 - 1)**2/3
Solve 12*d**2 - 2*d**2 - 20 - 5*d**3 + 5*d**2 = 0.
-1, 2
Let c = 904/3115 + -2/445. Determine s so that 0*s - 2/7*s**4 + 0 - 4/7*s**3 - c*s**2 = 0.
-1, 0
Let x(j) = -4*j**3 + 2*j**2 + 3*j - 1. Let r(u) = -u**3 + u**2. Suppose -4*n + 0 = 12. Let s(o) = n*x(o) + 15*r(o). Let s(c) = 0. Calculate c.
1
Let h(x) be the second derivative of -x**6/180 + x**4/24 + x**3/18 + 8*x. Factor h(b).
-b*(b - 2)*(b + 1)**2/6
Let t = 38 - 188/5. Let o(l) be the first derivative of -2 + t*l**3 - 8/5*l + 1/10*l**4 + 0*l**2. Factor o(j).
2*(j - 1)*(j + 2)**2/5
Let w(r) be the third derivative of r**5/30 + r**4/4 + 21*r**2. Factor w(g).
2*g*(g + 3)
Let g(k) be the second derivative of k**6/900 + k**5/150 - 2*k**3/3 - 4*k. Let f(s) be the second derivative of g(s). Factor f(a).
2*a*(a + 2)/5
Let r = -1 - 4. Let w = r + 5. Factor 0*a - 7/4*a**5 - 3*a**4 - 3/4*a**3 + w + 1/2*a**2.
-a**2*(a + 1)**2*(7*a - 2)/4
Let n(u) = -u**3 + 5*u**2 + 2*u - 5. Let m be n(5). Suppose g - 2 = -3*x, -4*x + m*g + 13 = -15. What is v in -v**x - v + v - 2*v - 1 = 0?
-1
Let o(k) be the second derivative of -k**9/60480 + k**8/26880 - k**4/4 - 2*k. Let a(w) be the third derivative of o(w). Suppose a(t) = 0. What is t?
0, 1
Let z(u) be the third derivative of -u**7/840 - u**6/1080 - u**3/3 - 7*u**2. Let j(h) be the first derivative of z(h). Factor j(f).
-f**2*(3*f + 1)/3
Let x(w) be the first derivative of -w**4/28 + 5*w**3/21 - w**2/2 + 3*w/7 + 26. Determine d so that x(d) = 0.
1, 3
Let j(p) be the third derivative of -p**5/105 + 2*p**4/21 - 2*p**3/7 + 6*p**2. Factor j(t).
-4*(t - 3)*(t - 1)/7
Let p(t) = 6*t**3 - 2*t. Let u(n) = n**4 + 25*n**3 + n**2 - 9*n. Let z(c) = 9*p(c) - 2*u(c). Factor z(a).
-2*a**2*(a - 1)**2
Let o = -60 - -241/4. Let a be ((-31)/(-16) - 2)/((-2)/8). Factor -o*s**4 + s - a + s**3 - 3/2*s**2.
-(s - 1)**4/4
Factor -24*y**3 - 106 - 2*y - 20*y**4 - 12*y**2 - 6*y**5 + 106.
-2*y*(y + 1)**3*(3*y + 1)
Suppose -f - 1 = n, 4*n - 2*f = -0*n + 26. Find h, given that -h**4 - 8*h**5 - 5*h**3 - 5*h**3 + 2*h**2 + 17*h**n = 0.
0, 1/2, 1
Let b(x) be the first derivative of -x**5/30 - x**4/12 - x**3/18 - 2*x - 5. Let j(i) be the first derivative of b(i). Factor j(v).
-v*(v + 1)*(2*v + 1)/3
What is t in -2/3*t**3 + 0 + 0*t - 1/3*t**4 + 0*t**2 = 0?
-2, 0
Let g be (0 + (-4)/(-10))/(27/450). Solve -20/3*s**2 - g*s**3 - 2/3*s**5 - 10/3*s**4 - 2/3 - 10/3*s = 0.
-1
Suppose 36 = 4*d - 4*h, -2*d + h + 21 - 7 = 0. Let w(l) = -8*l**3 + 17*l**2 - 20*l + 1. Let q(z) = z**3 - z**2 + z + 1. Let t(m) = d*q(m) + w(m). Factor t(j).
-3*(j - 2)*(j - 1)**2
Suppose w + 3*j = 8, 2*j - 1 - 1 = w. Let p**4 - 2*p**3 - 2 + p**2 + 4*p**3 + w = 0. Calculate p.
-1, 0
Let r(t) be the first derivative of -t**5/5 - t**4/4 + t**3/3 + t**2/2 - 1. Solve r(b) = 0 for b.
-1, 0, 1
Let a be (-1)/(7/2) + 102/357. Suppose -8 = 2*j - 6*j. Factor -4 + a*c**2 + c - 9*c + j - 6*c**2.
