 + c**5/135 - c**4/24 - 3*c**2. Let p(s) be the second derivative of j(s). Factor p(z).
-2*(z - 1)*(z + 2)**2/9
Let d(b) = -2*b**3 + b**2. Let v(w) = 2*w**3. Let z(s) = 6*d(s) + 5*v(s). Let z(g) = 0. Calculate g.
0, 3
Let v(c) be the second derivative of 1/30*c**5 - 6*c + 0 + 2/3*c**2 - 1/45*c**6 + 1/6*c**4 - 5/9*c**3. Let v(d) = 0. Calculate d.
-2, 1
Suppose -3*g = 2*f + 3, -62 = -2*f + 5*g - 25. Let h be ((-15)/f)/((-5)/3). Find i, given that h + 9/4*i + 3/4*i**2 = 0.
-2, -1
Let m(n) be the first derivative of 5*n**4/4 - 5*n**3 - 45*n**2/2 - 25*n + 15. Factor m(r).
5*(r - 5)*(r + 1)**2
Let u = 249331/169308 - 2/4703. Let j = u - 5/4. Find q, given that j*q**3 + 2/9*q**4 + 0 - 2/9*q - 2/9*q**2 = 0.
-1, 0, 1
Let v(w) be the third derivative of w**5/270 + w**4/36 + 2*w**3/27 - 35*w**2. Factor v(h).
2*(h + 1)*(h + 2)/9
Let l = -5 - -8. Factor -11*x - 3 + 14*x - l*x**2 + 3.
-3*x*(x - 1)
Let k(d) be the third derivative of d**5/90 + 17*d**4/108 + 10*d**3/27 - 25*d**2. Determine u, given that k(u) = 0.
-5, -2/3
Let u(a) be the first derivative of -9*a**5/35 + 3*a**4/28 + 2*a**3/7 - 52. Solve u(c) = 0.
-2/3, 0, 1
Let j(k) = k**3 - 3*k**2 - 3*k. Suppose 0 = -3*y + 13 - 1. Let u be j(y). Suppose 0*r + 8/3*r**5 + 0 + 2/3*r**3 + 8/3*r**u + 0*r**2 = 0. What is r?
-1/2, 0
Let s = 83/2 - 41. Find m such that 0*m + 1/2*m**2 + 0 + 0*m**3 - s*m**4 = 0.
-1, 0, 1
Suppose 2*u + 10 = 4*u. Suppose -9 = -3*q, -u*g - 3*q + 0*q + 9 = 0. Factor -1/5*y**4 + 0*y**3 + 0*y**2 + g + 0*y - 1/5*y**5.
-y**4*(y + 1)/5
Let l(q) be the third derivative of 3*q**5/80 + q**4/16 + 16*q**2. Factor l(c).
3*c*(3*c + 2)/4
Factor 0*l + 0*l**3 - 2/7*l**4 - 2/7 + 4/7*l**2.
-2*(l - 1)**2*(l + 1)**2/7
Let i = 1/73 - -214/365. Solve -i*a**2 - 3/5*a**4 - 6/5*a**3 + 0 + 0*a = 0 for a.
-1, 0
Let k(r) = r**4 - r**3 - r**2 + r + 1. Let v(u) = -4*u**3 + 4*u + 2. Let c(p) = 2*k(p) - v(p). Factor c(y).
2*y*(y - 1)*(y + 1)**2
Let c(m) = 2*m - 2. Let k be c(2). Let v be (2/k)/(1/2). Suppose 0*w - 2 + 3*w - w - 6*w - v*w**2 = 0. What is w?
-1
Let l(j) be the second derivative of -j**8/4200 + j**6/900 + j**3/6 - 2*j. Let h(m) be the second derivative of l(m). Factor h(k).
-2*k**2*(k - 1)*(k + 1)/5
Let o(a) be the first derivative of a**5/20 - 3*a**4/4 + 9*a**3/2 + a**2 - 4. Let p(b) be the second derivative of o(b). Determine r, given that p(r) = 0.
3
Let t(b) be the second derivative of b**7/5040 - b**6/1440 - b**4/6 - 3*b. Let l(p) be the third derivative of t(p). Factor l(j).
j*(j - 1)/2
Factor -4/3*q - 2/3*q**3 - 2*q**2 + 0.
-2*q*(q + 1)*(q + 2)/3
Let i(b) be the second derivative of -b**9/52920 + b**8/23520 - 5*b**4/12 - 7*b. Let f(m) be the third derivative of i(m). Solve f(x) = 0.
0, 1
Let -1 - l - 1/4*l**2 = 0. Calculate l.
-2
Factor -4*f**2 + 7*f**2 + f**2 - 2*f - 2*f**3.
