7, 1, 2
Let a = -132 - -142. Let 24*h**2 + 49*h + 49*h + 128 - 12*h + 2*h**3 + a*h = 0. Calculate h.
-4
Factor -6*j + 1/10*j**4 - 72/5 + 34/5*j**2 - 3/2*j**3.
(j - 6)**2*(j - 4)*(j + 1)/10
Factor -33/4 - 1/4*r**2 - 7/2*r.
-(r + 3)*(r + 11)/4
Let s(x) be the second derivative of -x**6/780 + x**5/390 + x**4/78 - 5*x**2 + 26*x. Let y(c) be the first derivative of s(c). Find b such that y(b) = 0.
-1, 0, 2
Let x(z) be the first derivative of z**5/90 - z**4/18 + z**3/9 + z**2 - 11. Let n(s) be the second derivative of x(s). Factor n(r).
2*(r - 1)**2/3
Let a(c) = c**3 + 4*c**2 - 2*c - 4. Let w be a(-4). Let k = -7025 + 7027. Suppose -k - w*z - 5/2*z**2 - 1/2*z**3 = 0. What is z?
-2, -1
Let u(a) be the second derivative of 5*a**7/21 + 5*a**6/2 + 13*a**5/2 + 5*a**4/4 - 25*a**3/3 + 32*a + 3. What is m in u(m) = 0?
-5, -2, -1, 0, 1/2
Let n(v) be the first derivative of 2*v**3 - 7*v**2/2 - 5*v + 23. Let d(i) = -3*i**2 + 4*i + 2. Let b(a) = -5*d(a) - 2*n(a). Let b(c) = 0. What is c?
0, 2
Let b be (-153)/612 + 2/8. Factor -1/3*t**3 - 1/3*t**4 + 1/3*t**5 + 0*t + 1/3*t**2 + b.
t**2*(t - 1)**2*(t + 1)/3
Let b(v) be the third derivative of 11*v**2 + 1/4*v**5 + 0*v - 1/42*v**7 + 1/24*v**6 + 0 - 5/24*v**4 - 5/3*v**3. Factor b(z).
-5*(z - 2)*(z - 1)*(z + 1)**2
Factor -2/3*o**3 + 40/3*o**2 - 84 + 18*o.
-2*(o - 21)*(o - 2)*(o + 3)/3
Let s = 4067 - 4064. Suppose -3/4*u + 3/4*u**2 - 3/4*u**4 + 3/4*u**s + 0 = 0. What is u?
-1, 0, 1
Suppose -2*t - 2*x = -0*t + 6, 15 = -3*x. Suppose -65*w**3 - 45*w**t - 58*w**3 - 100 + 120*w + 128*w**3 = 0. What is w?
2, 5
Let h be ((-21)/(-6) + -2)*(-22 - 4378/(-198)). Find z such that -h*z**4 + 1/6*z**2 + 1/3*z - 1/3*z**3 + 0 = 0.
-2, -1, 0, 1
Let k = 11 + -14. Let v(j) = -5*j**3 - 75*j**2 - 90*j + 10. Let o(w) = -2*w**3 - 25*w**2 - 30*w + 3. Let p(z) = k*v(z) + 10*o(z). Factor p(q).
-5*q*(q + 2)*(q + 3)
Suppose -6*l - 50*l = 0. Solve 4/7*a**3 + 2/7*a**5 + l - 6/7*a**4 + 0*a**2 + 0*a = 0.
0, 1, 2
Let a(n) = -5*n. Let t be a(-1). Factor 20*h**2 + 20*h**4 - 5*h**5 - t*h + 86 - 30*h**3 - 86.
-5*h*(h - 1)**4
Let b be (5 + -4 + -1)/2. Suppose 2*k - 5*j = 25, 0 = 3*k - 6*k + 4*j + 20. Let b + 1/5*d**3 + 0*d + k*d**2 = 0. Calculate d.
0
Let h(r) be the third derivative of 0 + 0*r + 1/3*r**5 + 1/2*r**4 + 3/10*r**3 + 35*r**2. Determine j so that h(j) = 0.
-3/10
Suppose -80 + 6*u + 5*u**4 - 15*u**2 + 90*u**2 - 91*u + 85*u**3 = 0. What is u?
-16, -1, 1
Let j = -46 - -54. Let o be j/(-28) - (-52)/35. Factor 8*t - 28/5*t**2 + o*t**3 - 16/5.
2*(t - 2)**2*(3*t - 2)/5
Let w(t) be the third derivative of -t**6/1140 - t**5/285 + t**4/76 + 40*t**2. Suppose w(k) = 0. What is k?
-3, 0, 1
Solve 2*u**2 + 0 - 20/3*u + 2/3*u**3 = 0 for u.
-5, 0, 2
Let j(h) be the second derivative of -h**8/6720 + h**6/720 + h**4/12 - 29*h. Let z(g) be the third derivative of j(g). Factor z(t).
-t*(t - 1)*(t + 1)
Suppose 142*