+ 15 + 9 + 14*s + m*s**3 - 26*s.
3*(s - 2)**2*(s + 2)
Determine j, given that -2/3*j**4 + 64 + 50/3*j**3 - 40/3*j**2 - 200/3*j = 0.
-2, 1, 2, 24
Let y(v) be the third derivative of -v**10/453600 - v**5/30 + 25*v**3/6 - v**2 - 5. Let j(c) be the third derivative of y(c). Determine w so that j(w) = 0.
0
Let h be 10*((-6)/(-60))/((-2)/(-16)). Find v, given that 894 - 219 - 5*v**2 + 76*v + h*v**2 + 14*v = 0.
-15
Let o(v) be the first derivative of -v**6/720 + v**5/30 - 60*v**3 + 87. Let s(c) be the third derivative of o(c). Suppose s(i) = 0. Calculate i.
0, 8
Let q(d) = -2*d**3 - 50*d**2 - 229*d - 4. Let i be q(-6). Let 0*r + 0 + 8/3*r**4 + 4/3*r**3 - 40/9*r**i + 4/9*r**5 = 0. What is r?
-5, -2, 0, 1
Let v be 25384/1729 + -14 + 231/(-91) + 3. Find y such that -4/7*y**2 - v*y + 12/7 = 0.
-3, 1
Let y be 6/(-21) + 2178/126. Suppose -3*s - 4*o + y = 0, -14*o - 9 = -s - 17*o. Let 297/7*t + 57/7*t**2 + 3/7*t**s + 243/7 = 0. Calculate t.
-9, -1
Let s(j) be the second derivative of j**5/20 + j**4/4 - 3*j**3/2 - 101*j**2/2 - 4*j + 12. Let c(b) be the first derivative of s(b). Factor c(x).
3*(x - 1)*(x + 3)
Let i(c) be the second derivative of 6*c**5/5 + 2*c**4/3 + 11*c**3/3 + 9*c**2 + 17*c. Let u(x) = -x**3 - x**2 - x - 1. Let d(z) = 2*i(z) + 36*u(z). Factor d(h).
4*h*(h - 1)*(3*h - 2)
Suppose -6*n = 3*n - 27. Suppose -5*p**3 + 8*p**3 - 3*p**2 + 6*p + n*p**2 - 9*p**2 = 0. Calculate p.
0, 1, 2
Let 109*l**2 + 113*l**2 - 2*l**3 - 29*l**3 - 5*l**4 + 6*l**4 - 5178 + 320*l + 4666 = 0. Calculate l.
-2, 1, 16
Let o = -21593 - -21596. Factor -152*a**2 - 292/9*a - 36*a**o - 16/9.
-4*(a + 4)*(9*a + 1)**2/9
Let p = 81 - 81. Suppose -5*f - 4*h + 45 = 0, p = 2*f - 5*h + 61 - 46. Solve -4/7 - 4/7*s + f*s**2 = 0.
-2/7, 2/5
Let g(w) be the second derivative of -w**4/15 - 388*w**3/15 - 768*w**2/5 + 1334*w. Find p such that g(p) = 0.
-192, -2
Let q(t) be the first derivative of t**6/16 - 15*t**5/8 + 141*t**4/32 - 23*t**3/8 - 11079. Factor q(n).
3*n**2*(n - 23)*(n - 1)**2/8
Let d(x) = -13*x - 201. Let t be d(-17). Let w be 210/t + -10 + (-14)/44. Find c such that -w - 2/11*c**2 + 4/11*c = 0.
1
Let r(u) be the third derivative of -u**5/240 - 2209*u**4/48 - 4879681*u**3/24 + 138*u**2 - 2*u - 2. Factor r(f).
-(f + 2209)**2/4
Let j(d) be the third derivative of d**5/30 - 227*d**4/6 + 904*d**3/3 - 3*d**2 + 78*d - 2. Suppose j(a) = 0. Calculate a.
2, 452
Let q(h) be the third derivative of 1/60*h**4 + 3 - h**2 - 1/150*h**5 + 0*h + 4/5*h**3. Factor q(c).
-2*(c - 4)*(c + 3)/5
Let l(x) be the first derivative of -123*x**4/20 + 2*x**3/5 + 370. Factor l(g).
-3*g**2*(41*g - 2)/5
Let x(h) = h**4 - h**3 - h**2 + 3. Let d(f) = -12*f**4 + 112*f**3 - 648*f**2 + 1504*f - 1176. Let v(j) = -d(j) - 8*x(j). Factor v(w).
4*(w - 18)*(w - 4)*(w - 2)**2
Let j be (35/30)/(52/312). Let m(c) be the second derivative of 2/105*c**6 + 0*c**3 + 1/147*c**j + 0*c**2 - 16*c + 0*c**4 + 1/70*c**5 + 0. Factor m(o).
