)**2
Let i be 3/(-108)*-6 - (-2)/(-12). Factor -4/3*o**3 + 2*o**2 + i + 4/3*o.
-2*o*(o - 2)*(2*o + 1)/3
Suppose -4*j + 6 = -4*i - 6, -3*i = -j + 9. Let -2/13*l**2 - 2/13*l + j = 0. Calculate l.
-1, 0
Let l be ((-4)/12)/((-1)/3). Suppose -5*r - l + 11 = 0. Factor -2/3*j**r + 2/3 - 2/3*j**3 + 2/3*j.
-2*(j - 1)*(j + 1)**2/3
Let l = 11 + -5. Suppose -3*s + l = -b, b - 1 + 3 = s. Factor 2/3*d**4 + 2/3*d**3 + 0*d + 0 + 0*d**s.
2*d**3*(d + 1)/3
Let g(t) be the first derivative of 0*t**2 - 1/3*t**4 + t + 2 - 1/6*t**3. Let s(n) be the first derivative of g(n). Factor s(m).
-m*(4*m + 1)
Suppose 15*u - 36*u + 63 = 0. Factor 1/4 - 1/2*i**2 - 1/2*i**u + 1/4*i**5 + 1/4*i**4 + 1/4*i.
(i - 1)**2*(i + 1)**3/4
Suppose j + 1 = 6, -5*j = 2*k - 29. Let v(o) be the second derivative of 0 - 1/3*o**3 - 1/3*o**2 + k*o + 2/9*o**4. Solve v(a) = 0 for a.
-1/4, 1
Let s(z) be the first derivative of 2*z**4 - 44*z**3/3 + 34*z**2 - 24*z + 15. Factor s(j).
4*(j - 3)*(j - 2)*(2*j - 1)
Let i = -108 + 64. Let d be (1/(-2))/(77/i). Suppose -d*y + 2/7*y**2 + 0 = 0. Calculate y.
0, 1
Suppose 4*x - 12 = p - 0*x, 4*p + 4 = 5*x. Let d(g) = -3*g**3 + g**2 - 5*g - 5. Let i(u) = u**3 + u + 1. Let q(t) = p*i(t) + d(t). Factor q(y).
(y - 1)*(y + 1)**2
Suppose -2*q = -3*w - 13, -7 = 4*q + 5*w - 0. Let i(z) be the first derivative of 2*z**q + 2*z - 3 + 2/3*z**3. Let i(r) = 0. What is r?
-1
Suppose 2*l**2 + 107*l**4 - 109*l**4 + 0*l + l**5 - l = 0. Calculate l.
-1, 0, 1
Factor 0 - f**2 + 2/3*f + 0*f**3 + 1/3*f**4.
f*(f - 1)**2*(f + 2)/3
Factor -4/5 + 53/5*i**3 + 33/5*i**4 + 31/5*i**2 + 0*i + 7/5*i**5.
(i + 1)**3*(i + 2)*(7*i - 2)/5
Let s(a) be the second derivative of 0*a**2 + 1/14*a**3 + 3*a + 0 - 1/28*a**4. Find r such that s(r) = 0.
0, 1
Solve -g**5 - 4*g + 4*g**4 + 3*g**5 + 2*g - 4*g**2 + 0*g**5 = 0 for g.
-1, 0, 1
Factor 0*f**2 + 1/5*f**5 + 0*f + 0 + 2/5*f**3 + 3/5*f**4.
f**3*(f + 1)*(f + 2)/5
Factor 3/5*c**2 + 0 - 6/5*c.
3*c*(c - 2)/5
Let l(u) be the first derivative of -u**4/4 + 3*u**3/2 - 3*u**2 + 4*u + 2. Let r(j) be the first derivative of l(j). Let r(s) = 0. What is s?
1, 2
Let t(k) be the second derivative of -k**6/720 - 3*k**2 - 3*k. Let m(g) be the first derivative of t(g). Determine x, given that m(x) = 0.
0
Let c(b) be the first derivative of 8/33*b**6 + 12/55*b**5 - 2/33*b**3 + 0*b + 1 - 3/22*b**4 + 0*b**2. Let c(f) = 0. What is f?
-1, -1/4, 0, 1/2
Let u(g) be the second derivative of 5*g - 1/30*g**5 + 0*g**3 + 0 + 1/9*g**4 + 0*g**2. Solve u(b) = 0.
0, 2
Let t(k) be the first derivative of -1/3*k**3 + 0*k + 2 + 0*k**2 + 1/300*k**5 + 0*k**4 + 1/900*k**6. Let h(p) be the third derivative of t(p). Factor h(s).
2*s*(s + 1)/5
Let r = -25 + 27. Suppose -2*s + s = -r. Solve -1/3*h**4 + 0 + 0*h - 2/3*h**3 - 1/3*h**s = 0.
