he first derivative of -9*z - 1/3*z**3 - 3*z**y - 5. Factor d(x).
-(x + 3)**2
Let d(z) be the third derivative of z**6/510 - z**5/510 - z**4/102 + z**3/51 + 187*z**2. Factor d(k).
2*(k - 1)*(k + 1)*(2*k - 1)/17
Let m = 18 - 12. Suppose 3*g + r = g + 12, -2*g - 4*r = -m. Factor -3*f**2 - g*f**4 - 9*f**4 + 15*f**4 - 3*f**3 - f.
-f*(f + 1)**3
Let c be (-12)/(-27) + 4/(-18). Let k(s) be the first derivative of 0*s + c*s**2 - 1/18*s**4 + 2/27*s**3 - 3. Determine x, given that k(x) = 0.
-1, 0, 2
Suppose -2*z - 5*z = -28. Let d be (1 - (3 + -3))/z. Let -d*x**4 + 1/2*x**3 + 3/4*x**2 - x - 1 = 0. What is x?
-1, 2
Let x(c) be the second derivative of c**6/10 - 4*c**5/15 - 2*c**4/3 + 14*c**2 + 16*c. Let d(p) be the first derivative of x(p). Solve d(f) = 0.
-2/3, 0, 2
Factor 0 + 22/9*c**2 + 4/3*c + 4/3*c**3 + 2/9*c**4.
2*c*(c + 1)*(c + 2)*(c + 3)/9
Let a(j) be the third derivative of 7/64*j**6 + 0*j + 0*j**3 + 7/80*j**7 + 0 - 13/160*j**5 + 25*j**2 + 1/64*j**4. Determine w, given that a(w) = 0.
-1, 0, 1/7
Let d(t) be the first derivative of -1/270*t**5 + 0*t + 0*t**4 + 0*t**3 - 1/2*t**2 + 7 - 1/270*t**6. Let l(w) be the second derivative of d(w). Factor l(v).
-2*v**2*(2*v + 1)/9
Let m = 12546/7 - 1792. Factor -3/7*h**4 + 1/7*h**5 + 1/7*h**3 - m*h + 0 + 3/7*h**2.
h*(h - 2)*(h - 1)**2*(h + 1)/7
Let s(z) be the second derivative of -z**6/135 - 2*z**5/45 + z**4/54 + 16*z**3/27 + 4*z**2/3 - 7*z - 5. Find l such that s(l) = 0.
-3, -2, -1, 2
Let j = 115 + -121. Let x(a) = -4*a**4 - 24*a**3 + 10*a**2 + 24*a. Let p(k) = 4*k**4 + 24*k**3 - 11*k**2 - 24*k. Let r(s) = j*p(s) - 7*x(s). Factor r(n).
4*n*(n - 1)*(n + 1)*(n + 6)
Factor 24*s**2 - 11*s + s - 12*s**2 + 15*s**4 + 39*s**3 - 2*s.
3*s*(s + 1)*(s + 2)*(5*s - 2)
Suppose -14*d + 46 = -24. Let h(v) be the second derivative of 0 + 0*v**3 - 1/105*v**6 + 1/70*v**5 - d*v + 1/42*v**4 + 0*v**2 - 1/147*v**7. Factor h(p).
-2*p**2*(p - 1)*(p + 1)**2/7
Let v(o) be the third derivative of 0*o + 1/42*o**4 - 2*o**2 + 0 + 0*o**3 + 1/210*o**5. Factor v(m).
2*m*(m + 2)/7
Suppose 3*u - 18 = -0*u. Suppose 2*f = -3*f - u*f. Solve f*q**2 - 1/6*q**3 + 1/6*q + 0 = 0.
-1, 0, 1
Let d(x) be the third derivative of x**6/90 - x**5/30 + x**4/24 + 8*x**3 - 45*x**2. Let u(o) be the first derivative of d(o). Factor u(f).
(2*f - 1)**2
Let s(d) be the first derivative of 2*d**6/15 + d**5/5 - 2*d**4 - 8*d**3/3 + 16*d**2 - 6*d + 16. Let w(i) be the first derivative of s(i). Factor w(n).
4*(n - 2)*(n - 1)*(n + 2)**2
Let m(p) be the third derivative of p**6/120 - 3*p**5/20 - 5*p**4/12 + p**3/3 + p**2. Let q be m(10). Factor -2*u + 4*u + 6*u**q - 21*u**3 - 2*u.
-3*u**2*(7*u - 2)
Let g = -4859/2 - -2430. Find u, given that 3/8*u**3 + 0 + 1/8*u**5 - g*u + 1/2*u**2 - 1/2*u**4 = 0.