-2*f*(f - 1)**2
Suppose 0 = -f + 4. Factor -2*w**3 + w**4 - f*w**5 - 9*w**4 + 2*w**4.
-2*w**3*(w + 1)*(2*w + 1)
Let c(g) be the first derivative of -g**5/60 - g**4/18 - g**3/18 - 3*g + 2. Let q(p) be the first derivative of c(p). Let q(b) = 0. Calculate b.
-1, 0
Let n be 6/63*-138*3/(-6). Determine r so that 60/7*r - n*r**2 + 8/7*r**3 + 18/7 = 0.
-1/4, 3
Let k(h) be the second derivative of 1/12*h**4 + 0*h**2 + 0 + 3*h + 1/90*h**6 + 1/18*h**3 + 1/20*h**5. Find n such that k(n) = 0.
-1, 0
Let n be (-1)/(-4) - (-11)/4. Factor -155*l**2 + 155*l**2 - n*l**5 + 3*l**3.
-3*l**3*(l - 1)*(l + 1)
Let c(h) = 4*h**4 + h**3 - 5*h**2 - 5. Let b(m) = -m**3 - 3 + 6 + 0 + 4*m**2 - 3*m**4 + 1. Let o(r) = -5*b(r) - 4*c(r). Determine y so that o(y) = 0.
0, 1
Suppose -20 = -5*y + p - 2*p, -5*p = -4*y + 45. Suppose 0 = 6*n - n + y*j - 45, 5*n - 4*j = 0. Factor 2/5*o**5 + 0 - 4/5*o**3 + 0*o**2 + 0*o**n + 2/5*o.
2*o*(o - 1)**2*(o + 1)**2/5
Let x = -7 + 10. Let w = 6 - x. Determine l, given that 2 + 2*l**2 - 4*l**2 - l + 3*l - 2*l**w = 0.
-1, 1
Let y be (0 - -4)/((-4)/(-6)). Suppose 2*m + 20 = y*m. Solve 7 + 31*a + 80*a**2 - 3 + 100*a**3 + 60*a**4 - a + 14*a**m = 0 for a.
-1, -2/7
Let h(y) be the first derivative of y**5/210 + y**4/84 + 3*y**2/2 + 6. Let n(b) be the second derivative of h(b). Factor n(f).
2*f*(f + 1)/7
Determine v so that -4/11*v**4 + 6/11*v**2 + 6/11*v**3 + 0 - 4/11*v = 0.
-1, 0, 1/2, 2
Let p(w) be the second derivative of -w**7/21 - 2*w**6/15 + w**4/3 + w**3/3 - 6*w. Find q, given that p(q) = 0.
-1, 0, 1
Let r(g) be the third derivative of -g**5/15 + g**4/6 - 2*g**2. Solve r(y) = 0.
0, 1
Factor 24/11 + 2/11*d**2 - 14/11*d.
2*(d - 4)*(d - 3)/11
Factor 5*q**5 + 11*q + 4*q**2 - 10*q**4 - 11*q + 4*q**3 - 3*q**4.
q**2*(q - 2)*(q - 1)*(5*q + 2)
Let d(t) be the second derivative of -t**9/5040 + t**7/840 - 5*t**4/12 + t. Let r(s) be the third derivative of d(s). Suppose r(f) = 0. What is f?
-1, 0, 1
Let s(f) be the second derivative of 0*f**2 + 0 - 7*f + 1/48*f**4 + 0*f**3 + 7/160*f**5. Suppose s(n) = 0. Calculate n.
-2/7, 0
Factor -2/5 + 2/5*a**2 - 2/5*a**3 + 2/5*a.
-2*(a - 1)**2*(a + 1)/5
Let g(n) be the first derivative of n**4/12 - n**2/2 - 2*n/3 + 8. Suppose g(x) = 0. What is x?
-1, 2
Let w be (-2 + 4)*6/3. Factor 0*c**2 + 0 + 0*c**3 + 0*c - 1/3*c**w.
-c**4/3
Factor -1/4*a**3 + 0*a + 0 - 1/2*a**2.
-a**2*(a + 2)/4
Let r = 1/17 - -31/51. Suppose -2/3 - 1/3*q + r*q**2 + 1/3*q**3 = 0. Calculate q.
-2, -1, 1
Let n(x) = 4*x**3 + 19*x**2 + 43*x + 32. Let d(r) = 2*r**3 + 9*r**2 + 21*r + 16. Let v(h) = -5*d(h) + 3*n(h). Suppose v(k) = 0. Calculate k.
-2
Let x(i) = -i**2 + 3*i + 1. Let k be 6*(15/6)/5. Let h be x(k). Find u, given that -3 - u**3 + 3*u**3 + 2*u**2 + h - 2*u = 0.