-1, 0
Let h = 14 - 4. Suppose 5*m - 5 + 20 = 0, 0 = 2*w + 3*m + 3. Find l such that -10 - w*l**4 + h = 0.
0
Let j(i) be the first derivative of i**3 + 6*i**2 + 9*i - 31. Factor j(p).
3*(p + 1)*(p + 3)
Let t(b) be the third derivative of b**7/700 - b**6/225 + b**5/300 + b**3/3 + 4*b**2. Let j(f) be the first derivative of t(f). Factor j(c).
2*c*(c - 1)*(3*c - 1)/5
Let h(o) be the first derivative of 1/70*o**5 + 0*o**3 + 0*o**2 - 2*o + 2 + 1/42*o**4. Let t(c) be the first derivative of h(c). Factor t(s).
2*s**2*(s + 1)/7
Let b(p) be the first derivative of -1/9*p**3 - 1/6*p**2 + 1/12*p**4 + 0*p + 1 + 1/15*p**5. Suppose b(i) = 0. Calculate i.
-1, 0, 1
Solve -d**5 - 6*d**4 + 3*d - 2*d**3 + 15*d**4 - 8*d**4 + 1 + 2*d**2 - 4*d**4 = 0 for d.
-1, 1
Let m(h) be the second derivative of -1/6*h**4 + 9*h - 1/3*h**3 + 2*h**2 + 0. Factor m(u).
-2*(u - 1)*(u + 2)
Let j = 3 - 9. Let f be (2/j)/((-6)/72). Suppose a**2 + 0*a**4 + a**2 - 2*a**f = 0. What is a?
-1, 0, 1
Let g(x) be the second derivative of x**6/240 - x**5/20 + 5*x**4/32 + x**3/6 - x**2 + 13*x. Determine k so that g(k) = 0.
-1, 1, 4
Let k(s) be the second derivative of 0 - 1/2*s**2 - 1/30*s**5 + 1/3*s**3 + 2*s + 0*s**4. Let z(t) be the first derivative of k(t). Factor z(b).
-2*(b - 1)*(b + 1)
Let b(k) = 5*k - 16. Let y(p) = -3*p + 11. Let l(h) = -5*b(h) - 8*y(h). Let g be l(-8). Factor -2/3*t**3 - 2/3*t + 4/3*t**2 + g.
-2*t*(t - 1)**2/3
Let 0*f**2 + 1/2*f**3 + 0 - 1/2*f = 0. Calculate f.
-1, 0, 1
Let h(j) = -3*j - 3. Let o be h(-2). Let i be (-6)/8 - (-304)/64. Suppose 6/7*f**5 + 0 - 4/7*f**o + 0*f - 2/7*f**i + 0*f**2 = 0. What is f?
-2/3, 0, 1
Let 4/7*v**2 + 0 - 4/7*v**4 + 2/7*v**3 + 0*v - 2/7*v**5 = 0. Calculate v.
-2, -1, 0, 1
Let m(g) be the second derivative of 2*g**7/7 - 8*g**6/15 - 8*g**5/5 + 2*g**4 + 10*g**3/3 - 4*g**2 - g + 11. Find s, given that m(s) = 0.
-1, 1/3, 1, 2
Factor 2/9*z**2 + 2/9*z**3 + 0 + 0*z.
2*z**2*(z + 1)/9
Let h(a) be the third derivative of 8*a**7/735 + a**6/210 - 4*a**5/105 - a**4/42 + 3*a**2. Let h(g) = 0. What is g?
-1, -1/4, 0, 1
Let y(a) be the third derivative of a**9/30240 + a**8/5040 + a**7/2520 + a**5/30 - 4*a**2. Let b(c) be the third derivative of y(c). Factor b(v).
2*v*(v + 1)**2
Let h(f) be the second derivative of -f**6/1620 - 4*f**3/3 - f. Let j(g) be the second derivative of h(g). Factor j(k).
-2*k**2/9
Let b = 15 - 11. Suppose -13 = -3*z - b. Let -2/7*f + 2/7*f**z + 0 + 0*f**2 = 0. What is f?
-1, 0, 1
Let h(v) be the second derivative of -v**5/140 - v**4/84 + v**3/21 - v. Determine i so that h(i) = 0.
-2, 0, 1
Solve -8/3 - 1/3*v**3 - 4*v - 2*v**2 = 0 for v.
-2
Let 2*n**2 + 0 + 4/3*n + 2/3*n**3 = 0. What is n?
-2, -1, 0
Let i be 1 - (2 + 0)/(-1). Suppose 4*w + 0*w - 2*s = 0, 5*w + 2*s = 18. Determine r so that 0*r - r**w + 0 - 1/2*r**i = 0.
