r**8/392 + 107*r**7/245 + 211*r**6/140 + 3*r**5/2 - 16023*r**2. Determine o, given that l(o) = 0.
-105, -1, 0
Let m(i) be the third derivative of -i**9/1008 + i**7/280 - i**3/6 - 45*i**2. Let d(g) be the first derivative of m(g). Factor d(k).
-3*k**3*(k - 1)*(k + 1)
Let i(s) be the first derivative of s**7/3780 + s**6/270 + s**5/108 - 79*s**3/3 - 70. Let v(d) be the third derivative of i(d). What is r in v(r) = 0?
-5, -1, 0
Let m be 5 + -1 - (-36)/(9 + -21). Suppose 52*x - 1 + m + 303*x**2 - 307*x**2 = 0. What is x?
0, 13
Let p = -4582 - -54985/12. Let j(h) be the third derivative of -1/32*h**4 + 0*h + 0*h**5 + 1/480*h**6 + p*h**3 + 0 - 9*h**2. Factor j(o).
(o - 1)**2*(o + 2)/4
Factor -10702*d**2 + 5*d**3 + 391 - 10629*d**2 - d - 4*d**3 + 20940*d**2.
(d - 391)*(d - 1)*(d + 1)
Let g(n) be the first derivative of 25*n**6/27 - 22*n**5/3 + 17*n**4 - 164*n**3/27 - 25*n**2/3 - 2*n - 952. What is v in g(v) = 0?
-1/5, 1, 3
Let f(y) = 161*y + 647. Let a be f(-4). Let i(n) be the first derivative of -15/2*n**a - 3/2*n - 6/5*n**5 - 21/4*n**2 - 3 - 39/8*n**4. What is z in i(z) = 0?
-1, -1/4
Suppose 0 = 4*j - 4*k - 28, -2*j = 5*k - 4*k - 2. Factor -30*v**2 - 7*v**3 + 3 - 10*v**3 - 3*v + 7*v**j - 14*v**3.
-3*(v + 1)*(2*v + 1)*(4*v - 1)
Suppose -o = 50*t - 47*t - 34551, 0 = -o - t + 34557. Factor -1415*u**2 + 4*u**4 + 2157*u**2 + 1706*u**2 + o - 164*u**3 - 15552*u + 0*u**4.
4*(u - 12)**3*(u - 5)
Let l(g) be the third derivative of 9*g**6/80 - 75*g**5/8 + 247*g**4/16 - 41*g**3/4 - 448*g**2 - g. Find v, given that l(v) = 0.
1/3, 41
Let d(k) = -29*k - 281. Let r be d(-10). Suppose 3*s + w - r = 0, -19 = -3*s + 5*w - 10. Factor 0 + 1/2*f**4 + 0*f**s + 0*f**2 + 0*f.
f**4/2
Suppose -v = 5*l + 58, -210 = 5*v + 4*l + l. Let n = v - -45. Factor -n + 12*x**4 + 4*x**5 - 3*x - 14*x**2 + 9 + 3*x**5 - 4*x**3.
(x - 1)*(x + 1)**3*(7*x - 2)
Suppose 106 = 16*j + 26. Determine y, given that 70*y**2 + 10*y**4 - 60*y**3 + 11*y**5 + 6*y**j - 25*y - 12*y**5 = 0.
-5, 0, 1
Let p(b) be the second derivative of -81*b**2 - 1/4*b**4 - 76*b + 29/2*b**3 + 0. Factor p(j).
-3*(j - 27)*(j - 2)
Let f be ((-61)/(-429))/1 + (-83)/913. Let q(p) be the second derivative of f*p**3 + 3/26*p**4 + 0*p**2 + 0 - 10*p. Factor q(g).
2*g*(9*g + 2)/13
Let t(n) be the first derivative of 1/2*n**6 - 12/5*n**5 + 0*n**2 + 145 + 0*n + 15/4*n**4 - 2*n**3. Find l, given that t(l) = 0.
0, 1, 2
Let i be 2/7 - 705/(-105) - 2. Determine l, given that 76/3*l**3 + 0 - 26/3*l**2 - 46/3*l**4 + 8/3*l**i - 4*l = 0.
-1/4, 0, 1, 2, 3
Let f(u) be the second derivative of -u**7/630 + u**6/60 + u**5/3 + u**4/2 - u**3/6 - 177*u. Let k(j) be the third derivative of f(j). Solve k(r) = 0 for r.
-2, 5
Let m(a) be the first derivative of 0*a - 39/4*a**4 - 9/2*a**6 + 12*a**5 + 60 + 2*a**3 + 0*a**2. Suppose m(q) = 0. Calculate q.