-1, 0, 1, 2
Let l(j) be the first derivative of -j**6/48 + j**5/10 - 5*j**4/32 + j**3/12 - 100. Factor l(i).
-i**2*(i - 2)*(i - 1)**2/8
Let u(r) be the first derivative of 3*r**5/10 - 93*r**4/4 + 61*r**3/2 - 152. Factor u(s).
3*s**2*(s - 61)*(s - 1)/2
Let q be 48/64*8/36. Let o(a) be the first derivative of 0*a**2 + 0*a**3 + 0*a - 2/5*a**5 + 1/4*a**4 + 4 + q*a**6. Suppose o(r) = 0. What is r?
0, 1
Suppose -6 = p - 11. Let y be p/((-70)/16)*7/(-28). Factor 0*c - y*c**2 + 0.
-2*c**2/7
Let k(d) be the second derivative of d**4/4 + 13*d**3/6 - 5*d**2 + 51*d + 2. Solve k(n) = 0 for n.
-5, 2/3
Let c(a) be the second derivative of -a**7/15120 - a**6/1080 - a**5/240 - a**4/2 + 10*a. Let r(j) be the third derivative of c(j). Factor r(z).
-(z + 1)*(z + 3)/6
Suppose -342 = 3*d - 327, 0 = -3*r - 3*d - 9. Factor 2/13*g**3 - 2*g + 0*g**r + 24/13.
2*(g - 3)*(g - 1)*(g + 4)/13
Let k = 4162 - 1173685/282. Let j = k - -5081/1410. Determine m, given that -12/5*m**4 - 32/5*m**2 + 2/5*m**5 + j*m + 28/5*m**3 - 4/5 = 0.
1, 2
Let f(d) = -d**2 + 151*d + 2741. Let k(a) = -5*a**2 + 905*a + 16445. Let z(h) = -34*f(h) + 6*k(h). Factor z(p).
4*(p + 37)**2
Let n = 220 + -200. Let d be (-8)/n - (-2)/1. Factor d - 2/5*t**2 - 4/5*t**3 + 16/5*t.
-2*(t - 2)*(t + 2)*(2*t + 1)/5
Let b(r) be the first derivative of -r**5/5 - 11*r**4/12 - 4*r**3/3 - 2*r**2/3 + 61. Factor b(d).
-d*(d + 1)*(d + 2)*(3*d + 2)/3
Factor 250*c - 531*c + 70 + 5*c**2 + 206*c.
5*(c - 14)*(c - 1)
Suppose 8*t + t - 8*t**3 + 47 - 44 - 4*t**3 = 0. Calculate t.
-1/2, 1
Let l(m) = 4*m**2 - 52*m + 139. Let d(h) = -4*h**2 + 52*h - 142. Let t(o) = 7*d(o) + 6*l(o). Factor t(n).
-4*(n - 8)*(n - 5)
Let y be (-3)/(-4) + -1 + (-2)/((-16)/18). Factor 4/9*n + 0*n**y - 2/9*n**4 + 2/9 - 4/9*n**3.
-2*(n - 1)*(n + 1)**3/9
Let n(t) = 9*t**2 + 94*t. Let a(w) = -55*w**2 - 565*w. Let v(o) = -4*a(o) - 25*n(o). Factor v(p).
-5*p*(p + 18)
Let s(z) = -z**2 - z. Let a be 4 - 6/((-9)/(-3)). Let x(c) = -2*c - a*c**2 + 5*c - 4*c. Let o(v) = 3*s(v) - 2*x(v). Factor o(n).
n*(n - 1)
Let j(u) be the third derivative of -7*u**5/90 - 2*u**4/3 - u**3 + 256*u**2. Find p, given that j(p) = 0.
-3, -3/7
Factor -2/9*r**5 + 16/9*r**2 + 0 + 10/3*r**3 + 0*r + 4/3*r**4.
-2*r**2*(r - 8)*(r + 1)**2/9
Let i be 94/6 + 16/48. Let s(f) = 2*f**2 + 9*f + 2. Let q be 7/(14/8) - -1. Let l(b) = -6*b**2 - 28*b - 6. Let t(d) = i*s(d) + q*l(d). What is z in t(z) = 0?
-1
Suppose 3*c + 15 = 3*d, 3*c - 3 = -5*d - 2. Factor -b**2 + 8 + d + 0*b + 3*b.
-(b - 5)*(b + 2)
Suppose 8 = 4*f + 4. Suppose 29*r - f + r**2 + 5 - 33*r = 0. What is r?
2
Let h = 66 - 40. Suppose 28*u = h*u + 4. Suppose 1/3*n**3 - 1/3*n + 1/3*n**4 + 0 - 1/3*n**u = 0. Calculate n.
