 first derivative of d**6/3 - 4*d**5/5 + 4*d**3/3 - d**2 + 8. Factor b(f).
2*f*(f - 1)**3*(f + 1)
Let j(f) be the first derivative of -f**3/24 + f**2/8 - f/8 + 16. Determine g so that j(g) = 0.
1
Let h = 29 + -85/3. Let g(x) be the second derivative of 3*x + 0 + 1/6*x**4 + 0*x**2 - h*x**3. What is c in g(c) = 0?
0, 2
Let f(z) = -z**2 + z + 1. Let d(r) = -4*r**2 - 12*r - 6. Let m(p) = -d(p) - 6*f(p). Factor m(u).
2*u*(5*u + 3)
Let n(b) be the second derivative of b**5/14 - b**4/6 + 2*b**3/21 - 2*b. Find d such that n(d) = 0.
0, 2/5, 1
Let i = 14 + -22. Let y = 10 + i. Factor 0 + 0*a + 2/5*a**y.
2*a**2/5
Let v(u) be the first derivative of -1/2*u**4 + u**2 + 0*u**3 + 1/5*u**5 + 2 - u. Find j such that v(j) = 0.
-1, 1
Let t(k) be the second derivative of k**3/6 + 4*k**2 + k. Let u be t(-6). Determine q so that -2/9 - 2/9*q**u - 4/9*q = 0.
-1
Factor -26/11*q**2 + 2/11*q**4 + 0 + 14/11*q + 10/11*q**3.
2*q*(q - 1)**2*(q + 7)/11
Let j be -1 + 2 - 1/3. Factor 1/3*o**2 - o + j.
(o - 2)*(o - 1)/3
Let z(k) be the third derivative of -1/10*k**5 - 1/210*k**7 + k**2 - 1/6*k**4 + 0*k - 1/30*k**6 + 0 - 1/6*k**3. Factor z(j).
-(j + 1)**4
Suppose -2/3*x - 4/3*x**2 - 2/3*x**3 + 0 = 0. Calculate x.
-1, 0
Let l(j) be the first derivative of -1/9*j**3 - 1/18*j**6 + 1/12*j**4 + 0*j**2 - 7 + 1/15*j**5 + 0*j. Factor l(k).
-k**2*(k - 1)**2*(k + 1)/3
Let s(t) = -t + 9. Let y be s(5). Suppose 0*h = -2*h + y. Determine a so that 1/5*a**h + 0 + 0*a = 0.
0
Factor -4 - 1 - 169*b**2 + 174*b**2.
5*(b - 1)*(b + 1)
Let x be (-92)/(-22) - 8/44. Determine z, given that 2*z**x - 4*z**2 + 4*z**3 - 2*z**5 - 5*z + 3*z + 2 + 0*z = 0.
-1, 1
Determine x so that 4/7*x**3 + 0*x + 0 - 4/7*x**2 = 0.
0, 1
Let s(i) = -9 + 7*i**2 - 3*i**4 + 3*i**2 + 2*i**2 - 15*i + 6*i**3. Let q(n) = n**2 - n - 1. Let v(x) = 9*q(x) - s(x). Factor v(m).
3*m*(m - 2)*(m - 1)*(m + 1)
Suppose -4*g = -0*g - 8. Suppose -g*b**2 + 1 - 6*b + 3*b**2 + 4*b = 0. Calculate b.
1
Let h(q) be the first derivative of -q**3/15 - q**2/10 - 4. What is m in h(m) = 0?
-1, 0
Let x(s) be the third derivative of 1/30*s**5 - 3*s**2 + 0*s - 2/3*s**3 - 1/12*s**4 + 0. Suppose x(t) = 0. What is t?
-1, 2
Suppose -3*g = -v + 6 - 17, -3*v + 7 = -g. Factor 0 + 0*x + 1/3*x**5 + x**3 + x**v + 1/3*x**2.
x**2*(x + 1)**3/3
Let w(a) be the third derivative of a**8/30240 - a**7/2520 + a**6/540 + a**5/20 + 3*a**2. Let v(y) be the third derivative of w(y). Factor v(i).
2*(i - 2)*(i - 1)/3
Let b = -23 + 27. Let g(y) = 6*y**4 - 9*y**3 + 9*y + 15. Let j(p) = p**4 - 2*p**3 + 2*p + 3. Let x(d) = b*g(d) - 21*j(d). Factor x(t).
3*(t - 1)*(t + 1)**3
Let n be (-4)/(-2) + 0 + 1. Suppose 0 = 6*d - n*d - 6. Factor 0*w - 2/7 + 2/7*w**d.
2*(w - 1)*(w + 1)/7
Let g = -659/2 + 330. Factor g - j + 1/2*j**2.
(j - 1)**2/2
Let d(p) be the second derivative of 0*p**2 + 0 - 4/3*p**3 + p**4 - 1/5*p**5 + 5*p. Suppose d(z) = 0. What is z?
