**3 + 0*x + 0 = 0.
0, 2
Let d(p) be the second derivative of p**5/180 - p**4/108 - p**3/27 + 31*p. Find x such that d(x) = 0.
-1, 0, 2
Determine g, given that 7/5*g**2 - g**3 + 0 - 2/5*g**4 + 0*g = 0.
-7/2, 0, 1
Factor -2*n + 0*n - n**2 + 4*n - n**2.
-2*n*(n - 1)
Let y = -6 - -8. Factor 1 + 4*v**2 - y*v**2 - 3*v**2.
-(v - 1)*(v + 1)
Factor -2*s + 3*s**2 - 3*s**2 - 2*s**3 + 4*s.
-2*s*(s - 1)*(s + 1)
Let n(q) be the third derivative of -q**8/1512 + 2*q**7/945 + q**6/180 + q**2. Factor n(c).
-2*c**3*(c - 3)*(c + 1)/9
Let h(v) be the first derivative of 2*v + 1/12*v**3 + 5/24*v**4 + 3/40*v**5 - 1/4*v**2 + 1. Let k(n) be the first derivative of h(n). Factor k(a).
(a + 1)**2*(3*a - 1)/2
Let s = 5 - 3. Factor 2*d**s + 2*d + 2*d**2 + 2*d**3 - 8*d**2.
2*d*(d - 1)**2
Let v(r) = -2*r**2 + 6*r - 24. Let l(w) = 2*w**2 - 5*w + 25. Suppose 0 = -2*o - 1 - 11. Let s(q) = o*l(q) - 7*v(q). Find b, given that s(b) = 0.
3
Factor -15*k**4 + 0*k**2 - 5*k**2 + 12*k**5 - 17*k**5 - 15*k**3.
-5*k**2*(k + 1)**3
Factor 8*h**4 - 7*h**3 - 11*h**3 + 4*h**5 + 22*h**3.
4*h**3*(h + 1)**2
Let q be 1 + 7 + (13 - 14). Factor -18*k - 6*k**5 - 32*k**2 + q*k**5 - 4 - 28*k**3 - 3*k**5 - 12*k**4.
-2*(k + 1)**4*(k + 2)
Let i(v) be the first derivative of -v**4/18 - 2*v**3/3 - 3*v**2 - 6*v + 10. Factor i(k).
-2*(k + 3)**3/9
Let u be (-4)/(-16)*(0 + 1). Let b = -28 + 33. Factor 0 + 1/4*j**3 - 1/4*j**b + 0*j - 1/4*j**4 + u*j**2.
-j**2*(j - 1)*(j + 1)**2/4
Let c be ((-4)/13)/(18 + -20). Factor 0 + c*w + 2/13*w**2.
2*w*(w + 1)/13
Solve 17*m**4 - 12*m**3 - 39*m**4 + 26*m**4 + 12*m**4 - 4*m**5 = 0.
0, 1, 3
Let x(c) be the first derivative of c**3/4 - 3*c/4 - 7. Solve x(o) = 0 for o.
-1, 1
Let f be (0 + 30/9)*3. Suppose 0*w + 5*w = f. Factor -2 + 4*j**3 - 12*j**2 + 2*j**w + 0*j**3 + 8*j.
2*(j - 1)**2*(2*j - 1)
Suppose -20*b + 0 + 40 = 0. Let w(s) be the first derivative of 10/9*s**3 - 4 - 8/3*s + 8/3*s**b. Find c such that w(c) = 0.
-2, 2/5
Suppose 4*y + 4*k = -4, -4*k = 4*y + k. Let s be 1/(y/(-4) - 1). Suppose -64/3*j**s + 2/3*j - 20/3*j**2 + 64/3*j**3 + 0 = 0. Calculate j.
0, 1/4, 1/2
Let a = 194 - 194. Factor -3/5*r**2 + 0 + a*r.
-3*r**2/5
Let i(r) be the third derivative of r**2 + 0*r**3 + 0 + 0*r**5 + 0*r + 0*r**4 + 1/90*r**6. Factor i(g).
4*g**3/3
Solve 32 + 80*j - 7*j**3 - 29*j**2 + 19*j**3 + 23*j**2 + 62*j**2 = 0.
-2, -2/3
Factor 20*n + 4 + 1 + n**2 + 19 - 5*n**2.
-4*(n - 6)*(n + 1)
Factor -2*l + 17*l**2 - 7*l**2 - 7*l**2.
l*(3*l - 2)
Let n(y) be the third derivative of 3/40*y**5 + 1/16*y**6 - 1/56*y**8 - 1/16*y**4 + 0 - 3/140*y**7 + 0*y + 7*y**2 + 0*y**3. Find a such that n(a) = 0.
-1, 0, 1/4, 1
Let p(x) be the first derivative of -x**3/12 + 5*x**2/8 - 8. Solve p(a) = 0 for a.