-1, 1
Let y be ((-14)/4)/(6/(-1428)). Let s = 7513/9 - y. Factor -308/9*i**2 + s - 40/9*i + 98*i**3.
2*(7*i - 2)**2*(9*i + 2)/9
Let c(h) be the first derivative of -486*h**3/5 - 108*h**2/5 - 8*h/5 - 27. Let c(s) = 0. Calculate s.
-2/27
Let w(o) be the second derivative of -5*o**4/36 - 5*o**3/6 - 5*o**2/3 + 10*o. Let w(s) = 0. Calculate s.
-2, -1
Let i = 2 + 0. Factor 2*c**3 + c**2 - c**2 - i*c**2.
2*c**2*(c - 1)
Factor -2/3*o**3 - 2/3*o**2 + 0 + 4/3*o.
-2*o*(o - 1)*(o + 2)/3
Let o(s) be the second derivative of -s**4/12 - s**3/6 - s**2/2 + s. Let r(x) = -2*x + 5*x + 0*x**2 + 15 - 10 + x**2. Let p(i) = -3*o(i) - r(i). Factor p(h).
2*(h - 1)*(h + 1)
What is t in -1/5*t**3 - 3/5*t - 1/5 - 3/5*t**2 = 0?
-1
Let d(h) = -51*h**3 - 231*h**2 - 471*h - 249. Let k(f) = -5*f**3 - 23*f**2 - 47*f - 25. Let g(r) = 2*d(r) - 21*k(r). Find p such that g(p) = 0.
-3, -1
Let a(o) = -9*o**4 + 9*o**3 - 12*o**2. Let t(w) = 19*w**4 - 18*w**3 + 25*w**2. Let r(u) = -13*a(u) - 6*t(u). Find p, given that r(p) = 0.
0, 1, 2
Let s(v) be the second derivative of -1/40*v**5 - 1/6*v**3 + 1/8*v**4 + 0*v**2 + 6*v + 0. Factor s(l).
-l*(l - 2)*(l - 1)/2
Let j be 1*(-12)/(-46) - 0. Let d = j + 16/115. Determine q, given that d*q**3 + 4/5*q**2 + 2/5*q + 0 = 0.
-1, 0
Let c(i) be the third derivative of -i**7/420 - i**6/240 + 2*i**2. Solve c(k) = 0 for k.
-1, 0
Let z(o) = 2*o. Let r be z(1). Find u such that 1/5*u**r - 1/5*u + 0 = 0.
0, 1
Let c(y) be the second derivative of 3*y + 0 + 2/9*y**3 + 1/18*y**4 + 0*y**2 - 1/30*y**5. Factor c(n).
-2*n*(n - 2)*(n + 1)/3
Let d(m) = m - 8. Let y(f) = 2*f - 17. Let g(a) = 9*d(a) - 4*y(a). Let o be g(6). Factor 3*t - t**2 + o - 3*t - t**2.
-2*(t - 1)*(t + 1)
Let f(s) be the third derivative of s**5/300 - s**4/12 + 5*s**3/6 - 3*s**2. Let f(b) = 0. Calculate b.
5
Let t(k) be the first derivative of k**4/12 - k**3/9 + 21. Solve t(a) = 0 for a.
0, 1
What is t in 0 - 10/3*t**4 + 4/3*t - 2/3*t**2 - 16/3*t**3 = 0?
-1, 0, 2/5
Let v(t) be the first derivative of -t**4 - 8*t**3/3 + 6*t**2 - 8. Find o such that v(o) = 0.
-3, 0, 1
Solve -5/2*i**2 + 2*i**3 + i + 0 - 1/2*i**4 = 0 for i.
0, 1, 2
Factor -3*h**3 + 4*h**5 + 390*h - 8*h**3 + 3*h**3 - 386*h.
4*h*(h - 1)**2*(h + 1)**2
Let g(i) be the first derivative of -1/16*i**4 + 1/6*i**3 - 1/8*i**2 + 0*i - 3. What is c in g(c) = 0?
0, 1
Let j be (13 - (-21)/(-7))*(-2)/(-6). Suppose 8*s - 8/3 - j*s**2 = 0. Calculate s.
2/5, 2
Let c(s) be the first derivative of -s**4 - 8*s**3/3 - 2*s**2 + 3. Let c(v) = 0. Calculate v.
-1, 0
Solve -20 - 2*c**2 + 5*c - 15 + 33 = 0 for c.
1/2, 2
Suppose -j + 2*v = -3*j + 14, 0 = v + 3. Suppose -j = -3*g - 1. Factor 0*w**3 - 3*w**3 + w - g - 4*w**2 + 5.
-(w + 1)**2*(3*w - 2)
Let s(w) be the second derivative o