 0*n. Let o(t) be the second derivative of y(t). Factor o(u).
3*(u - 1)*(u + 1)/8
Suppose 23 = 1003*l - 66*l - 1851. Determine u so that -2/5*u + 2/5*u**3 - 2/5 + 2/5*u**l = 0.
-1, 1
Suppose -4*l + 17*l = 3*l. Let j(v) be the first derivative of 0*v + l*v**2 + 0*v**5 - 2 + 0*v**3 + 1/6*v**6 - 1/4*v**4. Determine c, given that j(c) = 0.
-1, 0, 1
Let m(w) be the first derivative of w**4/6 - 260*w**3/9 - 88*w**2 + 312. Factor m(i).
2*i*(i - 132)*(i + 2)/3
Let z(f) be the third derivative of 0*f - 1/20*f**5 + 0*f**3 + f**2 + 0 - 1/4*f**4. Solve z(x) = 0 for x.
-2, 0
Suppose 0 = -4*q + 3*y + 32, 0 = 2*q + 4*y - 5 + 11. Let t(r) be the second derivative of -27*r + 1/21*r**4 - 8/21*r**3 + 1/35*r**q + 0 - 8/7*r**2. Factor t(b).
4*(b - 2)*(b + 1)*(b + 2)/7
Let v(f) be the first derivative of 290/3*f**3 + 320*f**2 + 35/4*f**4 + 160*f - 4. Determine w, given that v(w) = 0.
-4, -2/7
Let r(u) be the first derivative of 3*u**4/16 - 35*u**3/4 + 36*u**2 + 1575. Factor r(f).
3*f*(f - 32)*(f - 3)/4
Let a(u) = 2*u**2 + 83*u + 43. Let i be a(-40). Let z = -151/2 - i. Solve z*c - 1 - 1/2*c**2 = 0 for c.
1, 2
Suppose 5*n + 216 - 716 = 0. Let n*u**2 - 210*u**2 - 2*u**3 - 5*u + 7*u**3 + 110 = 0. Calculate u.
-1, 1, 22
Let m(t) be the second derivative of -2*t**7/21 - 14*t**6/15 + 2*t**5/5 + 104*t**4/3 + 448*t**3/3 + 256*t**2 + 8261*t. Suppose m(s) = 0. What is s?
-4, -2, -1, 4
Let l(p) be the third derivative of 12/5*p**5 + 0*p**3 + 0*p - 11/10*p**6 + 11*p**2 + 0*p**4 - 2 - 1/84*p**8 + 4/21*p**7. Factor l(q).
-4*q**2*(q - 4)*(q - 3)**2
Let j be 2 + 109329/(-84) + (-6)/(-21). Let z = -1293 - j. Determine y, given that -z*y + 5 + 5/4*y**2 = 0.
1, 4
Let d(k) be the third derivative of 2*k**7/105 + 14*k**6/3 + 92*k**5/5 - k**2 + 2403*k. Suppose d(y) = 0. What is y?
-138, -2, 0
Let c(d) = -3*d - 103. Let k be c(-35). What is b in 72*b + 66*b + 8*b**2 - 65*b**k - 2*b**3 + 3*b**4 - 10*b**3 - 72 = 0?
-4, 1, 6
Let h(m) be the third derivative of 0 + 114*m**2 + 0*m + 2/45*m**5 - 1/360*m**6 + 0*m**3 + 0*m**4. Factor h(b).
-b**2*(b - 8)/3
Let o(y) be the second derivative of -3*y**5/100 + 13*y**4/10 - 71*y**3/10 + 69*y**2/5 + y - 235. Find f, given that o(f) = 0.
1, 2, 23
Let f(r) be the second derivative of -r**5/4 - 55*r**4/6 + 7*r + 10. Let f(h) = 0. What is h?
-22, 0
Suppose -306 = 724*j - 877*j. Factor 0*t + 0 + 5/4*t**j - 27/8*t**3 + 5/8*t**4.
t**2*(t - 5)*(5*t - 2)/8
Let v(k) = -k. Let q(o) = 6*o**3 + 56*o**2 + 108*o - 100. Suppose 8*n + 6 = -10. Let i(m) = n*v(m) + q(m). What is t in i(t) = 0?
-5, 2/3
Suppose -z + 377 + 636 = 0. Let u = 1017 - z. What is y in 0*y + 1/11*y**u + 2/11*y**2 - 3/11*y**3 + 0 = 0?
0, 1, 2
Let i = 47 - 34. Suppose -12*v = -10*v - q - 8, 0 = -v + 5*q + i. Factor 10*s - 424*s**3 + 216*s**v + 210*s**3 - 10*s**2 - 4 + 2*s**2.