0, 5
Let t(m) be the third derivative of 2/3*m**3 + 0*m + 3*m**2 + 1/30*m**5 + 0 + 1/4*m**4. Determine s so that t(s) = 0.
-2, -1
Let o be -5 - (-1)/((-1)/(-7)). Factor 0 - 2/7*j**o + 4/7*j.
-2*j*(j - 2)/7
Let x = 10 - 3. Suppose 1 = -3*s + x. Determine t so that -4*t + t**3 + 2*t**2 + 0*t**s - 2 + 3*t**3 = 0.
-1, -1/2, 1
Let f(y) be the first derivative of 2*y**3/3 + 13. Determine n, given that f(n) = 0.
0
Suppose 29 = -4*q + q + 5*a, -3*a = -3*q - 21. Let m be (q/(-15))/((-12)/(-40)). Determine x so that 2/3*x**3 + 0 - m*x**2 + 0*x = 0.
0, 1
Let i be (0 - 4)/(-8)*1. Let q(f) be the first derivative of 1/4*f**4 - i*f**2 - f - 1 + 1/3*f**3. Suppose q(c) = 0. Calculate c.
-1, 1
Let m = 0 + 2. Factor a**3 - 1 - 2*a**2 + 1 - m*a**3.
-a**2*(a + 2)
Factor -3*b**3 - 9*b + 6 - 3*b**4 + 27*b**2 - 12*b**3 - 12*b + 6*b**4.
3*(b - 2)*(b - 1)**3
Let v(t) be the third derivative of t**6/40 + 3*t**5/20 + t**4/4 - 2*t**2. Factor v(h).
3*h*(h + 1)*(h + 2)
Let z = 7 - 7. Suppose 6*j - j - 25 = z. Factor 6*k**3 - 3*k**4 - 5*k + j*k - 3*k**2.
-3*k**2*(k - 1)**2
Let w = -787/4 - -197. Let 0 + w*r**2 + 1/2*r = 0. What is r?
-2, 0
Let a = 5/34 - -6/17. Let d(g) be the second derivative of -1/10*g**5 + 1/15*g**6 - a*g**4 + 0 + 5/3*g**3 - 2*g**2 + 2*g. Factor d(t).
2*(t - 1)**3*(t + 2)
Let m(o) be the third derivative of 3*o**6/280 + o**5/10 + 17*o**4/56 + 3*o**3/7 - 4*o**2. Solve m(r) = 0.
-3, -1, -2/3
Let i(m) = -38*m**2 + 4*m. Let n(a) = -25*a**2 + 3*a. Let u(f) = 5*i(f) - 8*n(f). Factor u(k).
2*k*(5*k - 2)
Factor 2/15*l**3 + 0 + 0*l**2 + 0*l.
2*l**3/15
Let x = 359/28 - 88/7. Let d(s) be the second derivative of 2*s - 3/20*s**5 + 0*s**2 + 0*s**3 + 0 - x*s**4. Let d(j) = 0. Calculate j.
-1, 0
Suppose 4*q - 80 = -q. Suppose 0 = 2*u + 2*b + 2*b - q, 4*u = 3*b + 10. Find x, given that -2*x - 4*x**2 + 3*x**4 + x**u + 2*x**5 + 0*x = 0.
-1, 0, 1
Let w(l) be the first derivative of -l**4/12 + l**3/2 - l**2 - 4*l + 3. Let q(d) be the first derivative of w(d). Let q(r) = 0. Calculate r.
1, 2
Let s be (27/(-18))/((-2)/8). Suppose 5*h + s - 16 = 0. Factor 0*k - 32/7*k**3 - h*k**4 + 0 - 8/7*k**2.
-2*k**2*(k + 2)*(7*k + 2)/7
Let d(c) = -2*c + 636 - 645 + 3*c. Let h be d(12). Factor -8/7*n**2 - 8/7*n**4 + 2/7*n**5 + 2/7*n + 12/7*n**h + 0.
2*n*(n - 1)**4/7
Let w(s) = -2*s**4 + 8*s**3 - 6*s + 4. Let u(b) = 3*b**4 - 16*b**3 + 11*b - 8. Let m(j) = 2*u(j) + 5*w(j). Factor m(h).
-4*(h - 1)**3*(h + 1)
Let s(a) be the second derivative of -a**5/180 - a**4/24 - a**3/9 - 2*a**2 + 2*a. Let j(v) be the first derivative of s(v). Suppose j(h) = 0. What is h?
-2, -1
Suppose 0 = 3*v - 12. Factor 49/3*i**v + 0 + 20*i**2 + 8/3*i + 42*i**3.
i*(i + 2)*(7*i + 2)**2/3
Factor -14/9*w**3 + 0 + 4/9*w - 10/9*w**2.
