Let f = 21 + -21. Let b(q) be the second derivative of -1/4*q**4 - 3/5*q**5 + f - 7/30*q**6 + 1/3*q**3 - q + 0*q**2. Factor b(i).
-i*(i + 1)**2*(7*i - 2)
Let n(i) be the second derivative of -i**6/15 - i**5/2 - 2*i**4/3 - 22*i. Factor n(y).
-2*y**2*(y + 1)*(y + 4)
Let q(z) be the first derivative of 0*z**2 + 2 - 1/10*z**4 + 2/25*z**5 + 0*z - 4/15*z**3. Factor q(u).
2*u**2*(u - 2)*(u + 1)/5
Let o be (54/4)/(2/4). Suppose 4*x + 1 = 4*z - o, 5*z + 5*x = -5. Factor -2*l**z - 4*l + 7*l - l**3.
-3*l*(l - 1)*(l + 1)
Let y = 3/28 - 2/35. Let n(f) be the second derivative of 1/6*f**3 - 1/12*f**4 + 0*f**2 + 1/30*f**6 - 3*f - y*f**5 + 0. Solve n(j) = 0 for j.
-1, 0, 1
Let u be (3 - 6) + 1 + 2. Let z = 51/140 + -4/35. Suppose -1/4*h + z*h**2 + u = 0. Calculate h.
0, 1
Suppose p = -p + 4. Factor 0*j + j**4 + 1/3*j**p + 0 + j**3 + 1/3*j**5.
j**2*(j + 1)**3/3
Let c be 2/6*(21 - 3). Suppose 2*n**4 + 2*n**2 - n**2 + 3*n**3 + 0*n**4 - c*n**3 = 0. What is n?
0, 1/2, 1
Let b be (-9)/15 + (-2)/(-2). Factor 0*o + 0*o**3 - b*o**5 - 3/5*o**4 + 0 + 1/5*o**2.
-o**2*(o + 1)**2*(2*o - 1)/5
Factor -1/2*k - 3/4 + 1/4*k**2.
(k - 3)*(k + 1)/4
Let w(v) be the second derivative of -v**4/6 - v. Factor w(n).
-2*n**2
Let w = 11 + -11. Let i be (12/8 + w)/3. Factor 0 + 0*u**2 - 1/2*u**3 + i*u.
-u*(u - 1)*(u + 1)/2
Let s be (-1 + 2 - -1) + 3. Let -3*p**3 + 7*p - s*p**3 + 4 + 9*p - 10*p**2 - 2*p = 0. Calculate p.
-2, -1/4, 1
Let z(t) be the second derivative of t**5/90 - t**4/18 - t**3/27 + t**2/3 + 8*t. Factor z(h).
2*(h - 3)*(h - 1)*(h + 1)/9
Let b(h) be the third derivative of -h**7/525 + h**6/300 + h**5/50 - h**4/60 - 2*h**3/15 + 36*h**2. Find g, given that b(g) = 0.
-1, 1, 2
Determine t, given that 3 - 13*t**5 + 1 + 19*t**3 + 25*t**2 + 3*t**4 + 14*t**5 + 16*t + 4*t**4 = 0.
-2, -1
Let t(c) be the third derivative of -c**8/504 + c**6/45 - c**5/45 - c**4/12 + 2*c**3/9 + 6*c**2. Determine h, given that t(h) = 0.
-2, -1, 1
Suppose 5*k = 3*k + 10. Suppose 2*m = -8, -4*j = -k*m - 33 - 7. Factor 0*l - 6/5*l**4 + 6/5*l**3 - 2/5*l**2 + 0 + 2/5*l**j.
2*l**2*(l - 1)**3/5
Let d(y) = 3*y**2 - 20*y + 25. Let s(i) = 9*i**2 - 61*i + 74. Suppose -2*n + 21 = n. Let m(j) = n*d(j) - 2*s(j). Factor m(b).
3*(b - 3)**2
Let y(g) be the first derivative of g**4 + 4*g**3/3 - 10*g**2 + 12*g + 12. Factor y(v).
4*(v - 1)**2*(v + 3)
Let o be (-7)/(-14) - (-13)/2. Let u = 7 - o. Find y, given that 2/5*y + u*y**2 + 0 - 2/5*y**3 = 0.
-1, 0, 1
Let j = -12 + 0. Let l be 1/3 + (-12)/j. Let l*f + 0 + 2/3*f**2 = 0. Calculate f.
-2, 0
Let d(l) be the first derivative of 2/3*l**3 + 6*l**2 + 3 + 18*l. Factor d(f).
2*(f + 3)**2
Suppose t - 6*t = -15. Let r be (-20)/(-21) - 4/6. Find h, given that -r*h**t + 0 - 2/7*h**2 + 0*h = 0.
