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Let a = 11 + -8. Let s(q) be the first derivative of 1/12*q**a + 9/4*q - 1 + 3/4*q**2. Suppose s(w) = 0. What is w?
-3
Let r(u) = -u**3 - 3*u**2 - 2*u - 1. Let m be r(-3). Solve -1 + 2*a**2 + a**m + 1 - a**4 - a**2 - a**3 = 0 for a.
-1, 0, 1
Factor -8/7 - 2/7*x**3 + 6/7*x**2 + 0*x.
-2*(x - 2)**2*(x + 1)/7
Let v = -41/14 + 7/2. What is i in 0 - 4/7*i**2 + v*i = 0?
0, 1
Let q = -266 + 1334/5. Factor 2/5*c**2 - 2/5*c - q.
2*(c - 2)*(c + 1)/5
Let p(t) be the first derivative of t**7/42 - t**5/10 + t**3/6 + 5*t + 5. Let m(x) be the first derivative of p(x). Suppose m(w) = 0. Calculate w.
-1, 0, 1
Let z(w) be the second derivative of w**7/126 - 11*w**6/90 + 43*w**5/60 - 73*w**4/36 + 28*w**3/9 - 8*w**2/3 + 58*w. Find g such that z(g) = 0.
1, 4
Let l = 22 - 16. Suppose -2*r - j = 3, 2*r - 2*j - 18 = -l. Solve 3*y**2 + r + 1 - 6 - y**3 = 0 for y.
-1, 2
Suppose -c - 1 + 4 = 0. Let 4*y**2 - 3*y**3 + 0*y**c - 3*y**2 = 0. Calculate y.
0, 1/3
Factor 1/3*x**2 - 7/3*x + 2.
(x - 6)*(x - 1)/3
Let o be (-34)/4 + (-2 - 0). Let j = -9 - o. Solve 0 - 3*z**2 + 3/2*z + j*z**3 = 0 for z.
0, 1
Let f(m) = -2*m**3 + 2*m**2 + 3. Let s be (3/1 - -4)/(-1). Let z(n) = -7 - n**3 + 2*n**2 + 6*n**3 - 6*n**2. Let u(r) = s*f(r) - 3*z(r). Factor u(b).
-b**2*(b + 2)
Let t(r) be the third derivative of -r**9/5040 - 3*r**8/2240 - r**7/280 - r**6/240 + r**4/8 - r**2. Let z(p) be the second derivative of t(p). Factor z(y).
-3*y*(y + 1)**3
Let s(b) be the third derivative of -b**7/1470 + b**6/420 + b**5/420 - b**4/84 + 12*b**2. Factor s(v).
-v*(v - 2)*(v - 1)*(v + 1)/7
Let o be 2 - (-3)/(0 + 1). Factor 2*x**2 + 4 - 2*x**2 - 3*x**3 - o*x**2 + 4*x.
-(x - 1)*(x + 2)*(3*x + 2)
Let i = -371 - -373. Factor 0*n**i - 1/4*n**4 + 1/2*n - 1/2*n**3 + 1/4.
-(n - 1)*(n + 1)**3/4
Let h(c) be the third derivative of -c**6/600 + c**5/150 - 3*c**2 - 10. Let h(w) = 0. Calculate w.
0, 2
Suppose 5*s = 4*i - 72, -81 = -5*i - 0*s + 4*s. Suppose 5*v + 3 = i. Solve v*l**2 + 4/5*l + 0 = 0.
-2/5, 0
Suppose 4 = -2*y + 10. Find k, given that 0 - 2*k**4 + k - k**3 + 4*k**2 - k**2 - y + 2 = 0.
-1, 1/2, 1
Let c(j) = j**3 + 4*j**2 + 2*j - 1. Let w be c(-2). Let m(k) be the first derivative of 2/27*k**w + 0*k - 2 + 0*k**2. Factor m(q).
2*q**2/9
Suppose -8*u + 55 - 39 = 0. Factor -16/9*w**3 - 2/9*w**4 - 4*w**u + 6 + 0*w.
-2*(w - 1)*(w + 3)**3/9
Let m(f) be the third derivative of f**5/150 - f**4/15 - f**3/3 + 4*f**2. Factor m(d).
2*(d - 5)*(d + 1)/5
Let c(q) be the first derivative of q**4/36 - q**3/9 + q**2/6 - q + 1. Let l(j) be the first derivative of c(j). Factor l(g).
(g - 1)**2/3
Let v(j) be the first derivative of 0*j - 3 + 1/6*j**2 - 1/9*j**3. Factor v(c).
-c*(c - 1)/3
Let i(w) be the second derivative of 3*w**5/20 - 5*w**4/4 + 2*w**3 + w - 2. Determine b, given that i(b) = 0.