0, 1, 2
Let r(y) be the first derivative of -y + 2/3*y**3 - 4 - 1/2*y**2. Factor r(i).
(i - 1)*(2*i + 1)
Let l(b) be the third derivative of b**5/180 - b**4/72 + 40*b**2 - b. Factor l(f).
f*(f - 1)/3
What is p in 1/4*p - 1/4*p**4 + 0 - 1/4*p**3 + 1/4*p**2 = 0?
-1, 0, 1
Factor -8/3 - 4/3*f**3 - 2*f**2 + 2/3*f**4 + 16/3*f.
2*(f - 2)*(f - 1)**2*(f + 2)/3
Let c(o) be the third derivative of -5/48*o**4 + 1/40*o**5 - 1/6*o**3 + o**2 + 0 + 0*o. Factor c(q).
(q - 2)*(3*q + 1)/2
Factor 1125 + 26*p**2 + 34*p**2 - 48*p + 198*p - 55*p**2.
5*(p + 15)**2
Suppose -5*o = -11 + 1. What is j in 0 - 8/9*j**o - 2/9*j**3 - 8/9*j = 0?
-2, 0
Let n be (-30)/(-7) + 10/(-35). Let f be 5 - (-5)/((-10)/n). Suppose 1/2*d**4 + d - d**f + 0*d**2 - 1/2 = 0. What is d?
-1, 1
Suppose -k = -24 + 6. Let c = -14 + k. Factor 0 - 1/5*m**3 - 1/5*m**c + 1/5*m**2 + 1/5*m.
-m*(m - 1)*(m + 1)**2/5
Let f(a) = a. Let d be f(3). Suppose 0 = -2*s + 6 + 2, -2*k - 4 = -2*s. Factor 6*b**k + 48/7*b - 14*b**d + 8/7.
-2*(b - 1)*(7*b + 2)**2/7
Let c(y) = -y**3 + 4*y**2 - y - 5. Let p be c(4). Let j be ((-6)/(-9))/((-3)/p). Factor 1 - 5/2*x + j*x**2 - 1/2*x**3.
-(x - 2)*(x - 1)**2/2
Let c = 2/29 + 25/58. Let c*v**2 - 1/2*v + 0 = 0. Calculate v.
0, 1
Suppose 3*j + j - 5*w = 49, -5*w = -2*j + 17. Suppose -2*l - s - 1 = -7, 4*l - 2*s = 12. Factor -2*h + 3*h - 4 + j*h**2 + h + 10*h**l.
2*(h + 1)**2*(5*h - 2)
Let m(q) be the first derivative of q**4/36 + 4*q**3/27 - 2*q**2/9 - 16*q/9 + 45. Solve m(x) = 0 for x.
-4, -2, 2
Let g = 27/35 + -4/7. Let i(d) = -d**3 + 4*d**2 - d - 4. Let b be i(3). Factor -1/5*c**3 + 1/5*c - 1/5 + g*c**b.
-(c - 1)**2*(c + 1)/5
Factor -1/5*h**3 + 1/5 + 3/5*h**2 - 3/5*h.
-(h - 1)**3/5
Let k(f) = 35*f**4 + 55*f**3 + 15*f**2 - 55*f - 20. Let q(r) = -5*r**4 - 8*r**3 - 2*r**2 + 8*r + 3. Let c(z) = 2*k(z) + 15*q(z). Factor c(b).
-5*(b - 1)*(b + 1)**3
Let c(j) = j - 10. Let p be c(15). Factor 0 + 10/7*w**4 + 0*w + 2*w**p + 0*w**2 - 4/7*w**3.
2*w**3*(w + 1)*(7*w - 2)/7
Suppose -4*g - 5*z + 47 = 0, 3*z + 0*z + 31 = 5*g. Suppose 9 = -4*k + 5*a - g, -a = 4*k - 13. Find v, given that -v - 4*v**2 + 2*v**k + 3*v**2 = 0.
0, 1
Let r(n) = -n**3 + 3*n**2 + 52. Let o be r(5). Let f = 6318/7 - 900. Solve -2*b - f*b**o - 2/7*b**4 - 10/7*b**3 - 4/7 = 0 for b.
-2, -1
Let i(q) be the first derivative of 0*q**2 + 1/3*q**3 + 7 - 1/16*q**4 + 0*q. Factor i(h).
-h**2*(h - 4)/4
Let o = 2230081/480 + -4646. Let b(n) be the third derivative of 1/96*n**4 + 0*n**3 + 0 + 0*n - o*n**6 + 0*n**5 + 3*n**2. Factor b(a).
-a*(a - 1)*(a + 1)/4
Let o = -641/6 + 107. Factor -1/6*h + 0 - 1/6*h**4 + 1/6*h**2 + o*h**3.
