2*i**2 + 160*i + 100. Let g(k) = 7*k**4 - 128*k**3 + 87*k**2 + 640*k + 400. Let t(o) = 2*g(o) - 9*u(o). What is v in t(v) = 0?
-1, 5
Let y(x) be the first derivative of x**5/20 + x**4/8 - x**2/2 + 1. Let h(n) be the second derivative of y(n). Factor h(l).
3*l*(l + 1)
Let 2*s**5 + 0*s**2 - 4*s**2 + 4*s**4 + s**3 - s**3 - 2*s = 0. What is s?
-1, 0, 1
Let z(p) = 5*p**5 + 5*p**4 - p**3 - p**2 + 4*p. Let a(s) = 6*s**5 + 6*s**4 - s**3 - s**2 + 5*s. Let c(g) = 4*a(g) - 5*z(g). Factor c(j).
-j**2*(j - 1)*(j + 1)**2
Let p(o) = -3*o**2 + 2. Let d be p(-2). Let v(m) = 4*m**4 - 3*m**3 - 2*m**2 + 5. Let u(c) = 2*c**4 - c**3 - c**2 + 2. Let n(f) = d*u(f) + 4*v(f). Factor n(w).
-2*w**2*(w + 1)*(2*w - 1)
Suppose 4*t = -4*g, 5 - 1 = 3*g + t. Factor 0 + 2/7*x**g + 4/7*x.
2*x*(x + 2)/7
Suppose 0 = v + 2 - 6. Factor -v*w + 0 + 0 + 0*w + 4*w**2.
4*w*(w - 1)
Suppose 2*d = -4 + 8. Suppose -7/3*k**3 - 2/3*k**d + 0 + 0*k = 0. Calculate k.
-2/7, 0
Let x(g) be the second derivative of g**7/84 - g**5/20 + g**3/12 + 5*g. Find t, given that x(t) = 0.
-1, 0, 1
Let p(o) be the third derivative of 0 + 1/105*o**7 + 0*o**6 + 0*o + 1/336*o**8 - 1/24*o**4 - 6*o**2 - 1/30*o**5 + 0*o**3. Factor p(w).
w*(w - 1)*(w + 1)**3
Let r(m) = -20*m**2 - 5*m + 10. Let p(q) = 20*q**2 + 5*q - 9. Let o(i) = -5*p(i) - 6*r(i). Factor o(x).
5*(x + 1)*(4*x - 3)
Let n be -49*(-2)/(-12)*-2. Let h = n - 16. Factor h*b + 1/3*b**2 + 0.
b*(b + 1)/3
Let s(y) be the first derivative of 3*y**5 + 5*y**4/2 - 35*y**3/3 + 5*y**2 - 16. Determine m, given that s(m) = 0.
-2, 0, 1/3, 1
Let y(c) be the first derivative of 0*c - 3/4*c**2 + 4 - 1/2*c**3. Factor y(f).
-3*f*(f + 1)/2
Let t = 4892/453 + -20/151. Let -2/3 + 6*q + t*q**3 - 16*q**2 = 0. Calculate q.
1/4, 1
Let a(s) = 132*s**2 - 108*s - 24. Let i(m) = -33*m**2 + 27*m + 6. Let c(p) = 2*a(p) + 9*i(p). Suppose c(f) = 0. What is f?
-2/11, 1
Let g = 116101/300 - 387. Let t(z) be the third derivative of 0*z**3 - g*z**5 - 1/60*z**4 + 0 + 0*z + 4*z**2. Factor t(p).
-p*(p + 2)/5
Suppose 18*h = 16*h. Let r(i) be the second derivative of 0*i**2 + h*i**4 + 1/24*i**3 - 1/40*i**5 + 1/168*i**7 + 2*i + 0*i**6 + 0. Determine x so that r(x) = 0.
-1, 0, 1
Suppose 0 = -q - 3*r + 25, -q + 4*q + 2*r = 40. Let 8*g - q*g**2 - 11*g - g = 0. What is g?
-2/5, 0
Solve k**4 - k**3 + 0 + 1/3*k**2 + 0*k - 1/3*k**5 = 0 for k.
0, 1
Suppose 0 = -0*u + u - 3. Factor 4*i + 0*i**3 + 14*i**2 + 6*i**3 - 2*i**u + 6*i**3.
2*i*(i + 1)*(5*i + 2)
Suppose 7*r + 0*r - 28 = 0. Let x(k) be the first derivative of k**r - 2*k**2 - 1 + 8/5*k**5 - 5/2*k**3 - 1/2*k. Solve x(c) = 0 for c.
-1, -1/4, 1
Let m = 86 - 84. Suppose -2*r = -5*u - 26, 4*r + 0*u + 5*u = -8. Find n such that 24*n**m - 54*n**r - 8/3*n + 0 = 0.