-2*(c + 1)*(3*c + 1)
Let w = 39 + -35. Suppose 5*g + 4*u = 10, 3*g + 2*u - 2 = w. Factor 3/4*r**g + 0 + 3/2*r.
3*r*(r + 2)/4
Let n(i) be the third derivative of i**6/420 + i**5/60 + i**4/42 + i**3/3 + 5*i**2. Let w(d) be the first derivative of n(d). Suppose w(t) = 0. What is t?
-2, -1/3
Find h such that 1/8*h**4 + 0*h + 0*h**3 + 0 - 1/8*h**2 = 0.
-1, 0, 1
Let b = 32/5 + -31/5. Let f = -4/87 + 194/435. Find z such that f*z - 1/5*z**2 - b = 0.
1
Let m be 0/((-6)/(-9)*3). Suppose m*g - 1 = -g. Factor 2*v**2 + 2 + g - 5.
2*(v - 1)*(v + 1)
Let k(i) be the first derivative of i**4/6 + 8*i**3/9 - 6. Factor k(b).
2*b**2*(b + 4)/3
Suppose 3*g = -2*g - 10. Let w be (4/g)/2*-6. Determine a, given that 1 - 3 - w*a + 2*a**2 + 3 + 3 = 0.
1, 2
Let s be (45/10)/((-33)/(-4)). Factor -2/11*w**2 + 0*w + 0 - s*w**3 - 6/11*w**4 - 2/11*w**5.
-2*w**2*(w + 1)**3/11
Let l(a) = a**3 + 3*a**2 + a. Let b be l(0). Factor 2/5*z**2 - 1/5 + b*z + 0*z**3 - 1/5*z**4.
-(z - 1)**2*(z + 1)**2/5
Suppose 12 - 9 = z. Let t(o) be the first derivative of 0*o + 1/4*o**2 + 1/12*o**3 + z. Let t(m) = 0. What is m?
-2, 0
Let q = 0 - -1/3. Let i(h) be the second derivative of 1/10*h**5 - h + 0 + q*h**3 + 1/3*h**4 + 0*h**2. Factor i(m).
2*m*(m + 1)**2
Let x(c) be the second derivative of -3/50*c**5 - 1/30*c**4 + 1/5*c**2 + 0 - c + 1/5*c**3. Let x(d) = 0. Calculate d.
-1, -1/3, 1
Let m = 1746 + -15664/9. Factor 40/9*t**3 + 0*t + 8/9*t**2 + 0 + m*t**4.
2*t**2*(5*t + 2)**2/9
Factor -6/7*z - 2/7*z**3 + 0 - 8/7*z**2.
-2*z*(z + 1)*(z + 3)/7
Let z(m) be the third derivative of -m**8/8640 - m**7/7560 - m**5/30 + m**2. Let u(j) be the third derivative of z(j). Factor u(o).
-o*(7*o + 2)/3
Let d(h) = 4*h**4 + 4*h**3 - 44*h**2 + 36*h - 8. Let i(j) be the first derivative of -j**3/3 - j**2/2 + j - 2. Let n(q) = d(q) - 8*i(q). Factor n(f).
4*(f - 1)**3*(f + 4)
Let v(d) = -d - 1. Let p be v(-2). Suppose -9 = -2*m - p. What is t in m*t**2 - 3*t + 3*t - 1 - 3*t = 0?
-1/4, 1
Let j = -11 + 14. Let -3*l**5 - 5*l**3 - 3*l**4 - 3*l**2 - 6*l**4 - 4*l**j + 0*l**2 = 0. What is l?
-1, 0
Let n = 14144/1929 - -2/1929. Let o = -107/15 + n. Suppose 1/5 - 1/5*c**2 + o*c**3 - 1/5*c = 0. What is c?
-1, 1
Factor -4*n + 0*n**2 + 25 + n**2 + 9*n + 5*n.
(n + 5)**2
Let q be 20/15*9/6. Factor k - 3*k**3 - 3*k + q*k.
-3*k**3
Let o(g) be the first derivative of -2/27*g**3 + 0*g**2 + 0*g - 4. Find b, given that o(b) = 0.
0
Let j(o) = o**3 - 14*o**2 + 18*o - 2. Let n be j(13). Let m be 114/n - (-12)/(-18). Factor m*b**2 - 2/7*b**3 - 10/7*b + 4/7.
-2*(b - 2)*(b - 1)**2/7
Let z(p) = p**3 + 7*p**2 + 3. Let u be z(-7). Suppose -3*h + 13 = 4*c, 2*h = -0*c + u*c + 3. What is v in 0*v + 0 - 3/4*v**4 + 0*v**h + 3/4*v**2 = 0?
-1, 0, 1
Let q(f) be the first derivative of -f**6/9 + 2*f**5/15 + f**4/3 - 4*f**3/9 - f**2/3 + 2*f/3 - 1. Factor q(o).