2*(s - 2)*(s - 1)**2
Let -1760/9 - 4/9*b**4 + 2168/9*b - 20*b**2 - 224/9*b**3 = 0. Calculate b.
-55, -4, 1, 2
Let u(x) = 2*x**2 + 47*x + 2. Let j(i) be the first derivative of i**3/3 + 8*i**2 + i + 14. Suppose 3 = -3*w + 21. Let n(a) = w*u(a) - 17*j(a). Factor n(m).
-5*(m - 1)**2
Suppose 1006*x**2 + 543*x - 501*x**2 - 502*x**2 - 375 - 723 = 0. Calculate x.
-183, 2
Solve -255 + 1149*z - 27/4*z**2 = 0.
2/9, 170
Let m(s) = 4*s**2 + 2*s + 4. Suppose -p + 9*p = 32. Let z(n) = -19*n**2 - 7*n - 15. Let r(q) = p*z(q) + 18*m(q). Suppose r(b) = 0. Calculate b.
-1, 3
Suppose 0 = -5*k + 2*q + 105, -54 = -4*k - 4*q + 30. Factor -36 - 53*d + 91 + 3*d + 16*d**2 - k*d**2.
-5*(d - 1)*(d + 11)
Suppose -462*z**2 + 230*z**2 + 3*z - 15*z + 231*z**2 - 2*z - 13 = 0. What is z?
-13, -1
Let s(o) = 2*o**2 - 2892*o + 1071652. Let q(g) = -4*g**2 + 5775*g - 2143305. Let l(v) = 4*q(v) + 9*s(v). Factor l(i).
2*(i - 732)**2
Let y(v) be the first derivative of -2/33*v**3 + 4/11*v**2 - 78 - 8/11*v. Suppose y(j) = 0. Calculate j.
2
Let i = 212024 + -212019. What is z in -14/11*z + 6/11*z**i - 28/11*z**4 - 8*z**3 - 68/11*z**2 + 0 = 0?
-1, -1/3, 0, 7
Let m = -64 - -68. Suppose -5*k = -u - 2*u + m, -u - 5*k + 8 = 0. Solve -5*f + u + f**3 + 7*f + 7*f**2 - 2*f**2 + 5*f = 0 for f.
-3, -1
Let z = 304170 + -304167. Suppose -3/2*q**z + 0 - 6*q - 15/2*q**2 = 0. What is q?
-4, -1, 0
Factor -3*b**2 - 21*b**3 - 3*b**2 - 104*b**4 + 0*b**2 + 38*b**4 + 54*b**4 + 3*b.
-3*b*(b + 1)**2*(4*b - 1)
Suppose 4*c + 2*i + 39 - 15 = 0, -2*i - 24 = -4*c. Solve -6/5*s**5 + 13/5*s**4 - 13/5*s**2 + 4/5*s**3 + 2/5*s + c = 0 for s.
-1, 0, 1/6, 1, 2
Let a(c) be the third derivative of -4/525*c**7 + 1/100*c**6 + 167*c**2 + 0 + 1/30*c**4 + 3/50*c**5 + 0*c**3 + 0*c. Find d such that a(d) = 0.
-1, -1/4, 0, 2
Let -676/11*c + 674/11*c**2 + 2/11*c**3 + 0 = 0. What is c?
-338, 0, 1
Suppose -u - 5*a - 3 = 0, 7 = -2*u + 5*a + 16. Let s(q) be the second derivative of 250*q**u + 25*q**3 + 0 + 3*q + 5/4*q**4 + 1/40*q**5. Factor s(p).
(p + 10)**3/2
Let w be 6/(-21) + (6 - 3595/35). Let f = -97 - w. Factor 0*p**2 + 2/13*p**5 + 0*p + 0*p**3 + f + 2/13*p**4.
2*p**4*(p + 1)/13
Let i = 1974 + -1970. Let k(d) be the first derivative of -1/21*d**6 + 8/35*d**5 + 8/21*d**3 + 0*d + 9 - 1/7*d**2 - 3/7*d**i. Suppose k(v) = 0. What is v?
0, 1
Let m(g) = -3*g**2 + 60*g - 42. Let t be m(22). Let n = -695/4 - t. Factor -l + n*l**2 + 3/4.
(l - 3)*(l - 1)/4
Let k(n) be the first derivative of -19*n + 1/10*n**4 + 12/5*n**2 - 28 - 4/5*n**3. Let d(t) be the first derivative of k(t). Factor d(h).
6*(h - 2)**2/5
Let m(i) be the first derivative of 3*i**2 - 33/4*i**4 + 0*i - 9*i**3 + 56. Let m(b) = 0. What is b?