-1, 0, 1
Let w(f) be the second derivative of -2*f**7/21 - 4*f**6/15 + 6*f**5/5 + 20*f**4/3 + 38*f**3/3 + 12*f**2 + 189*f. Suppose w(h) = 0. What is h?
-2, -1, 3
Let x(l) be the third derivative of -l**7/420 + 37*l**6/60 - 1369*l**5/20 + 50653*l**4/12 - 1874161*l**3/12 + 205*l**2. Determine f so that x(f) = 0.
37
Let f = -20 + 24. Let v be -1*(8/2 - f). Factor 10*n**3 - 3*n**4 - 3*n**4 + v*n**3 - 4*n**2.
-2*n**2*(n - 1)*(3*n - 2)
Let k(m) = -m**5 + m**2 + m. Let c(g) = 8*g**4 - 8*g**3 - 6*g**2 + 8*g - 4. Let j(u) = -c(u) - 2*k(u). Solve j(r) = 0 for r.
-1, 1, 2
Let r be 1/(-14)*4 + (-62)/(-168). Let j(o) be the second derivative of 1/84*o**7 - 1/6*o**4 - r*o**6 + 1/5*o**5 + 0*o**3 + 0*o**2 + 0 + 4*o. Factor j(z).
z**2*(z - 2)**2*(z - 1)/2
Let a(i) be the second derivative of i**5/4 + 5*i**4/2 + 10*i**3 + 20*i**2 + 539*i. Solve a(f) = 0.
-2
Let o = -3983/99 - -367/9. Factor -12/11*r**3 + 2/11*r - o*r**5 + 0*r**2 + 0 + 16/11*r**4.
-2*r*(r - 1)**3*(3*r + 1)/11
Let o(i) be the third derivative of i**5/90 + i**4/3 + 3*i**3 - 7*i**2 + 21. Let o(g) = 0. What is g?
-9, -3
Let c(n) be the first derivative of 2/3*n**6 + 0*n**2 - 4/3*n**3 + 4/5*n**5 - 7 + 0*n - n**4. Factor c(q).
4*q**2*(q - 1)*(q + 1)**2
Let b be (-13)/(-65) - (-388)/60. Suppose b*a + 40/3*a**3 - 4/3 - 40/3*a**2 - 20/3*a**4 + 4/3*a**5 = 0. Calculate a.
1
Let w(d) be the first derivative of -10/3*d**3 + 10*d**2 - 5/4*d**4 + 40*d - 15. Suppose w(k) = 0. Calculate k.
-2, 2
Suppose 1 = r - 1. Find c, given that -1 - 12*c**r - 2 + 6*c + 9*c = 0.
1/4, 1
Let f(p) be the second derivative of p**7/231 + p**6/15 + 27*p**5/110 + 25*p**4/66 + 8*p**3/33 + p + 39. Suppose f(r) = 0. Calculate r.
-8, -1, 0
Let y(o) be the first derivative of -o**7/3780 + o**6/1620 + o**5/540 - o**4/108 + 11*o**3/3 - 12. Let h(q) be the third derivative of y(q). Factor h(g).
-2*(g - 1)**2*(g + 1)/9
Let b(h) be the third derivative of -5*h**8/112 - h**7/3 + 13*h**6/12 + 2*h**5/3 - 115*h**4/24 + 5*h**3 + 2*h**2 + 29*h. Let b(n) = 0. What is n?
-6, -1, 1/3, 1
Find s such that -3 - 27 - 23*s + 6*s + 2*s**3 + 6*s**2 + s - 10*s = 0.
-5, -1, 3
Suppose 0 = 2*u + 2*o - 30, 81 = 4*u - 2*o - 3. Suppose -17*w = -u*w. Let w*a**2 + 0 + 0*a - 2/11*a**3 = 0. Calculate a.
0
Let r(k) be the first derivative of k**3/3 - 12*k**2 + 23*k - 28. Factor r(d).
(d - 23)*(d - 1)
Factor 1/8*y**2 + 225/2 + 15/2*y.
(y + 30)**2/8
Suppose -12 = -3*z + 3*n, 0 = -z + 4*n - 28 + 38. Let p(s) be the second derivative of 0*s**z + 1/42*s**4 - 3*s + 0 - 1/21*s**3. Factor p(u).
2*u*(u - 1)/7
Let j(c) = -c**2 - 1. Let l(p) be the third derivative of 6*p**2 + 0*p**4 + 0 - 1/10*p**5 - 7/6*p**3 + 0*p. Let g(z) = -14*j(z) + 2*l(z). Factor g(t).
2*t**2
Let c(k) be the first derivative of 3/2*k**4 + 2*k**2 + 0*k - 1/3*k**6 - 7 - 10/3*k**3 + 2/5*k**5. Factor c(m).
-2*m*(m - 1)**3*(m + 2