-h*(h - 1)**2*(h + 1)/6
Let s = -38/11 - -690/187. Let -s*t**4 + 6/17*t**2 + 2/17*t**3 - 2/17 - 2/17*t = 0. What is t?
-1, -1/2, 1
Let t(p) be the second derivative of -p**7/294 + 2*p**6/105 - 3*p**5/140 - p**4/21 + 2*p**3/21 + 3*p. What is r in t(r) = 0?
-1, 0, 1, 2
Factor 0 + 0*a**2 - 1/3*a**3 + 1/3*a.
-a*(a - 1)*(a + 1)/3
Let g = -208/3 - -70. Factor 1/3*j**2 + 1/3 - g*j.
(j - 1)**2/3
Let r(x) be the second derivative of 10/27*x**4 - 8/27*x**3 - 1/189*x**7 + 4*x - 1/5*x**5 + 7/135*x**6 + 0 + 0*x**2. Find p such that r(p) = 0.
0, 1, 2
Let x = 0 + 2. Let t(m) be the first derivative of -1/3*m**3 + 0*m**x + 0*m - 1. Factor t(d).
-d**2
Let z = -6 - -8. What is s in 0*s**3 + 4/3*s**4 + 0 - 2/3*s + 2/3*s**5 - 4/3*s**z = 0?
-1, 0, 1
Suppose 4 = -4*g + 12. Solve -2/3*q**g + 0 + 2/3*q = 0 for q.
0, 1
Let i = 13 - 8. Let g = -2/151 + 163/906. Factor -d**3 - 1/6*d + 0 + 2/3*d**4 + 2/3*d**2 - g*d**i.
-d*(d - 1)**4/6
Let s(n) = n**2 - 7*n + 4. Let f be s(5). Let d be 4*-1 - (-12 - f). Factor -20/7*c**d - 6/7*c**3 + 16/7 - 8/7*c.
-2*(c + 2)**2*(3*c - 2)/7
Let a be 28*(-4)/(-24) + 2/6. Factor 18/7*l**3 + 10/7*l**a + 4/7*l**2 + 0*l + 0 + 24/7*l**4.
2*l**2*(l + 1)**2*(5*l + 2)/7
Let z = -36 - -42. Let a(j) be the first derivative of 0*j**3 + 2/15*j**5 + 2/3*j**z - 1/6*j**4 + 0*j**2 - 1 + 0*j. Factor a(x).
2*x**3*(2*x + 1)*(3*x - 1)/3
Let i(o) = -3*o**2 - 5*o + 8. Let w(q) = -4*q**2 - 8*q + 12. Let l(g) = -7*i(g) + 5*w(g). Factor l(j).
(j - 4)*(j - 1)
Let s = -54 + 164/3. Let j(o) be the third derivative of -1/15*o**5 + 4/105*o**7 - 1/168*o**8 - s*o**3 - 1/15*o**6 + 5/12*o**4 + 0*o + 0 - 4*o**2. Factor j(w).
-2*(w - 2)*(w - 1)**3*(w + 1)
Let u(f) be the second derivative of 0*f**4 + 0 + 0*f**2 - 1/420*f**5 + 1/1260*f**6 + 1/3*f**3 + 4*f. Let r(s) be the second derivative of u(s). Factor r(m).
2*m*(m - 1)/7
Let d = 30 + -27. Factor 4/3*m - 4/3*m**d + 1/3 - 1/3*m**2.
-(m - 1)*(m + 1)*(4*m + 1)/3
Factor -6/7*t - 9/7*t**2 + 0 - 3/7*t**3.
-3*t*(t + 1)*(t + 2)/7
Let q(z) = -3*z + 32. Let m be q(9). Let f(j) be the third derivative of -1/60*j**m - 1/6*j**3 + 3*j**2 + 0*j + 0 - 1/12*j**4. Let f(s) = 0. What is s?
-1
Let h(u) = u**3 - 9*u**2 + 8*u - 5. Let r be h(8). Let j = -5 - r. Factor 0*v + 0 + 1/3*v**2 + j*v**3 - 1/3*v**4.
-v**2*(v - 1)*(v + 1)/3
Let q(g) be the second derivative of -g**6/60 + g**5/8 - g**4/6 - 8*g. Factor q(y).
-y**2*(y - 4)*(y - 1)/2
Let a = -15/11 - -97/55. Factor 0*v + 0*v**3 + 0 + 0*v**2 - a*v**4 + 2/5*v**5.
2*v**4*(v - 1)/5
Let r(s) be the third derivative of -s**5/45 - s**4/8 - s**3/9 + 7*s**2. Suppose r(w) = 0. What is w?
-2, -1/4
Let i = -299 + 302. Solve 4/11*v**2 + 2/11*v**i - 2/11*v - 4/11 = 0.
-2, -1, 1
Suppose 4*n = 3*n - 5. Let f(g) = 7*g**4 + 9*g**3 + g + 3. Let s(c) = 6*c**4 + 8*c**3 + 2. Le