0, 2/9, 1
Factor 1/8*d**3 - 9/8*d - 1/8*d**4 + 21/8*d**2 - 27/2.
-(d - 4)*(d - 3)*(d + 3)**2/8
Let i(a) = -3*a**2 - 8*a + 7. Let b be i(-3). Let p be (-55)/(-11) - -6*(-2)/b. Find q, given that -27/4*q**p - 9*q - 3 = 0.
-2/3
Suppose -2265*y = -2252*y - 65. Let z(d) be the first derivative of -30 + 0*d**3 - 3*d**4 + 4/5*d**y + 8*d**2 + 0*d. Determine k, given that z(k) = 0.
-1, 0, 2
Let y(s) be the second derivative of -s**4/13 + 29*s**3/39 + 82*s**2/13 - 327*s + 2. Factor y(r).
-2*(r + 2)*(6*r - 41)/13
Find i such that 40/17*i**2 - 70/17*i**4 + 0*i + 0 - 208/17*i**3 + 22/17*i**5 = 0.
-2, 0, 2/11, 5
Let x(n) = -12*n**2 + 82*n + 34. Suppose -11*b + 8*b + 18 = 0. Let s(h) = h**2 + 3*h. Let k(d) = b*s(d) + x(d). Factor k(f).
-2*(f - 17)*(3*f + 1)
Let x(f) be the third derivative of f**5/45 + 5*f**4/18 - 28*f**3 + f**2 - 575*f. Factor x(d).
4*(d - 9)*(d + 14)/3
Factor 0 + 148/13*b**3 - 2/13*b**4 + 0*b - 2738/13*b**2.
-2*b**2*(b - 37)**2/13
Determine g, given that -1/4*g**2 + 4*g + 84 = 0.
-12, 28
Let t(h) = -8*h**3 + 156*h**2 + 12*h + 1924. Let d(x) = -23*x**3 + 414*x**2 + 37*x + 5771. Let f(u) = 4*d(u) - 11*t(u). Factor f(k).
-4*(k - 5)*(k + 8)*(k + 12)
Let o(u) = -2*u**3 - 44*u**2 - 118*u - 73. Let d(p) = 7*p**3 + 174*p**2 + 473*p + 293. Let x(b) = 3*d(b) + 13*o(b). Factor x(z).
-5*(z + 1)*(z + 2)*(z + 7)
Factor 87*a**4 - 236 - 10*a**2 - 82*a**4 + 236 + 5*a**3.
5*a**2*(a - 1)*(a + 2)
Let f(b) be the first derivative of -4*b - 1/3*b**3 + 0*b**2 + 37 - 1/12*b**4. Let k(x) be the first derivative of f(x). Suppose k(j) = 0. What is j?
-2, 0
Let g(t) = -t**2 - 2. Suppose -3*x = l + 42, 2*x + l = -4*l - 15. Let m(r) = -2*r**2 - 13*r + 16. Let h(s) = x*g(s) + 5*m(s). Factor h(n).
5*(n - 11)*(n - 2)
Let z(i) be the third derivative of 25*i**2 + 127/12*i**4 + 0 + 86/3*i**3 - 1/10*i**5 + 0*i. Factor z(g).
-2*(g - 43)*(3*g + 2)
Suppose 0 - 73/3*u**3 + u**4 - 44*u**2 + 52/3*u = 0. Calculate u.
-2, 0, 1/3, 26
Let z = 4429 + -4427. Let m(u) be the first derivative of -5/4*u**4 + z*u**5 - 5/6*u**6 - 10 + 0*u + 0*u**3 + 0*u**2. Suppose m(c) = 0. What is c?
0, 1
Let s(k) = 6*k**2 + 22*k + 96. Let x(r) = -8*r**2 - 21*r - 117. Let g(w) = 6*s(w) + 4*x(w). Let g(i) = 0. What is i?
-9, -3
Let w = 160263 - 480769/3. Find l such that 18*l**2 + w*l**4 + 29/3*l + l**5 + 16*l**3 + 2 = 0.
-3, -1, -2/3
Let h(q) be the first derivative of -q**4/14 - 22*q**3/21 - 36*q**2/7 - 72*q/7 + 399. Let h(t) = 0. Calculate t.
-6, -3, -2
Let n(x) be the first derivative of x**6/8 - 27*x**5/20 + 15*x**4/16 + 129*x**3/4 - 513*x**2/4 + 162*x + 662. Determine a, given that n(a) = 0.
-4, 1, 3, 6
Let y(p) = -397 - 130*p - 197 - 418 + 195 + 170. Let x be y(-5). Solve -27/8*b**2 - 3/8*b**x + 0 + 15/4*b = 0 for b.