0, 2/9
Let i = 3 - 1. Let t be (-36)/16*-1 - i. Factor t*s**4 - 1/4*s**2 - 1/4*s**3 + 0 + 1/4*s.
s*(s - 1)**2*(s + 1)/4
Let t(r) = -r**2 + 5*r + 2. Let z(h) = h**3 - h**2 + h + 5. Let s be z(0). Let i be t(s). Suppose 0*w**i + 4*w**2 - 2*w - 3*w**2 + 1 = 0. What is w?
1
Let g(a) be the third derivative of a**6/240 - a**5/120 - a**4/24 + 8*a**2. Solve g(w) = 0.
-1, 0, 2
Factor 2/11*c**3 + 0 - 2/11*c**5 - 2/11*c**2 + 0*c + 2/11*c**4.
-2*c**2*(c - 1)**2*(c + 1)/11
Suppose 50 = 4*v + v. Let s be -10*(6/v)/(-1). Factor -2*t**3 - 4*t - 2*t**2 + 2*t**2 + s*t**3 + 2 - 2*t**4.
-2*(t - 1)**3*(t + 1)
Suppose 1/2*c + c**4 + 0 + 2*c**3 + 5/3*c**2 + 1/6*c**5 = 0. What is c?
-3, -1, 0
Let x(q) be the first derivative of -q**5/80 - q**4/24 - 4*q - 6. Let m(g) be the first derivative of x(g). Factor m(y).
-y**2*(y + 2)/4
Let 0 - 2*t**2 + 2*t + 1/2*t**3 = 0. Calculate t.
0, 2
Factor 2/3*q**3 + 16*q + 32/3 + 6*q**2.
2*(q + 1)*(q + 4)**2/3
Suppose 6*h = h + 10. Find b such that -8/3 - 2/3*b**h + 8/3*b = 0.
2
Suppose -3*o = -5*h + 8, o - 6*h = -h - 16. Factor 2*d**5 + 0*d**o - d**3 + 3*d**4 - 4*d**4.
d**3*(d - 1)*(2*d + 1)
Let k = 317/9 - 35. Let k*x**2 + 8/9 - 8/9*x = 0. Calculate x.
2
Let d(f) = f**2 - 7*f + 4. Let n be d(7). Suppose -5*s = -n*s. Suppose -2/3*c**3 + 4/3*c**4 + 0*c**2 - 2/3*c**5 + 0 + s*c = 0. Calculate c.
0, 1
Factor -4/3*b**3 - 2/3*b**4 + 0 - 2/3*b**2 + 0*b.
-2*b**2*(b + 1)**2/3
Suppose -5*j + 7 = -3*q, -j - 3 = -4*q - 1. Suppose 4*v + v**j + v**2 - 6*v = 0. What is v?
0, 1
Let a be 3/(-5) + (-4 - -5). Let p be 9/3 - 39/15. Factor 0 + 0*h - a*h**4 - p*h**2 + 4/5*h**3.
-2*h**2*(h - 1)**2/5
Let g = 0 + 7. Suppose 4*l - a - 33 + 8 = 0, 0 = 5*l - a - 32. Suppose 3*q**2 + l - g = 0. What is q?
0
Let j(o) be the third derivative of 9/16*o**4 + 0 - 9*o**2 + 1/240*o**6 + 3/40*o**5 + 9/4*o**3 + 0*o. Solve j(i) = 0 for i.
-3
Suppose h - 7 = -2*v, -v = -h - 2 + 3. Factor -l + 14*l**2 - 3*l**v + 16*l**3 + 7*l**4 + 3*l.
l*(l + 1)**2*(7*l + 2)
Factor 4 + 14*m + 17*m - 4*m**2 - 2*m**3 - 48*m + 19*m.
-2*(m - 1)*(m + 1)*(m + 2)
Let o(z) be the second derivative of -1/120*z**6 + 1/30*z**5 + 4*z + 0 + 0*z**3 - 1/24*z**4 + 1/2*z**2. Let l(h) be the first derivative of o(h). Factor l(c).
-c*(c - 1)**2
Suppose -6*v = -0*v - 30. Find s such that -3*s - v*s + 12*s - s**2 = 0.
0, 4
Let b be -1 - (8/(-10))/(6/8). Let l(g) be the third derivative of 0 + 0*g + 1/150*g**5 + 1/60*g**4 - b*g**3 + 3*g**2 - 1/300*g**6. Factor l(c).
-2*(c - 1)**2*(c + 1)/5
Suppose 0 = g + 2 - 5. Factor -12*d**5 - 3*d**3 + d**3 - d**3 + 0*d**g + 15*d**4.
-3*d**3*(d - 1)*(4*d - 1)
Let p = -3845/4 + 962. Factor -3/4*w**2 - 3/2*w - p.
