s(a) = a**2 + 1. Let d(b) = b**3 + 5*b**2 - 3*b + 3. Let t(v) = d(v) - 5*s(v). Factor t(y).
(y - 2)*(y + 1)**2
Let x be 34/85 + 2/(-5). Let w(z) be the third derivative of z**2 - 1/60*z**6 + 0*z**5 + 1/12*z**4 + 0*z**3 + 0*z + x. Suppose w(u) = 0. Calculate u.
-1, 0, 1
Let -10/3*q + 2/3 + 8/3*q**2 = 0. What is q?
1/4, 1
Let m be ((-9)/(-15))/(2/20). Suppose -3*i**2 + i**3 + 3 - 5*i**4 + i - 2*i - 1 + m*i**4 = 0. What is i?
-2, -1, 1
Let i(o) be the third derivative of o**5/300 - 7*o**4/60 + 49*o**3/30 + 40*o**2. Let i(f) = 0. What is f?
7
Let w(h) = 3*h. Let i be w(1). Let p be 22/(-70) - i/(-5). Factor 4/7*s**3 - p*s**5 - 2/7*s + 0 + 0*s**2 + 0*s**4.
-2*s*(s - 1)**2*(s + 1)**2/7
Factor 0 - 4/7*a + 2/7*a**2.
2*a*(a - 2)/7
Let r be (-19)/76 - 2/(-8). Let g(m) be the third derivative of 0*m + 0*m**7 + 0*m**6 + r*m**5 + 0*m**3 - 4*m**2 + 0*m**4 + 0 + 1/112*m**8. Factor g(c).
3*c**5
Let h(q) = -28*q**2 + 32*q + 68. Let s(g) = -9*g**2 + 11*g + 23. Let o(v) = -3*h(v) + 8*s(v). Find z, given that o(z) = 0.
-1, 5/3
What is g in -18*g**2 - 3*g - 5 + 43*g - 3 = 0?
2/9, 2
Let n(s) = -s**3 - 3*s**2 - 5*s - 5. Let h(f) = -3 + f**2 + 0 + f + 3 + 1. Let m(z) = -15*h(z) - 3*n(z). Find o, given that m(o) = 0.
0, 2
Let f = -40/3 + 929/69. Let k = 101/69 - f. Factor k*r**2 - r**4 + 0 + 1/3*r**5 + 0*r + 0*r**3.
r**2*(r - 2)**2*(r + 1)/3
Let g(k) be the second derivative of 7*k**6/30 + 9*k**5/20 - 5*k**4/12 - 3*k**3/2 - k**2 + 10*k. Find l, given that g(l) = 0.
-1, -2/7, 1
Let b be 5 - 6/((-2)/(-1)). Suppose 0 + 0*i + 0*i**b - 1/2*i**3 = 0. What is i?
0
Let b be (18/(-15))/(8/(-10)). Determine x, given that -1/2*x**5 + 0 - b*x**4 - 1/2*x**2 + 0*x - 3/2*x**3 = 0.
-1, 0
Let a(h) be the first derivative of h**3/3 - 3*h**2 + 9*h - 14. Find d such that a(d) = 0.
3
Let u(c) = -15*c + 3. Let a be u(2). Let y be 3*(-3)/a*1. Find d such that -1/3*d + 0 - y*d**2 = 0.
-1, 0
Let n(k) be the first derivative of 3 + 3*k**2 - 2/3*k**3 - 4*k. Solve n(y) = 0 for y.
1, 2
Factor -22/13*n**2 + 6/13*n**3 + 16/13 - 12/13*n.
2*(n - 4)*(n + 1)*(3*n - 2)/13
Let n(y) be the second derivative of -y**7/189 + y**6/135 + y**5/90 - y**4/54 - 9*y. Factor n(l).
-2*l**2*(l - 1)**2*(l + 1)/9
Let c be ((-8)/(-6))/(2/9). Suppose c*u - 14*u - 4*u**2 - 2*u**3 - 4*u**2 = 0. What is u?
-2, 0
Suppose 2*i - 4 - 8 = -3*f, 2*f - 4*i + 8 = 0. Suppose 0 = -f*q + q. Factor -2/5*v**5 + 2/5*v - 4/5*v**4 + 0*v**3 + 4/5*v**2 + q.
-2*v*(v - 1)*(v + 1)**3/5
Suppose 2*u + 5*c - 16 = 0, c - 3*c = -u - 1. Let h(t) be the second derivative of 3*t - 1/3*t**4 - t**2 - 5/6*t**u + 0 - 1/20*t**5. Factor h(l).
-(l + 1)**2*(l + 2)
Factor 3/8*b**4 + 0*b**2 - 1/8*b**5 - 1/4*b**3 + 0*b + 0.