2*o**3*(o + 1)**2/7
Factor 6394*u**2 + 775*u + 15*u**3 - 2881*u**2 - 690 - 3133*u**2.
5*(u + 3)*(u + 23)*(3*u - 2)
Let i be ((-19)/(-684))/(12/16). Let d(k) be the first derivative of 0*k**2 - 2/15*k**5 + 0*k - 18 + 8/27*k**3 + 0*k**4 + i*k**6. Factor d(o).
2*o**2*(o - 2)**2*(o + 1)/9
Let m(b) be the first derivative of 16*b - 16 + 4/5*b**2 - 4*b**3 + 7/10*b**4 + 2/25*b**5. Let m(o) = 0. What is o?
-10, -1, 2
Let h(a) be the first derivative of -a**4/26 + 14*a**3/3 + a**2/13 - 14*a + 7718. Factor h(x).
-2*(x - 91)*(x - 1)*(x + 1)/13
Factor -5/2*d**3 - 19*d**2 + 16 - 32*d.
-(d + 4)**2*(5*d - 2)/2
Let j(v) be the third derivative of 2*v**7/105 + 71*v**6/15 + 2208*v**5/5 + 16128*v**4 - 147456*v**3 - 120*v**2 + 4. Factor j(g).
4*(g - 2)*(g + 48)**3
Factor -1/5*l**2 + 6 - 13/5*l.
-(l - 2)*(l + 15)/5
Let p(u) = u - 225. Let d be p(-23). Let k = 997/4 + d. Factor -1 - k*w - 1/4*w**2.
-(w + 1)*(w + 4)/4
Let i(d) be the first derivative of 7/15*d**6 - 120 + 20*d**3 - 48/5*d + 108/25*d**5 + 29/2*d**4 + 28/5*d**2. Determine k so that i(k) = 0.
-3, -2, -1, 2/7
Factor 668168 + 8*p**2 + 1188*p + 5*p**2 - 27*p**2 + 16*p**2 + 1124*p.
2*(p + 578)**2
Let j(f) = -25*f + 123. Let i be j(5). Let w be ((-270)/(-75))/(1 - 1/i). Suppose -w*d - 3/5*d**2 - 12/5 = 0. Calculate d.
-2
Let a be (((-90)/(-28))/(132/154))/((-270)/(-72) + -3). What is s in -1/2*s**3 + 0 - 2*s**4 + 0*s**2 - 3/2*s**a + 0*s = 0?
-1, -1/3, 0
What is z in 2126884/9*z**2 - 3364/9*z**4 + 702220/9*z**3 + 712336/9 + 4/9*z**5 + 2133632/9*z = 0?
-1, 422
Let j(h) be the second derivative of -h**7/105 - h**6/30 + 2*h**5/15 + h**4/6 - h**3 - 70*h**2 + 3*h - 7. Let r(x) be the first derivative of j(x). Factor r(p).
-2*(p - 1)**2*(p + 1)*(p + 3)
Find y such that -7/2*y**3 - 1/4*y**4 - 16 - 26*y - 15*y**2 = 0.
-8, -2
Suppose -5*b - 5*s + 15 = 0, 5*b + 10 = s + 37. Let a(f) be the first derivative of -2/45*f**b - 8/9*f**3 + 10/9*f**2 + 1/3*f**4 - 5 - 2/3*f. Factor a(j).
-2*(j - 3)*(j - 1)**3/9
Let d(s) be the second derivative of -s**6/45 - 22*s**5/15 - 40*s**4/3 + 11200*s**3/9 + 128000*s**2/3 - 14*s + 155. Let d(v) = 0. Calculate v.
-20, 16
Let k = 125473 + -250941/2. Factor -13/8*f**3 + 0 + 0*f - 9/8*f**5 - 1/4*f**2 - k*f**4.
-f**2*(f + 1)**2*(9*f + 2)/8
Find p such that -5/4*p**4 + 25/2*p**2 - 45/4 - 10*p**3 + 10*p = 0.
-9, -1, 1
Let h = 83840 + -83840. Factor h + 0*r - 1/2*r**2 - 1/6*r**3.
-r**2*(r + 3)/6
Suppose 0 = -3*o + 146 - 149. Let h be (-1 - -3) + 1 - o. Factor 16*w**2 + 3*w**3 + 3*w**3 + 13*w**3 + 4*w**h + w**3.
4*w**2*(w + 1)*(w + 4)
Let w(d) = -d - 2. Let t(j) = 1. Let h(l) = 3*t(l) + w(l). Let z(y) = -2*y**3 - 4*y**2 + 8*y - 10. Let u(m) = -10*h(m) - z(m). Factor u(k).