0, 1, 4
Let m(k) be the third derivative of k**7/420 - k**6/90 - k**5/60 + k**4/6 + k**3/2 + 3*k**2. Let s(z) be the first derivative of m(z). Factor s(i).
2*(i - 2)*(i - 1)*(i + 1)
Suppose -9 = 3*w - 15. Suppose -2/3*p**w + 4/3*p + 0 = 0. What is p?
0, 2
Find j, given that -2/5*j**2 + 6/5 - 4/5*j = 0.
-3, 1
Let u(m) be the third derivative of m**5/80 - m**4/12 + m**3/6 - 7*m**2. Determine p so that u(p) = 0.
2/3, 2
Let h = 5 + 3. Suppose k - 2*k - 5*g - 8 = 0, 5*k - h = -g. Determine c so that -2*c**4 - c + 5*c**3 + 3 + 3*c**2 - k + 4*c**4 - 2 = 0.
-1, 1/2
Let p(k) be the third derivative of k**7/3780 - k**5/180 - k**4/6 - 3*k**2. Let d(r) be the second derivative of p(r). Factor d(m).
2*(m - 1)*(m + 1)/3
Let h(c) = 3*c**2 - 3. Let a(b) = b**3 + 1. Let k(n) = -3*a(n) - h(n). Suppose k(y) = 0. What is y?
-1, 0
Let p(t) be the second derivative of 1/24*t**4 + 0*t**3 + t - 1/4*t**2 + 0. Factor p(r).
(r - 1)*(r + 1)/2
Solve -32/5*a**3 + 32/5*a + 4/5*a**4 - 64/5 + 12*a**2 = 0.
-1, 1, 4
Let o be (2/4)/(4/48). Suppose 0*c + o = -3*b + 3*c, 4*c - 8 = 3*b. Suppose 2/9*t**3 + 0 + b*t - 2/9*t**2 = 0. Calculate t.
0, 1
Suppose -37*g - 83 + 231 = 0. Find x such that 0 - 2/9*x**3 + 2/9*x**2 + 0*x - 2/9*x**g + 2/9*x**5 = 0.
-1, 0, 1
Let o(g) be the third derivative of 0*g + 0*g**3 - 1/1470*g**7 - 1/210*g**5 + 0*g**4 - 1/280*g**6 + 0 - 5*g**2. Factor o(u).
-u**2*(u + 1)*(u + 2)/7
Let d(v) be the first derivative of v**6/1800 + v**5/300 + v**4/120 - 2*v**3/3 + 5. Let i(k) be the third derivative of d(k). Factor i(x).
(x + 1)**2/5
Factor -10/11*y**2 - 12/11 + 26/11*y.
-2*(y - 2)*(5*y - 3)/11
Let q be 26/(-7) + 44 + -40. Factor 0*c + 0 - q*c**3 + 2/7*c**2.
-2*c**2*(c - 1)/7
Factor -4/9*q**2 - 2/9*q - 2/9*q**3 + 0.
-2*q*(q + 1)**2/9
Let v(i) be the second derivative of -i**8/40320 - i**7/5040 - i**6/1440 - i**5/720 - 5*i**4/12 - 3*i. Let k(x) be the third derivative of v(x). Factor k(d).
-(d + 1)**3/6
Let i = -7631/504 - -106/7. Let w(f) be the third derivative of 0*f - 1/36*f**4 + 0*f**3 + 1/45*f**5 + 0*f**6 + i*f**8 + 0 - 2/315*f**7 + 2*f**2. Factor w(v).
2*v*(v - 1)**3*(v + 1)/3
Let s(i) be the second derivative of -i**8/336 - i**7/70 - i**6/40 - i**5/60 - 3*i**2/2 + 2*i. Let c(k) be the first derivative of s(k). Factor c(o).
-o**2*(o + 1)**3
Let s(x) be the first derivative of 28*x**5/5 - 30*x**4 + 172*x**3/3 - 48*x**2 + 16*x + 7. Solve s(d) = 0.
2/7, 1, 2
Suppose -5*c = -8*c. Factor 0*u**4 - 1/2*u + u**3 + 0 - 1/2*u**5 + c*u**2.
-u*(u - 1)**2*(u + 1)**2/2
Suppose -t - 1 = -4. Let m(x) = -x**3 - 4*x - 2*x**3 + 8*x**2 - x**t - 2. Let w(n) = -n**3 + n**2 - 1. Let f(p) = m(p) - 2*w(p). Suppose f(u) = 0. Calculate u.
0, 1, 2
Let f(l) be the second derivative of 3*l**5/50 + 11*l**4/60 + l**3/5 + l**2/10 - 5*l. Factor f(d).