-b**3*(b - 2)*(b - 1)/8
Suppose -2*d + 7 + 1 = 0. Let s(o) be the first derivative of 33/5*o**5 - 3/2*o**6 - 40/3*o**3 + 16*o - d*o**4 + 8*o**2 - 1. Suppose s(u) = 0. What is u?
-2/3, 1, 2
Let k(s) be the third derivative of 3/5*s**5 - s**2 + 0*s + 0 + 9/8*s**3 + 9/8*s**4 + 2/15*s**6. Factor k(h).
(4*h + 3)**3/4
Suppose -a + 4 + 6 = 5*p, p = 2*a + 2. Factor a + 0*v**2 + 1/2*v - 1/2*v**3.
-v*(v - 1)*(v + 1)/2
Let p(t) be the second derivative of t**6/480 - t**5/80 - t**3/2 - 9*t. Let c(h) be the second derivative of p(h). Factor c(q).
3*q*(q - 2)/4
Let w(i) be the second derivative of -i**5/4 - 5*i**4/3 - 10*i**3/3 + 25*i. Let w(z) = 0. What is z?
-2, 0
Let i be ((-4)/(-20)*0)/1. Let p(r) be the second derivative of -2*r - 1/2*r**2 - r**3 + i - 3/4*r**4 - 1/5*r**5. Factor p(v).
-(v + 1)**2*(4*v + 1)
Let u(y) be the second derivative of -y**6/5 - y**5 - 2*y**4/3 + 8*y**3/3 + 38*y. Factor u(w).
-2*w*(w + 2)**2*(3*w - 2)
Let t be (3 - 1) + (-2)/2. Solve -t + 17*f**4 - 7*f**4 + 4*f**5 + 20*f**3 + 10*f**2 + 0 + 5*f**4 = 0 for f.
-1, 1/4
Let f(t) = 5*t**4 - 7*t**3 - 7*t**2 + 7*t. Let q(w) = 24*w**4 - 36*w**3 - 34*w**2 + 36*w - 1. Let a(d) = 11*f(d) - 2*q(d). Factor a(o).
(o - 1)**2*(o + 1)*(7*o + 2)
Let q(n) be the third derivative of -n**6/40 + 3*n**5/4 - 75*n**4/8 + 125*n**3/2 + 22*n**2. Solve q(z) = 0.
5
Suppose -23 = -5*z + 3*c, 6 = -2*z - 0*z + 5*c. Suppose -3*m + z*m = 8. Suppose -5*o + 2*o - 3*o**3 + 5*o**m + o**2 = 0. Calculate o.
0, 1
Let f be (-4)/6 + (-81)/(-120). Let q(m) be the third derivative of -m**2 + 0 + f*m**6 - 1/60*m**5 + 0*m + 0*m**3 + 0*m**4. What is w in q(w) = 0?
0, 1
Let d(k) be the first derivative of k**4/4 - 2*k**3/3 + 5*k**2/8 - k/4 + 1. Factor d(z).
(z - 1)*(2*z - 1)**2/4
Let u(o) be the third derivative of o**8/6720 - o**7/1680 + o**5/15 + 8*o**2. Let h(x) be the third derivative of u(x). Factor h(i).
3*i*(i - 1)
Suppose -3*p - 5*c + 37 = -0, 5 = c. Let j(o) be the first derivative of -2/15*o**3 + 1/10*o**p - 2/5*o**2 + 0*o + 3. Solve j(i) = 0 for i.
-1, 0, 2
Suppose 4*h + 0*h - 16 = 0. Suppose -5*c = 5*o + 15, -h*o + 2*c = -2*c - 12. Factor 2*j**2 - 4 - 2*j + 0*j + o*j.
2*(j - 2)*(j + 1)
Let p(x) = -4*x**5 + 13*x**4 - 5*x**3 - 8*x**2 + 9*x + 5. Let g(h) = -h**4 + h**3 - h - 1. Let b(f) = 5*g(f) + p(f). Factor b(q).
-4*q*(q - 1)**3*(q + 1)
Find i, given that 0 + 1/5*i**4 - 6/5*i**3 + 9/5*i**2 - 4/5*i = 0.
0, 1, 4
Suppose -i - 9 = 2*b - 5*b, 4*i + 12 = 4*b. Suppose 4*q - 6 - 2 = i. What is u in 2/3*u**q + 2/3*u + 0 = 0?
-1, 0
Suppose -n - 4*t + 8 = 0, 2*n + t + 0 = 9. Let -72*f - 14*f**3 - 22*f**2 + n + 12 + 82*f**2 = 0. Calculate f.
2/7, 2
Let b(j) = 2*j - 44. Let z be b(22). Factor 0*m**2 + 0*m + 1/2*m**3 + z.
m**3/2
Let k = 129/2 + -63. Factor -1/2*g**2 - k*g**4 + 0 - 3/2*g**3 - 1/2*g**5 + 0*g.