2*k*(k + 1)**2
Let o(r) = -2*r**5 + r**4 - r**2 - 2*r + 1. Let f(j) = 38*j**4 + 108*j**3 + 90*j**2 - 100*j - 142. Let w(z) = -f(z) + 2*o(z). Suppose w(i) = 0. Calculate i.
-3, -2, 1
Suppose 4*x - 165 = -21. Let f = -34 + x. Find k such that -5*k**5 + f*k**5 - 15*k**4 - 2*k**5 - 10*k**3 = 0.
-2, -1, 0
Let f(b) be the first derivative of -b**4/18 + 82*b**3/27 - 62*b**2/3 + 48*b + 3765. Factor f(g).
-2*(g - 36)*(g - 3)*(g - 2)/9
Let z = -2271 - -211205/93. Let d = z + 548/465. Suppose d + 2/15*p**2 + 4/5*p = 0. What is p?
-3
Let m be 2 - -12 - (73 - 6342/84). Factor 3/2*z**2 - m + 15*z.
3*(z - 1)*(z + 11)/2
Let z(o) = -15*o - 25. Let g be z(-2). Let -g*m**2 - 30 - 34*m - 6*m + 4*m + 11*m = 0. What is m?
-3, -2
Let m be (21*(-1)/(-9))/((-2)/(-6)). Let l = 9 - m. Solve 2*n**l - 2*n - n**3 + 0*n**2 + 4 + 3*n**3 - 6 = 0 for n.
-1, 1
Let l(q) be the third derivative of q**5/12 + 135*q**4/4 + 800*q**3/3 - 6841*q**2. Factor l(v).
5*(v + 2)*(v + 160)
Let k(p) = 57*p**2 - 51*p - 200. Let m(z) = -921*z**2 + 816*z + 3201. Let u(d) = -33*k(d) - 2*m(d). Factor u(y).
-3*(y - 3)*(13*y + 22)
Let u(c) = -11*c**4 + 15*c**3 - 13. Let l(k) = -23 + 0*k**4 + 8 - 5*k**4 + 7*k**3 + 9. Let g(z) = 13*l(z) - 6*u(z). Determine o, given that g(o) = 0.
-1, 0
Let g = 1613000/3 + -537652. Let -g - 1/3*s**2 + 8*s = 0. Calculate s.
2, 22
Suppose -10*t - 52 + 122 = 0. Factor 50*r + 28 + 6*r**4 + 22*r**2 - 12 - 14*r - r**4 - t*r**4.
-2*(r - 4)*(r + 1)**2*(r + 2)
Let n(l) = l**3 - 5*l**2 - 352*l - 780. Let t be n(-15). Let 4/3*r**2 - 2/3*r**3 + t + 0*r - 4/3*r**4 + 2/3*r**5 = 0. Calculate r.
-1, 0, 1, 2
Let g(a) be the second derivative of a**6/120 - a**5/12 - 13*a**4/24 - 7*a**3/6 - 41*a**2 + a - 10. Let t(f) be the first derivative of g(f). Factor t(d).
(d - 7)*(d + 1)**2
What is p in 91/3*p - 30 - 1/3*p**2 = 0?
1, 90
Let r(l) be the third derivative of l**6/300 + 7*l**5/75 + 2*l**4/5 + 34*l**2 + 12*l. Solve r(y) = 0 for y.
-12, -2, 0
Let a = 147 + -141. Let d be (54/(-9) + a)*(1 + 0). Factor 0*n - 1/4*n**3 + d*n**2 + 1/4*n**4 + 0.
n**3*(n - 1)/4
Suppose -414*t + 412*t = 3*z + 38, -4*z - 473*t = 10398. Factor -14/15*m - 26/15*m**3 + z*m**2 + 2/15 + 8/15*m**4.
2*(m - 1)**3*(4*m - 1)/15
Let v(b) be the third derivative of -b**5/20 - 495*b**4/4 - 245025*b**3/2 + 2954*b**2. Solve v(h) = 0.
-495
Suppose -3*j + 18 + 174 = 0. Suppose -7*m - 3*l + 3 = -4*m, l + 23 = 5*m. Factor 80*k**2 + 17*k**3 + 14 + k**m + 7 - 21 + j*k.
k*(k + 1)*(k + 8)**2
Let n = -5/649 + 1099/58410. Let s(p) be the third derivative of -n*p**5 + 0*p - 1/18*p**4 + 1/180*p**6 + 0*p**3 + 0 + 12*p**2. What is j in s(j) = 0?
-1, 0, 2
Let d be -4 - 0/(-3 - -2). Le