(d + 1)*(2*d + 1)*(3*d + 1)/5
Let d be 3 + (-22)/8 - 5/(-60). Solve -d + 2/3*r**3 - 1/3*r**5 + 2/3*r**2 - 1/3*r - 1/3*r**4 = 0 for r.
-1, 1
Let p(l) = -9*l**2 + 5*l. Let y(r) = 4*r**2 - 2*r. Let h(n) = -3*p(n) - 7*y(n). Let j(w) = w**3 - 3*w**2 - 4*w. Let o(x) = 4*h(x) - j(x). Factor o(b).
-b**2*(b + 1)
Factor 4/5*c**3 + 0*c + 2/5*c**2 + 0 + 2/5*c**4.
2*c**2*(c + 1)**2/5
Let i = 12 + -10. Factor 5*t**2 + 7*t**2 + 3*t - 9*t**i.
3*t*(t + 1)
Let r(z) = z - 7. Let c be r(12). Let o(f) be the first derivative of 0*f + 0*f**3 - 1/27*f**6 + 0*f**c - 1/9*f**2 + 1/9*f**4 - 3. Find v, given that o(v) = 0.
-1, 0, 1
Let b be (-7 - -3)/(-12) - (-1)/(-39). Factor -2/13*o**2 - 2/13 + b*o.
-2*(o - 1)**2/13
Let i(x) = -3*x**4 - 2*x**3 - 6*x**2 - 3*x - 1. Let g(v) = -2*v**4 - v**3 - 3*v**2 - 2*v - 1. Let y(o) = -10*g(o) + 6*i(o). Solve y(d) = 0 for d.
-1, 1, 2
Let a be (-1*2)/(-6) + (-18 - -18). Suppose -a*q**4 + 1/3*q**3 + 1/3*q**2 - 1/3*q + 0 = 0. Calculate q.
-1, 0, 1
Let j(u) = -u**3 + 4*u**2 - 3*u. Let o be j(2). Let g be (o/4)/(-1 + 2). Factor -1/2*i**2 - i**3 + g*i**4 + 0 + i.
i*(i - 2)*(i - 1)*(i + 1)/2
Let p(m) = -m + 11. Let u = -5 + 16. Let b be p(u). Determine q so that -1/4*q + 1/2*q**2 + b - 1/4*q**3 = 0.
0, 1
Let u = 451 + -1803/4. Find z, given that 0 - 3/4*z**4 - 1/2*z**5 + u*z**3 + 3/4*z**2 + 1/4*z = 0.
-1, -1/2, 0, 1
Suppose 0*c - 5*c = -20. Factor -8/7*f**2 + 6/7*f**5 + 0 + 0*f + 22/7*f**c + 16/7*f**3.
2*f**2*(f + 2)**2*(3*f - 1)/7
Let q(l) be the second derivative of l**6/120 + l**5/40 + l**3/3 + 7*l. Let d(f) be the second derivative of q(f). Let d(s) = 0. What is s?
-1, 0
Let l = 40 - 38. Let w(i) be the first derivative of 1/5*i**l + 0*i - 2/15*i**3 + 1. Solve w(r) = 0.
0, 1
Solve c**5 + 6*c**5 - 4*c**5 - 3*c**3 = 0 for c.
-1, 0, 1
Let f(x) be the first derivative of -15*x**4/28 - 13*x**3/7 - 6*x**2/7 + 12*x/7 + 16. Factor f(v).
-3*(v + 1)*(v + 2)*(5*v - 2)/7
Let h(w) = -4*w**3 + 4*w + 6. Let j(m) be the second derivative of -7*m**5/20 - m**4/12 + 4*m**3/3 + 11*m**2/2 + 7*m. Let b(a) = 11*h(a) - 6*j(a). Factor b(t).
-2*t*(t - 2)*(t - 1)
Let l(j) = j + 12. Let y be l(-10). Let s be 0/(-3) - y*-1. Suppose 0*b**3 - 3*b**4 + b**4 + 2*b**2 - 2*b**3 + s*b + 0*b = 0. Calculate b.
-1, 0, 1
Let f be (4*6/(-4))/2. Let l be 1*f/2*-2. Factor -2/7*n**l + 2/7*n**2 + 0 + 0*n.
-2*n**2*(n - 1)/7
Let f = -7 + 12. Suppose 20 = -0*v + f*v. Let 0*c**2 + 0 + 1/4*c + 1/4*c**5 + 0*c**v - 1/2*c**3 = 0. What is c?
-1, 0, 1
Let g(i) = -i**2 - 6*i - 3. Let w = -5 + 0. Let t be g(w). Find a such that 32/3*a**3 - 22/3*a**t + 4/3*a - 14/3*a**4 + 0 = 0.
0, 2/7, 1
Let j be -1*(2/9 + 850/(-1071)). Let s(z) be the first derivative of 2/7*z**4 - 2/7*z - 3 + 16/35*