-g**2*(g + 1)**3/2
Let y(m) = 3*m**3 - 2*m**2 - m. Suppose 9*p = 4*p - 20. Let a(w) = -7*w**3 + 5*w**2 + 2*w. Let f(k) = p*a(k) - 9*y(k). Factor f(q).
q*(q - 1)**2
Suppose -6 + 16 = 2*w. Suppose 0 = w*j + 2*y + 10, 3*j - 3*y - 7 = 8. Factor -1/5*k**3 - 1/5*k**4 + j + 0*k + 1/5*k**5 + 1/5*k**2.
k**2*(k - 1)**2*(k + 1)/5
Let p(c) = 8*c - 12. Let n be p(4). Suppose -d + 25 = n. Factor -6/7*h**d + 2/7*h**3 + 0*h - 4/7*h**2 + 0 + 8/7*h**4.
-2*h**2*(h - 1)**2*(3*h + 2)/7
Let m = 2/95 + 87/380. Determine o so that m*o**2 + 0 - 1/2*o = 0.
0, 2
Suppose 2/3*q - 1/6*q**4 - 1/2*q**2 - 2/3*q**3 + 2/3 = 0. What is q?
-2, -1, 1
Factor 963/4*k**2 - 102*k - 102*k**3 + 12*k**4 + 12.
3*(k - 4)**2*(4*k - 1)**2/4
Let n(b) = -b**2 - 5*b - 2. Let r be n(-6). Let p = 15 + r. Find a, given that 2*a**4 - 3*a**5 + 7*a - p*a = 0.
0, 2/3
Let r(u) = 2*u**2 + 4*u - 4. Let h(l) = l. Let f(p) = 2*h(p) - r(p). Factor f(m).
-2*(m - 1)*(m + 2)
Let w(k) = 3*k**2 - 2*k + 2. Let r be w(2). Let p be 9/6*(3 - 1). Solve -4 + 9*c - 24*c**2 - c + r*c**p + 10*c = 0.
2/5, 1
Let m(l) = -l**2 + 4*l + 3. Let t be m(4). Suppose -t*n = -4 - 2. Find x such that x**2 + x**n + 6*x**4 + x**4 + 9*x**3 = 0.
-1, -2/7, 0
Let f = -77 + 233/3. Let a(v) = v**3 - 7*v**2 + 5*v + 8. Let w be a(6). Let -2/3*r**w + 2/3 - f*r**3 + 2/3*r = 0. What is r?
-1, 1
Let k = -170/29 + 81629/13920. Let u(p) be the third derivative of 0*p**3 + 1/240*p**5 + 0 + 0*p**4 + p**2 - k*p**6 + 0*p. Factor u(n).
-n**2*(n - 1)/4
Let u(h) be the second derivative of -h**7/42 + h**6/15 - h**4/6 + h**3/6 + 7*h. Factor u(a).
-a*(a - 1)**3*(a + 1)
Suppose 2*b = -2*b - 28. Let r(w) = -w**2 - 6*w + 10. Let k be r(b). Factor -f - 3*f**4 - 13 + 13 + k*f**2 + f**3.
-f*(f - 1)*(f + 1)*(3*f - 1)
Suppose h - 2 = 3. Find i, given that -3*i - i**3 + 10*i**2 - i - h*i**3 = 0.
0, 2/3, 1
Suppose 2*v + v = 12. Factor -2*m**4 + 2 + v*m - 16*m**3 - 6*m**5 + 2*m**5 - 12*m**4 - 4*m**2.
-2*(m + 1)**4*(2*m - 1)
Let y = 137 - 137. Let v(u) be the third derivative of 0*u**3 + 1/672*u**8 + 0*u**4 + 1/210*u**7 + 2*u**2 + 1/240*u**6 + 0 + 0*u**5 + y*u. Solve v(r) = 0.
-1, 0
Let p = -4 + 6. What is u in -3*u**3 + u**5 + 2*u**4 - u**3 - p*u**3 + 7*u**3 = 0?
-1, 0
Let d(y) be the second derivative of y**6/30 + y**5/4 + 7*y**4/12 + y**3/2 - 32*y. Let d(m) = 0. Calculate m.
-3, -1, 0
Solve 14*c**3 - 13*c**2 - c**5 - 16*c + 7*c**2 + 8 + 8*c**2 - 10*c**4 + 3*c**5 = 0.
-1, 1, 2
Let g(m) be the second derivative of -m**8/2240 - m**7/840 + m**4/4 - m. Let i(j) be the third derivative of g(j). Determine a so that i(a) = 0.
-1, 0
Determine v, given that 2*v**5 - 2*v**4 + 0*v - 56*v**3 + 0*v + 52*v**3 = 0.
-1, 0, 2
Factor 1/3*b - 5/6*b**2 + 0.
-b*(5*b - 2)/6
Let x = 69 + -69. Solve -1/5*c**2 - 1/5*c**3 + 1/5*c**4 + 1/5*c + x = 0 for c.
-1, 0, 1
Let n = 