-1, 0
Find v such that 3*v**2 + 5*v**2 + 4*v**3 + 3*v**2 - 16 + v**2 = 0.
-2, 1
Suppose 9 = 2*x + 3. Suppose -5*p = -h + 3, 0 = -2*h - x*p + 10 - 4. Factor -1/4*t + 1/4*t**4 + 1/4*t**h + 0 - 1/4*t**2.
t*(t - 1)*(t + 1)**2/4
Let k(a) be the first derivative of a**4/2 - 3*a**2 + 4*a - 6. Factor k(f).
2*(f - 1)**2*(f + 2)
Suppose 0 = 4*t - 7*t. Let u(f) be the first derivative of t*f**5 - 1/3*f**6 + 0*f**2 + 0*f + 0*f**3 + 1 + 1/2*f**4. Factor u(j).
-2*j**3*(j - 1)*(j + 1)
Find c such that -4/5*c + 8/5*c**2 + 0 - 4/5*c**3 = 0.
0, 1
Let r(g) be the second derivative of -g**4/3 + 12*g**3 - 162*g**2 - 27*g. Determine b, given that r(b) = 0.
9
Find y such that -33/4*y - 15/2 - 3/4*y**2 = 0.
-10, -1
Let l be (1 - 1)/(6/(-3)). Let t(v) be the third derivative of 0 + 0*v**3 - v**2 - 1/120*v**6 + 0*v**4 - 1/210*v**7 + l*v**5 + 0*v. Find a, given that t(a) = 0.
-1, 0
Let i = -52 + 54. Let 0 + 0*j - 4/5*j**2 - i*j**5 - 24/5*j**4 - 18/5*j**3 = 0. What is j?
-1, -2/5, 0
Let c(u) be the second derivative of 1/20*u**5 + 0*u**2 - 1/6*u**4 + u + 1/6*u**3 + 0. Factor c(r).
r*(r - 1)**2
Let q(k) be the first derivative of -k**8/60 - 41*k**7/840 + 7*k**6/90 - k**5/30 - 2*k**3/3 + 3. Let r(o) be the third derivative of q(o). Factor r(y).
-y*(y + 2)*(4*y - 1)*(7*y - 2)
Let h(i) = 3*i**4 - 6*i**3 + 9*i**2 + 9*i - 9. Let p(c) = c**3 - c**2 - c + 1. Let m(w) = h(w) + 9*p(w). Factor m(b).
3*b**3*(b + 1)
Let k(o) be the second derivative of o**5/20 - o**4/3 + 2*o**3/3 + 2*o**2 - 2*o. Let c(v) be the first derivative of k(v). Let c(w) = 0. What is w?
2/3, 2
Let s(d) be the first derivative of -d**3/5 + 12*d**2/5 - 48*d/5 - 12. Let s(x) = 0. What is x?
4
Let z(h) = -3*h**3 + h**3 - h**2 - h**3 + 2*h**3 - 6. Let q(w) = 1. Let a(x) = 6*q(x) + z(x). Determine o, given that a(o) = 0.
-1, 0
Let i be (0 + 3 + -11)/(-5). Let g be 5/75*39 + -1. Determine d so that 0 + i*d + g*d**2 + 2/5*d**3 = 0.
-2, 0
Factor -10*h**2 - h - 2*h + 4*h**2.
-3*h*(2*h + 1)
Let o(f) be the second derivative of 4*f - 1/189*f**7 + 0*f**3 + 0 - 1/90*f**5 + 0*f**2 - 2/135*f**6 + 0*f**4. Factor o(j).
-2*j**3*(j + 1)**2/9
Let s(h) be the second derivative of 9*h + 2/9*h**3 + 1/12*h**4 + 1/6*h**2 + 0. Find t such that s(t) = 0.
-1, -1/3
Solve -4/5 - 2/5*a + 2/5*a**2 = 0 for a.
-1, 2
Let r(s) be the third derivative of 0 + 1/96*s**4 + 0*s**3 + 3*s**2 + 0*s - 1/240*s**5. Factor r(t).
-t*(t - 1)/4
Let y(i) be the third derivative of -1/90*i**5 + 1/360*i**6 + 4/315*i**7 + 5/1008*i**8 + 0*i**4 + 0 + 0*i + 0*i**3 + 3*i**2. Factor y(n).
n**2*(n + 1)**2*(5*n - 2)/3
Let -5*b**3 - 3*b**4 - b**4 + 10*b**2 + 5*b**5 - 5*b**3 - b**4 + 5*b - 5 = 0. Calculate b.
-1, 1
Determine x so that 0 + 4/3*x**2 - 4/3*x = 0.
0, 1
Let k(b) be the second derivative of -b**6/8 - 7*b**5/20 - b**4/4 + 3*b**2/2 + 5*b. Let f(t) be the first derivative of k(t). Factor f(d).
