 derivative of j**6/40 + 3*j**5/20 - 27*j**2/2 + 29. Let z(s) be the second derivative of h(s). Determine w, given that z(w) = 0.
-3, 0
Determine k, given that -43 - 157*k + 6*k**2 - 3*k**2 - 92*k + 43 = 0.
0, 83
Let x(h) = 3*h**2 - h - 8. Let z(v) = v**3 + 21*v**2 - v + 12. Let k be z(-21). Let l(y) = 16*y**2 - 6*y - 41. Let i(o) = k*x(o) - 6*l(o). Factor i(r).
3*(r - 2)*(r + 3)
Let g(r) be the third derivative of -2*r**7/105 + r**5/5 + r**4/3 + 89*r**2. Solve g(s) = 0.
-1, 0, 2
Suppose -34*v + 77 = -59. What is s in -2/7*s + 0*s**3 + 0 + 2/7*s**5 + 4/7*s**v - 4/7*s**2 = 0?
-1, 0, 1
Let r(s) be the first derivative of -s**3/6 + 7*s**2/4 - 5*s - 272. Factor r(l).
-(l - 5)*(l - 2)/2
Suppose -2*u - u = -3*v + 45, -4*u = -12. Find t, given that -25*t**3 - 12*t**4 + 25*t - 5*t**4 + 5 - 3*t**4 - 3*t**2 + v*t**2 = 0.
-1, -1/4, 1
Let u be 217/77 + (-3)/((-33)/2). Let n(l) be the first derivative of 1/3*l**4 + 0*l**u + 8/3*l - 1 - 2*l**2. Factor n(k).
4*(k - 1)**2*(k + 2)/3
Let r(q) = 15*q**5 - 50*q**4 - 70*q**3 + 315*q**2 + 320*q. Let u(a) = -8*a**5 + 25*a**4 + 36*a**3 - 157*a**2 - 160*a. Let l(w) = 3*r(w) + 5*u(w). Factor l(h).
5*h*(h - 4)**2*(h + 1)*(h + 2)
Suppose 1/5*u**4 + 0 + 0*u - 4/5*u**2 + 3/5*u**3 = 0. What is u?
-4, 0, 1
Let n(u) be the first derivative of -u**8/168 + u**7/35 - u**6/20 + u**5/30 - 5*u**2 + 18. Let w(h) be the second derivative of n(h). Factor w(c).
-2*c**2*(c - 1)**3
Let g(u) = u**3 + u**4 + u**5 + 0*u**3 - 3*u + 2*u. Let i(h) = h**2 + 10*h + 22. Let n be i(-5). Let r(p) = 3*p**5 - p. Let l(f) = n*r(f) + 3*g(f). Factor l(k).
-3*k**3*(k - 1)*(2*k + 1)
Let n(m) be the second derivative of 1/4*m**4 + 14*m + 0 + 1/2*m**2 - 1/2*m**3 - 1/20*m**5. Determine s so that n(s) = 0.
1
Let d(f) be the first derivative of 15 + f**2 + 0*f + 5/3*f**3. Find x, given that d(x) = 0.
-2/5, 0
Let d(a) be the third derivative of -a**5/100 - a**4/40 - a**2 - 27. Factor d(c).
-3*c*(c + 1)/5
Let v(k) be the third derivative of -k**7/14 + 9*k**6/20 - 6*k**5/5 + 7*k**4/4 - 3*k**3/2 - 135*k**2. Factor v(z).
-3*(z - 1)**3*(5*z - 3)
Let z = 237 + -234. Let g(n) be the third derivative of 0*n + 0*n**z + 0 - 5*n**2 + 1/240*n**5 - 1/96*n**4. Suppose g(u) = 0. What is u?
0, 1
Let z(p) = -p**3 - 8*p**2 + 10*p + 3. Let o be z(-9). Let y be ((-3)/o)/(3/2). Suppose 1/3*d + 1/3*d**4 + 0 - 1/3*d**2 - y*d**3 = 0. Calculate d.
-1, 0, 1
Suppose 3*o - 2*o + 9 = 2*p, 21 = 4*p - 3*o. Let b(x) be the first derivative of 0*x - 2/27*x**p - 1/18*x**4 + 0*x**2 - 2. Determine s, given that b(s) = 0.
-1, 0
Let r(a) be the first derivative of 40*a + 50*a**3 - 125/4*a**4 + 90*a**2 + 13. Find c, given that r(c) = 0.
-2/5, 2
Suppose t = 4*o + 19, 0 = -2*t - 0*t - o + 11. Let i be (-9)/t - -1 - (-48)/21. Suppose 0*f**i - 2/3*f + 2/9*f**3 + 4/9 = 0. Calculate f.
-2, 1
Factor 1/4*o**2 - 1/4*o**4 + 5/4*o + 0 - 5/4*o**3.