-1, 0, 2/11
Let v(z) = -z**5 + 7*z**4 + 41*z**3 + 63*z**2 - 80*z + 5. Let r(p) = 2*p**4 + 2*p**3 + 2*p + 1. Let c(d) = -5*r(d) + v(d). Determine k so that c(k) = 0.
-6, -3, 0, 1, 5
Let i(s) = s**2 - 234*s + 13525. Let m be i(130). Let z(q) be the first derivative of 18 + 1/2*q**4 - 9*q - 3/2*q**2 - q**m + 1/6*q**6 + 14/3*q**3. Factor z(a).
(a - 3)**2*(a - 1)*(a + 1)**2
Let t(n) be the first derivative of -40*n + 26*n**2 - 8/3*n**3 - 79 - n**4. Factor t(r).
-4*(r - 2)*(r - 1)*(r + 5)
Suppose 4*l - 216 = 2*l. Determine j so that -49*j - l*j**2 + 20*j**3 + 160 + 209*j - 208 = 0.
2/5, 2, 3
Let t(y) be the second derivative of -y**6/50 - y**5/30 + 37*y**4/60 - 2*y**3/5 + 30*y**2 + 80*y. Let r(z) be the first derivative of t(z). Factor r(s).
-2*(s - 2)*(s + 3)*(6*s - 1)/5
Let z(n) be the first derivative of 12*n**5/5 - 63*n**4/4 + 5*n**3 - 8149. Factor z(b).
3*b**2*(b - 5)*(4*b - 1)
Let a(l) be the second derivative of 4/7*l**2 - 14*l + 4/21*l**3 - 2/35*l**5 - 1/105*l**6 + 5 - 1/14*l**4. What is z in a(z) = 0?
-2, -1, 1
Let x(a) be the first derivative of 2*a**3/3 + 48*a**2 + 640*a + 1289. Factor x(p).
2*(p + 8)*(p + 40)
Let g(v) be the third derivative of 9/20*v**4 + 19/100*v**6 + 0 - 90*v**2 - 8/5*v**3 + 0*v + 39/50*v**5 - 3/175*v**7. Find s such that g(s) = 0.
-1, 1/3, 8
Let q(c) = -c**3 - 2*c**2 + 20*c + 12. Let y be q(5). Let d be (-1 - -2) + 42/y - -2. Factor 8/3 - d*l - 1/3*l**2.
-(l - 1)*(l + 8)/3
Let l = -146 + 64. Let j = l - -84. Solve 13*b**2 - 5*b**3 - j - 11*b**2 + 5*b + 0*b**3 = 0.
-1, 2/5, 1
Let k(y) be the second derivative of -y**5/120 - 5*y**4/48 + 67*y**2/2 - 90*y. Let i(j) be the first derivative of k(j). Suppose i(v) = 0. What is v?
-5, 0
Determine l, given that 150817*l**4 - 96*l - 7 + 42 - 150814*l**4 + 1 + 87*l**2 - 30*l**3 = 0.
1, 2, 6
Let c(x) be the second derivative of 0*x**6 + 2*x - 1/168*x**7 + 1/10*x**5 - 7/24*x**3 + 46 - 3/4*x**2 + 1/8*x**4. Solve c(u) = 0.
-2, -1, 1, 3
Let o be 476/36 + -13 - (-16)/9. Suppose -6*g - 33*g**2 - 35*g**2 - 21*g + 66*g**o - 24 + g = 0. Calculate g.
-12, -1
Let f be -3 + -3 - ((-8)/4 + 3). Let h(u) = 3*u**2 - 51*u + 68. Let n(x) = -2*x**2 + 35*x - 45. Let l(z) = f*n(z) - 5*h(z). Solve l(t) = 0.
5
Let t(r) be the third derivative of 4/3*r**4 + 1/1008*r**8 + 0 - 17*r**2 - 6*r + 2*r**3 + 97/180*r**5 + 47/360*r**6 + 11/630*r**7. Solve t(g) = 0 for g.
-3, -2, -1
Let a = -5 + 7. Suppose a*h + 3*c = 26 - 5, 3*h + 4*c = 29. Factor -11*i - 4*i - 10*i**h + 10*i + 15*i**2.
-5*i*(i - 1)*(2*i - 1)
Let y(r) be the third derivative of r**8/168 + 5*r**7/168 - 11*r**6/72 + r**5/6 - 25*r**3/3 + 4*r**2 - 4. Let k(f) be the first derivative of y(f). Factor k(g).
5*g*(g - 1)*(g + 4)*(2*g - 1)
Let h(i) be the third derivative of -i**6/240 - 19*i**5/6 - 9025*i**4/12 + 3526*i**2. Find y s