-2, 0
Factor -32/3 - 2/3*l**3 - 40/3*l - 16/3*l**2.
-2*(l + 2)**2*(l + 4)/3
Factor 8*m - 99*m**2 + 199*m**2 - 99*m**2.
m*(m + 8)
Let k(y) be the second derivative of 0 - 1/6*y**4 + 0*y**2 - 1/3*y**3 - 2*y. Suppose k(p) = 0. Calculate p.
-1, 0
Factor 5/4*t + 1/4 + t**2.
(t + 1)*(4*t + 1)/4
Let o(d) be the first derivative of 2*d**5/75 - d**4/30 - 4*d**3/45 + 18. Factor o(w).
2*w**2*(w - 2)*(w + 1)/15
Let 15 + 3*n**2 + 5 + 28 + 0 + 24*n = 0. What is n?
-4
Let i(u) = -u**3 + 2*u**2 + 2*u - 1. Let z = 8 - 6. Let r be i(z). Factor 0*k**5 - 4*k**4 + 2*k**5 + k**r + k**3.
2*k**3*(k - 1)**2
Let l(x) be the third derivative of -x**5/15 + x**4/8 + x**3/6 - 3*x**2. Factor l(y).
-(y - 1)*(4*y + 1)
Let k be (-112)/(-63) + 4/18. Let x(l) be the first derivative of 0*l**3 + 0*l - 1/12*l**4 + k + 1/6*l**2. Determine b so that x(b) = 0.
-1, 0, 1
Factor 2/13*d**2 - 2/13*d**4 + 0*d**3 + 0*d + 0.
-2*d**2*(d - 1)*(d + 1)/13
What is i in -3/2*i**5 + 0*i**3 + 0 + 3/2*i + 3*i**2 - 3*i**4 = 0?
-1, 0, 1
Let j(q) be the second derivative of 0*q**2 - 3*q + 0 + 1/3*q**4 - 1/15*q**6 - 1/10*q**5 + 0*q**3. Factor j(y).
-2*y**2*(y - 1)*(y + 2)
Let j be (-21)/(-9) + 2/3. Suppose -10*w**4 - w - j*w**3 + 2*w**2 + 5*w - 13*w**3 - 4*w**2 = 0. Calculate w.
-1, 0, 2/5
Let j(a) be the first derivative of -4*a**3/5 + 3*a**2/2 - 3*a/5 + 5. Factor j(w).
-3*(w - 1)*(4*w - 1)/5
Let d = 200/3 + -66. Determine v so that -1/3*v**2 + 0 - d*v = 0.
-2, 0
Let w(n) be the third derivative of -n**5/90 + 5*n**4/6 - 25*n**3 - 14*n**2. Let w(b) = 0. Calculate b.
15
Let z = -3152 - -157607/50. Let t(h) be the second derivative of -z*h**5 - h + 0 + 2/3*h**3 - 2/5*h**2 - 17/60*h**4. Factor t(j).
-(j + 2)*(2*j - 1)*(7*j - 2)/5
Let v(p) be the second derivative of 6*p + 4/3*p**3 + 1/6*p**4 + 0 + 3*p**2. Determine a, given that v(a) = 0.
-3, -1
Let p(h) = 2*h**3 + h**2 - 1. Let q(f) = f**3 + f**2 + f - 1. Let z be 55/22 + (-1)/(-2). Let k(d) = z*p(d) - 3*q(d). Factor k(b).
3*b*(b - 1)*(b + 1)
Let d(f) = -2*f - 13. Let v(b) = b**3 + 6*b**2 + 2*b + 3. Let g be v(-6). Let i be d(g). Factor 7*x**2 + 12*x**4 - 3*x + 4 - 20*x**3 + i*x - 5.
(x - 1)*(2*x - 1)**2*(3*x + 1)
Let v(w) be the third derivative of 0*w + 0*w**4 + 0*w**5 - 1/2*w**3 + 0 + 1/1260*w**6 + w**2. Let u(o) be the first derivative of v(o). Solve u(l) = 0 for l.
0
Let n(g) = -g + 5. Let m(i) = -3*i. Let c be m(-1). Let t be n(c). Factor 2/5 - 2*q + 8/5*q**t.
2*(q - 1)*(4*q - 1)/5
Let y(j) be the second derivative of -j**6/10 + 9*j**5/10 - 13*j**4/4 + 6*j**3 - 6*j**2 + 4*j. Determine o, given that y(o) = 0.
1, 2
Let l(a) be the third derivative of -a**8/84 + 2*a**7/35 - a**6/30 - a**5/5 + a**4/3 + 21*a**2. Suppose l(f) = 0. Calculate f.
-1, 0