-2*(o - 1)**3*(o + 1)**2/3
Let n be (-2)/(-9) + (-364)/18. Let k be -2 + (-48)/n + 2. Solve 4/5*t**3 - k*t**2 + 14/5*t**4 - 2/5 + 6/5*t**5 - 2*t = 0.
-1, -1/3, 1
Let l(w) be the first derivative of 0*w**4 + 2/3*w**3 - 2/5*w**5 - 3 + 0*w**2 + 0*w. Factor l(g).
-2*g**2*(g - 1)*(g + 1)
Factor 8*f**3 + 4*f - 20*f**2 - 61 + 35 + 34.
4*(f - 2)*(f - 1)*(2*f + 1)
Let l = 24 - 23. Let z be (-1)/l - 30/(-20). Factor z - 3/4*b**2 + b**4 - 5/4*b + 2*b**3.
(b + 1)*(b + 2)*(2*b - 1)**2/4
Let o(p) be the first derivative of -2 + 2/5*p - 8/15*p**3 + 3/5*p**2. Factor o(c).
-2*(c - 1)*(4*c + 1)/5
Factor -6/5*r - 2*r**3 - 14/5*r**2 + 0 - 2/5*r**4.
-2*r*(r + 1)**2*(r + 3)/5
Suppose 0 = 6*s - 18. Factor 2/3*z**s + 0*z + 0 + 2/3*z**2.
2*z**2*(z + 1)/3
Suppose -2*j - 4*h = -2, -h - 2 = h. Suppose -5*v + 4*s = 2*s + 6, -j*v - 15 = -5*s. Factor v + 1/3*f + 0*f**2 - 1/3*f**3.
-f*(f - 1)*(f + 1)/3
Let b(g) be the third derivative of -2*g**6/75 + 6*g**5/25 - 11*g**4/40 + 2*g**3/15 - 8*g**2. Factor b(i).
-(i - 4)*(4*i - 1)**2/5
Suppose 0 = 2*x + 3*d + 6, 35 = 2*x + 3*x - 5*d. Suppose o - 8 = -x*o. Let -10/7*n**o - 4/7*n + 10/7*n**4 + 4/7*n**3 + 0 = 0. What is n?
-1, -2/5, 0, 1
Let i(q) be the third derivative of 1/240*q**5 + 1/96*q**4 - 2*q**2 + 0 + 0*q + 0*q**3. Find o such that i(o) = 0.
-1, 0
Let a(s) be the first derivative of s**4/2 - 16*s**3/15 + s**2/5 + 4*s/5 + 9. Suppose a(i) = 0. What is i?
-2/5, 1
Factor 3/4*p**2 + 0 - 3/4*p.
3*p*(p - 1)/4
Let k be (-39)/6 - 6/(-4). Let v = -2 - k. Solve 0*g**v - 2*g + 2*g**3 - 3 - 2*g**2 + 7 - 2 = 0.
-1, 1
Factor 4/3*p**2 + 0 + 2/3*p**4 + 0*p - 2*p**3.
2*p**2*(p - 2)*(p - 1)/3
Let g = -21 - -21. Factor -1/4*o**2 + 1/4*o**4 + g + 1/4*o**3 - 1/4*o.
o*(o - 1)*(o + 1)**2/4
Factor -6*b + b + 3 + 5*b - 3*b**2.
-3*(b - 1)*(b + 1)
Let y(r) be the third derivative of -r**6/5 + r**5/3 + r**4/2 - 4*r**3/3 + 7*r**2. Factor y(n).
-4*(n - 1)*(2*n - 1)*(3*n + 2)
Let v(s) = 21*s - 59*s + 52*s**2 + 20*s**3 - 5 - 19. Let c(b) = 7*b**3 + 17*b**2 - 13*b - 8. Let l(o) = -20*c(o) + 6*v(o). Let l(x) = 0. Calculate x.
-2, -2/5, 1
Let x(a) = a**3 + 3*a**2 + 2*a + 6. Let h be x(-3). Let h*l - 2/7*l**2 + 2/7*l**4 + 0*l**3 + 0 = 0. Calculate l.
-1, 0, 1
Let w(m) = 21*m**2 + 48*m + 16. Let d(p) = 42*p**2 + 96*p + 33. Let r(v) = 4*d(v) - 9*w(v). Factor r(c).
-3*(c + 2)*(7*c + 2)
Factor -8/7*c**2 + 2/7*c**5 + 0*c**3 + 0 + 0*c + 6/7*c**4.
2*c**2*(c - 1)*(c + 2)**2/7
Let s = 16 + -15. Let z be ((-13)/52)/(s/(-6)). Find l, given that -3/2*l**4 + 9/4*l**3 + 0*l + z*l**2 + 0 - 9/4*l**5 = 0.
-1, -2/3, 0, 1
Suppose -1