-3*d*(d + 1)*(5*d + 2)
Let z(h) be the first derivative of h**3 - 9*h**2/2 + 6*h + 13. Suppose z(v) = 0. Calculate v.
1, 2
Let o(w) be the first derivative of 2*w**5/5 + w**4 + 2*w**3/3 - 11. Determine b, given that o(b) = 0.
-1, 0
Let w = 36 + -36. Factor -1/3*k**3 + 0*k**2 + 1/3*k + w.
-k*(k - 1)*(k + 1)/3
Let v = -2 + 6. Suppose v*k = -l + 10 + 10, -5*l = 0. Find j such that -4/9*j**4 + 0*j + 0*j**2 - 2/9*j**3 + 0 - 2/9*j**k = 0.
-1, 0
Suppose -13 = 4*p - 21. Let k(o) be the second derivative of -1/60*o**4 + 3*o + 0 - 2/5*o**p + 2/15*o**3. Factor k(l).
-(l - 2)**2/5
Let s(z) = z. Let c be s(6). Let i = 4 - c. Let y(h) = 10*h**3 - h**2 + 5. Let u(a) = 5*a**3 + 2. Let j(r) = i*y(r) + 5*u(r). Factor j(d).
d**2*(5*d + 2)
Factor 2*r + 2*r**3 + 8*r**2 - 3*r - 12 + 3*r.
2*(r - 1)*(r + 2)*(r + 3)
Let f(s) be the second derivative of 6*s + 1/2*s**2 + 1/9*s**3 - 1/36*s**4 + 0. Solve f(c) = 0 for c.
-1, 3
Suppose -5*z = -2*h - 6, 2*z - 5*h + 2*h + 2 = 0. Factor 16/13 + 14/13*y**3 + 36/13*y**z + 2/13*y**4 + 40/13*y.
2*(y + 1)*(y + 2)**3/13
Let k be (-10)/35 - 60/(-14). Suppose 0*o + 4*o = 5*u - 26, -k*u - 4*o - 8 = 0. Factor 0*r**4 + 4*r**4 - 5*r**2 + r**2 - 2*r**3 - u*r**4.
2*r**2*(r - 2)*(r + 1)
Let g(v) = -v**5 + v**4 + v**3 + v + 1. Let f(p) = p**2 + p + 1. Let i(x) = -2*f(x) + 2*g(x). Solve i(w) = 0.
-1, 0, 1
Suppose -5*m = -32 + 2. Suppose -3/2*z**4 - 9*z**2 - m*z - 6*z**3 - 3/2 = 0. What is z?
-1
Let j be (-4)/2 - (-18 - -14). Let s = 13/12 - 19/84. Factor 2/7*l**j + 4/7 - s*l.
2*(l - 2)*(l - 1)/7
Factor -8*i + 9 - 17 + 0 - 2*i**2.
-2*(i + 2)**2
Let t(o) be the first derivative of -o**9/1008 + o**8/560 + o**7/280 - o**6/120 + 2*o**3/3 + 3. Let f(g) be the third derivative of t(g). What is h in f(h) = 0?
-1, 0, 1
Factor -475*z + 140*z**3 + 60*z**4 + 540*z**2 - 5*z**5 + 70*z - 410*z**3.
-5*z*(z - 3)**4
Let z be (-2 + (0 - -2))/2. Let o(v) be the second derivative of -1/84*v**7 - v + z*v**2 + 0*v**6 + 0*v**4 + 0*v**3 + 0*v**5 + 0. Factor o(c).
-c**5/2
Suppose 6*s - 21 = 3. Let f(j) be the first derivative of 0*j - 1/5*j**2 - 1 - 2/25*j**5 + 2/15*j**3 + 1/10*j**s. Let f(t) = 0. What is t?
-1, 0, 1
Let h(d) = -d**2 - 7*d - 4. Let i be h(-6). Let w(x) be the first derivative of -1/2*x**4 + 1 + 0*x + 4/3*x**3 - x**i. Factor w(b).
-2*b*(b - 1)**2
Let n(s) be the third derivative of -1/60*s**5 + s**2 + 1/210*s**7 + 0*s**3 + 1/120*s**6 - 1/24*s**4 + 0*s + 0. Factor n(i).
i*(i - 1)*(i + 1)**2
Let r(p) = p + 17. Let v be 13/(-3)*(4 + -1). Let u be r(v). Find h, given that -2/9*h**u + 0*h**2 + 4/9*h**3 + 2/9 - 4/9*h = 0.
-1, 1
Let l(x) be the first derivative of -x**4/12 + 7*x**3/9 - 5*x**2/2 + 3*x + 6. Let l(k) = 0. Calculate k.
1, 3
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