-o*(o - 1)*(o + 1)*(o + 5)/4
Factor 26/5*k + 4 - 2/5*k**3 + 4/5*k**2.
-2*(k - 5)*(k + 1)*(k + 2)/5
Solve -u - 16/5*u**2 - 8/5*u**4 - 1/5*u**5 + 0 - 18/5*u**3 = 0.
-5, -1, 0
Let j = 1887 + -1885. Factor 1/6*c**j - 1/3 - 1/2*c**3 + 1/2*c + 1/6*c**4.
(c - 2)*(c - 1)**2*(c + 1)/6
Let z(x) = 12*x**2 + 37*x + 5. Let t be z(-3). Let s(q) be the first derivative of -9 - 3/16*q**t + 0*q - 1/8*q**3. Factor s(h).
-3*h*(h + 1)/8
Suppose 55 - 43 = -4*t - 3*z, 0 = -3*t - 3*z - 12. Factor -3/5*w**5 + 3/5*w + t*w**3 - 6/5*w**2 + 0 + 6/5*w**4.
-3*w*(w - 1)**3*(w + 1)/5
Let p be (-21)/(-10 - -3) - (-13 + 1). Suppose p = -3*d + 21. Factor -15/4*c**3 - 27/4*c**d - 3/2 - 3/4*c**4 - 21/4*c.
-3*(c + 1)**3*(c + 2)/4
Let q = -710/7 - -2861/28. Suppose q + 0*o - 3/4*o**2 = 0. What is o?
-1, 1
Let k(u) be the first derivative of 0*u**3 - u**2 + 4 + 3/8*u**4 + 0*u + 1/10*u**5. Solve k(d) = 0.
-2, 0, 1
Suppose -3*v - 39 = -16*v. Let j(z) be the second derivative of -v*z + 5/18*z**4 + 0*z**2 + 1/45*z**6 - 2/9*z**3 - 2/15*z**5 + 0. Solve j(a) = 0 for a.
0, 1, 2
Let j(c) be the first derivative of 0*c + 5 + 0*c**2 - 1/1080*c**6 + 1/360*c**5 - c**3 + 0*c**4. Let s(a) be the third derivative of j(a). Factor s(d).
-d*(d - 1)/3
Let k(n) be the second derivative of n**7/210 - 29*n**6/25 + 7393*n**5/100 + 1276*n**4/5 + 3872*n**3/15 + 20*n - 3. Factor k(i).
i*(i - 88)**2*(i + 1)**2/5
Factor -5*p**3 + 128 + 2*p**4 - 9*p**3 + 12*p**2 - 128.
2*p**2*(p - 6)*(p - 1)
Let o = -38 + 66. Factor -40*t**2 + 2*t**3 + 1 + 7 - 6*t**3 + 4*t**4 + o*t**2 + 4*t.
4*(t - 2)*(t - 1)*(t + 1)**2
Let f = -166 + 247. Find z such that 81*z + f - 4*z**2 - 14*z**3 + 31*z**2 + 17*z**3 = 0.
-3
Let p be (-10)/(-6) - (-3)/9. Let u(h) be the first derivative of -1 + 9*h**p + 4*h + h + h**3 + 22*h. Factor u(k).
3*(k + 3)**2
Suppose -2*p - 5*l = -11, 5*p + 3*l = 14 + 4. Suppose 0 = 4*g + p*m + 3 - 9, -2*g + 4*m + 14 = 0. Factor 6*n**g - 101 - 4*n + 2*n**2 + 101.
2*n*(n + 1)*(3*n - 2)
Determine o so that 2/9*o**3 + 8/9*o**2 - 32/9 - 8/9*o = 0.
-4, -2, 2
Let y(i) = -4*i**5 - 8*i**4 - 5*i**3 + 5*i - 5. Let h(u) = 12*u**5 + 24*u**4 + 16*u**3 - 16*u + 16. Let p(b) = -5*h(b) - 16*y(b). Factor p(c).
4*c**4*(c + 2)
Let g(b) be the second derivative of -b**5/180 + 11*b**4/108 - 31*b**3/54 + 7*b**2/6 - 33*b + 4. Suppose g(r) = 0. What is r?
1, 3, 7
Let x(p) be the third derivative of 0 + 10*p**2 - 7/270*p**6 + 1/45*p**5 + 2/315*p**7 + 0*p + 1/18*p**4 - 4/27*p**3. Factor x(o).
4*(o - 1)**3*(3*o + 2)/9
Factor -4*k**4 + 5*k**5 + 13*k**2 + 7*k**3 - 3*k**2 - 12*k**3 - 6*k**4.
5*k**2*(k - 2)*(k - 1)*(k + 1)
Factor -3/2*k**3 - 9*k**2 + 0*k + 0.