-10, 0, 1
Let q = 38429 + -38423. Let x(y) be the first derivative of y - 7/8*y**4 + 5/4*y**2 - 1/10*y**5 - 1 - 1/6*y**3 + 1/6*y**q. Suppose x(b) = 0. What is b?
-1, -1/2, 1, 2
Let s(m) be the third derivative of -m**7/378 - 7*m**6/540 + 23*m**5/540 - m**4/54 + 1699*m**2. Let s(t) = 0. Calculate t.
-4, 0, 1/5, 1
Let x = 1226 + -1222. Suppose x*q = -3*q + 5*q. Factor 4/5*p**2 + 0 - 6/5*p**3 + 2/5*p**4 + q*p.
2*p**2*(p - 2)*(p - 1)/5
Suppose 2*i - 56 = -12*i. Factor -52*s**4 + s**2 + 113*s**i - 62*s**4.
-s**2*(s - 1)*(s + 1)
Let s(h) be the third derivative of 2607/20*h**5 + 1331*h**3 + 1 + 1/10*h**7 + 10043/8*h**4 + 0*h + 98*h**2 + 233/40*h**6. What is j in s(j) = 0?
-11, -2/7
Let x(z) be the second derivative of z**5/50 + 19*z**4/15 - 91*z**3/3 + 240*z**2 + z + 365. Find u such that x(u) = 0.
-48, 5
Let n(l) = -3*l**3 - 516*l**2 + 510*l - 1554. Let g be n(-173). Let r(h) = 2*h**2. Let t be r(1). Factor -46*i**g - 9/4*i**5 + 96*i**t + 0 - 36*i - 24*i**4.
-i*(i + 6)**2*(3*i - 2)**2/4
Let o(b) be the first derivative of 2/7*b**3 - 3/7*b**4 - 101 - 3/35*b**5 + 18/7*b**2 - 27/7*b. Find f such that o(f) = 0.
-3, 1
Let t(n) be the first derivative of n**5/25 + 39*n**4/10 - 28*n**3/5 - 199*n**2/5 - 237*n/5 - 13268. Factor t(b).
(b - 3)*(b + 1)**2*(b + 79)/5
Let c = 596967 + -4178767/7. Factor 74/7*d**3 + c*d**4 + 0 + 646/7*d**2 - 722/7*d.
2*d*(d - 1)*(d + 19)**2/7
Let z(x) be the third derivative of -x**6/160 + 108*x**5/5 - 31104*x**4 + 23887872*x**3 - 7*x**2 - 369*x. Factor z(a).
-3*(a - 576)**3/4
Let k = -5 - -9. Let p(f) = -3*f**2 + 8*f + 16. Let z be p(k). Factor 1/5*u**3 + 1/5*u + z - 2/5*u**2.
u*(u - 1)**2/5
Let p(b) be the second derivative of -250880*b**4/9 + 2240*b**3/3 - 15*b**2/2 + 11*b - 64. Suppose p(f) = 0. What is f?
3/448
Factor -60/7*w + 0 + 4*w**2 + 1/7*w**3.
w*(w - 2)*(w + 30)/7
Let a be 990/(-231)*(-54)/10. Suppose -24/7 - 108/7*f**4 - a*f**2 + 717/7*f**3 - 243/7*f**5 - 180/7*f = 0. Calculate f.
-2, -2/9, 1
Let w(n) be the second derivative of -n**4/8 - 17*n**3/2 + 105*n**2/4 + 47*n - 1. Factor w(q).
-3*(q - 1)*(q + 35)/2
Find a, given that 15/2*a - 45/4*a**4 - 135/2*a**3 - 55*a**2 + 25/4 = 0.
-5, -1, -1/3, 1/3
Let u be (-2008)/144 + 2 + 12. Let w(f) be the second derivative of -11*f + 0*f**2 - 1/60*f**5 + 0 + 0*f**4 + u*f**3. Let w(x) = 0. What is x?
-1, 0, 1
Suppose -52*n - 515 + 775 = 0. Let d(g) be the second derivative of 1/50*g**n + 0*g**3 + 0*g**4 + 0 + 0*g**2 + 19*g - 2/75*g**6. Factor d(i).
-2*i**3*(2*i - 1)/5
Let g = 52942/119241 - -6/13249. Determine m so that 0 + 20/9*m + g*m**2 = 0.
-5, 0
Let m be -1*(8/(-4))/((-4)/8). Let z(p) = 3*p**3 + 14*p**2 - 3*p - 10. Let b(s) = 7*s**3 + 29*s**2 - 7*s - 19. Let j(l) = m*b(l) + 10*z(l)