-2*w*(w + 1)*(7*w - 2)/9
Let y(d) be the first derivative of -d**4 + 28*d**3/3 - 25*d**2/2 + 6*d + 25. Factor y(q).
-(q - 6)*(2*q - 1)**2
Let p(z) be the third derivative of -z**8/84 + z**7/105 + z**6/60 + 21*z**2. Let p(g) = 0. Calculate g.
-1/2, 0, 1
Suppose 26 = 7*b - 2. Factor -b - c**2 + 10*c + 4 - 9*c.
-c*(c - 1)
Suppose 6*f - 4*f = 4. Let v(y) = -10*y**2 - 11*y - 10. Let u(w) = -3*w + 4*w - w**2 - 2*w - 1. Let m(d) = f*v(d) - 18*u(d). What is n in m(n) = 0?
-1
Factor -4*z**2 + 0*z + 8*z + 2 - 2 - 4.
-4*(z - 1)**2
Suppose 3*b - 10 = 11. Let s(r) = r**3 - 17*r**2 - 37*r - 5. Let q(o) = -o**3 + 8*o**2 + 19*o + 2. Let i(w) = b*q(w) + 4*s(w). Factor i(c).
-3*(c + 1)**2*(c + 2)
Let v(b) be the first derivative of -2*b**3/21 - 8*b**2/7 - 2*b - 24. Solve v(g) = 0 for g.
-7, -1
Let n(w) = 7*w. Let a be n(5). Suppose -2*p + 3*g = -19, -5*p + a = g - 6*g. Suppose 2*q**p + 2/3 - 2*q - 2/3*q**3 = 0. Calculate q.
1
Factor 1/5*k + 0 + 6/5*k**3 + 4/5*k**2 + 1/5*k**5 + 4/5*k**4.
k*(k + 1)**4/5
Factor -4 + 12*g - 63*g**2 - 45*g**4 - 8*g**3 + 20*g + 61*g**4.
(g - 2)*(g + 2)*(4*g - 1)**2
Let d = 1 + -3. Let r(c) = -c**3 - c**2 + c + 1. Let y(l) = -l**3 - l**2 + l + 1. Let g(b) = d*r(b) + y(b). Factor g(f).
(f - 1)*(f + 1)**2
Let h(w) be the third derivative of -w**6/1020 + w**5/255 + 9*w**2. Factor h(v).
-2*v**2*(v - 2)/17
Let x = 204 - 200. Determine k so that 0*k + 2/5*k**x - 2/5*k**2 + 2/5*k**5 + 0 - 2/5*k**3 = 0.
-1, 0, 1
Let s(t) be the second derivative of -1/48*t**4 + 0*t**3 + 3*t + 0 + 0*t**2. Factor s(c).
-c**2/4
Let b = 24 + -18. Let z(q) be the first derivative of -2/25*q**5 - 1 + 1/5*q**4 - 2/5*q + 4/15*q**3 - 1/5*q**2 - 1/15*q**b. Solve z(c) = 0.
-1, 1
Let n(w) be the first derivative of w**9/1008 + w**8/140 + 3*w**7/140 + w**6/30 + w**5/40 + w**3 + 2. Let z(u) be the third derivative of n(u). Factor z(k).
3*k*(k + 1)**4
Let u = -6 + 10. Factor -y**5 + 0*y**3 + 0*y**3 - 2*y**u - 2*y**3 + y**3.
-y**3*(y + 1)**2
Let v(g) be the third derivative of 3*g**8/112 - 2*g**7/35 - g**6/20 + g**5/5 - g**4/8 + 7*g**2. Solve v(s) = 0.
-1, 0, 1/3, 1
Let t be (2/3 - 0) + (-16)/(-24). Factor 4/3 - t*q + 1/3*q**2.
(q - 2)**2/3
Suppose -5*i + 25 = 2*r, -3*r - 2*r + i - 5 = 0. Let z be (-8)/(-20)*(-5)/(-6). Factor r - z*k - 1/3*k**2.
-k*(k + 1)/3
Let o(u) be the third derivative of u**11/388080 + u**10/264600 - u**9/211680 + u**5/15 + 5*u**2. Let b(a) be the third derivative of o(a). Factor b(v).
2*v**3*(v + 1)*(3*v - 1)/7
Let m(y) be the third derivative of -3*y**2 - 4/105*y**5 + 1/21*y**4 + 0*y + 1/84*y**6 - 1/735*y**7 + 0*y**3 + 0. Suppose m(z) = 0. Calculate z.
0, 1, 2
Let u be ((-186)/63 - -3)*6. Find j such that 6/7*j - 4/7 - u*j**2 = 0.
1, 2
Let g(d) be the second derivative of -d**6/120 + d**5/40 + d**4/16 - d**3/6 - d**2/2 - 22*d. Factor g(j).
-(j - 2)**2*(j + 1)**2/4