-3*k**2*(k + 6)/2
Let r(b) be the first derivative of 2*b**5/15 - b**4/2 + 2*b**3/9 - 35*b + 28. Let h(s) be the first derivative of r(s). Find c, given that h(c) = 0.
0, 1/4, 2
Let q(a) be the third derivative of -a**6/24 + 7*a**5/12 - 55*a**4/24 + 25*a**3/6 - 7*a**2 - 22*a. Determine g so that q(g) = 0.
1, 5
Let j(q) be the third derivative of 0*q**4 - 1/6*q**3 + 0*q**5 + 0 + 0*q - 9*q**2 + 1/360*q**6. Let g(m) be the first derivative of j(m). Factor g(v).
v**2
Suppose 8/23*v + 10/23*v**3 + 0 + 24/23*v**2 - 12/23*v**4 = 0. What is v?
-2/3, -1/2, 0, 2
Let r(q) = -6*q**3 - 276*q**2 - 552*q - 282. Let i(p) = -3*p**3 - 275*p**2 - 553*p - 281. Let f(j) = 3*i(j) - 2*r(j). Determine z, given that f(z) = 0.
-1, 93
Let w be -2 + 3/(9/(-12)). Let j = w - -16. Let o**2 + j*o + 0 + 0 + 1 - 12*o = 0. Calculate o.
1
Let x be ((-8)/(-22))/((-24)/(-264)). Let w(s) be the third derivative of 0*s**3 + 0 - 1/280*s**7 - 2*s**2 + 0*s**x - 1/80*s**6 - 1/80*s**5 + 0*s. Factor w(z).
-3*z**2*(z + 1)**2/4
Let y = 146 + -137. Suppose 12*x - y = 9*x. What is s in 21/8*s + 15/8*s**2 + 3/8*s**x + 9/8 = 0?
-3, -1
Factor -3*g + 8*g + 51*g**2 - 46*g**2.
5*g*(g + 1)
Factor 8/3*g**2 + 0 - 2/3*g**4 + 16/3*g - 4/3*g**3.
-2*g*(g - 2)*(g + 2)**2/3
Let g = 3 - -1. Suppose -g*u = -9*u + 15. Let i(q) = q**2 - 3*q + 2. Let v(o) = 2*o**2 - 5*o + 3. Let a(f) = u*v(f) - 5*i(f). Factor a(d).
(d - 1)*(d + 1)
Let i(l) be the third derivative of -l**5/150 - l**4/12 + 14*l**3/15 + l**2 + 19*l. Factor i(x).
-2*(x - 2)*(x + 7)/5
Let t be ((-20)/(-30))/((-22)/(-3)). Let d(c) be the second derivative of 4/11*c**4 + 0 + 3*c - 8/55*c**5 - 3/11*c**3 + t*c**2. What is y in d(y) = 0?
1/4, 1
Suppose 4*a = -4, 2*r - 6*r + 12 = -4*a. Let l(u) be the first derivative of -2 + u**r + 1/2*u**3 + 1/2*u. Determine p, given that l(p) = 0.
-1, -1/3
Let c = -68287687/99 - -689781. Let n = c + -5/99. Determine s, given that 8/3*s + 7/3*s**3 + n*s**2 - 4/3 = 0.
-2, -1, 2/7
Let o(a) = -19*a + 41. Let d be o(2). Factor -4/17*l**d + 4/17*l - 2/17*l**4 + 2/17 + 0*l**2.
-2*(l - 1)*(l + 1)**3/17
Let m(n) be the first derivative of n**4/9 - n**3/6 - n**2/6 - 6*n + 11. Let g(z) be the first derivative of m(z). Factor g(k).
(k - 1)*(4*k + 1)/3
Let w(d) = d**2 + 9*d + 4. Let x be w(-2). Let t be (3/(-3))/(8 + x). Suppose 3/4*z - z**3 - 1/2*z**2 + 0*z**4 + 1/4*z**5 + t = 0. What is z?
-1, 1, 2
Let b = 6201/4130 - 3/2065. Solve 0 - 3/2*c**3 + 0*c - 1/2*c**2 + b*c**5 + 1/2*c**4 = 0 for c.
-1, -1/3, 0, 1
Let k(g) = -g**3 + 4*g**2 + 2*g + 9. Let r be k(4). Factor r*n**2 - 10*n**3 - 25*n**3 + 15*n + 25*n**4 - 22*n**2.
5*n*(n - 1)**2*(5*n + 3)
Let w(y) be the third derivative of -4/105*y**5 + 0 + 0*y + 10/147*y**7 + 0*y**3 - 12*y**2 + 2/35*y**6 + 0*y**4 + 3/196*y**8. Let w(x) = 0. What is x?
-2, -1,