-3*(w + 1)**2/4
Suppose n**4 + 0*n**2 - n**2 + n - 3*n**3 + n**5 + 0*n**2 + n = 0. What is n?
-2, -1, 0, 1
Let k = -8 + 11. Factor 3*v**5 + k*v**4 + 9*v**3 - 2*v**5 + 3*v - 7*v**2 - v - 8*v**4.
v*(v - 2)*(v - 1)**3
Let q = 613/3311 + -1/301. Let -4/11*x + 0 + q*x**2 = 0. Calculate x.
0, 2
Let y(h) be the third derivative of -h**6/8 + h**5/12 + 5*h**4/12 + 36*h**2 + 2*h. Factor y(i).
-5*i*(i - 1)*(3*i + 2)
Let g be (16/50)/(12/30). Solve 0*t + g*t**2 - 4/5 = 0.
-1, 1
Let p(w) = w**2 - 4*w - 2. Let g(j) = 2*j**2 - 1 + 7 - 9*j - 10. Suppose 0 = x + 4*x + 15. Let a(q) = x*g(q) + 7*p(q). What is y in a(y) = 0?
-1, 2
Let k(s) be the first derivative of 2*s**6/45 + s**5/15 - 2*s**4/9 + 3*s - 9. Let z(d) be the first derivative of k(d). Let z(x) = 0. Calculate x.
-2, 0, 1
Solve 16*a - 5*a**2 - 2 + 7*a**2 + 2 = 0.
-8, 0
Let z(j) be the first derivative of j**6/165 - j**5/110 - j**4/66 + j**3/33 - 2*j - 9. Let w(v) be the first derivative of z(v). Find x such that w(x) = 0.
-1, 0, 1
Let n(z) be the second derivative of -2*z**6/15 - z**5 - z**4 + 6*z**3 - 30*z. Determine j, given that n(j) = 0.
-3, 0, 1
Let k(a) be the third derivative of -1/9*a**3 + 0*a + 1/72*a**4 - 1/360*a**6 + 8*a**2 + 1/90*a**5 + 0. Factor k(x).
-(x - 2)*(x - 1)*(x + 1)/3
Let m(j) be the first derivative of -7*j**4 - 76*j**3/3 + 68*j**2 - 32*j + 8. Factor m(r).
-4*(r - 1)*(r + 4)*(7*r - 2)
Let a(y) be the first derivative of -1/4*y**3 - 1/4*y**2 + 0*y + 3. Factor a(k).
-k*(3*k + 2)/4
Let c(s) be the first derivative of -2/3*s - 1 - 4/3*s**2 - 2/3*s**3. Solve c(g) = 0 for g.
-1, -1/3
Let c(x) = -x**2 + 16*x - 10. Let j be c(15). Let -4/3*o**j + 1/3*o**2 + 4/3*o**3 + 0 - 1/3*o**4 + 0*o = 0. What is o?
-1, -1/4, 0, 1
Suppose -4*c + 42 = -c. Suppose -5*d = -5*j + 10, j = -4*d - d + c. Solve 3*s**2 - 26*s - s**d + 26*s = 0 for s.
0
Let v be 32/(-144) - 14/(-9). Find s such that -v*s**2 - 2/3*s**5 + 4/3*s**3 - 2/3*s + 2/3 + 2/3*s**4 = 0.
-1, 1
Let h(n) be the third derivative of -n**5/90 + n**3/9 + 19*n**2. Factor h(r).
-2*(r - 1)*(r + 1)/3
Let v(a) be the first derivative of a**9/6048 - a**8/1680 + a**7/1680 - a**3/3 - 4. Let m(j) be the third derivative of v(j). Factor m(n).
n**3*(n - 1)**2/2
Let i(v) = -5*v**3 - v**2 - 2*v - 3. Let f(d) = -d**3 + d**2 - 1. Let r(q) = -3*f(q) + i(q). Factor r(c).
-2*c*(c + 1)**2
Let p(l) be the first derivative of 18*l**5/5 - 21*l**4 + 26*l**3/3 + 84*l**2 + 72*l + 6. Factor p(b).
2*(b - 3)**2*(3*b + 2)**2
Factor 12*p**3 - p**2 - 2*p**2 + 0*p**2.
3*p**2*(4*p - 1)
Let f(q) be the third derivative of q**9/9072 - q**8/2520 + q**7/2520 - q**3 - 7*q**2. Let a(v) be the first derivative of f(v). Factor a(w).
w**3*(w - 1)**2/3
Let l = -1 + 10. Suppose w = -s + 5, 5*s + 2*w - 31 = -l. Factor 4 - 3 - u**3 + 4*u + 5*u**3 + 6*u**2 + u**s.
(u + 1)**4
Let k(o) = 1. Let n(d) = -d - 2 - 2 - 2 + d**2 + 3. Let t be 1/((-2)/6)*-1. Let m(r) = t*k(r) +