2 - 5/3.
5*(u - 1)**3*(u + 2)/6
Let l = -17964 + 251501/14. Let z(d) be the first derivative of 5/7*d**2 + 2/7*d**3 + 2/35*d**5 - 8/7*d - l*d**4 - 11. Find i such that z(i) = 0.
-1, 1, 4
Let p(q) be the second derivative of 0*q**3 + 0*q**2 + 7/12*q**4 - 55*q + 0 + 1/20*q**5. Factor p(t).
t**2*(t + 7)
Let d(l) = 555*l**2 + 24970*l - 223. Let m be d(-45). Suppose 0*y + 0 + 1/4*y**m + 1/4*y**3 = 0. What is y?
-1, 0
Let m = -514 - -519. What is h in -36*h**4 + 116*h**2 + 5*h**m + 64 - h**5 + 23*h**3 - 3*h**3 + 209*h - 377*h = 0?
-2, 1, 8
Let y = 5657/175 - 226/7. Let g(b) be the first derivative of 1/20*b**4 - 1/30*b**6 + 0*b + 1/15*b**3 - y*b**5 + 11 + 0*b**2. What is m in g(m) = 0?
-1, 0, 1
Let h(j) be the first derivative of j**3/5 - 9*j**2/5 - 189*j + 718. Factor h(o).
3*(o - 21)*(o + 15)/5
Let s(z) be the first derivative of 185/6*z**2 + 256 - 5/9*z**3 + 0*z. Factor s(u).
-5*u*(u - 37)/3
Let c(j) be the third derivative of -j**5/15 + 3*j**4 + 80*j**3/3 - 154*j**2. Factor c(r).
-4*(r - 20)*(r + 2)
Let k be (-3 + 4)/((-65)/(-60) - 1). Factor 4*v**5 + 18*v**3 + 31*v**3 - 41*v**3 + k*v**4.
4*v**3*(v + 1)*(v + 2)
Let s(h) be the first derivative of -8*h**2 + 124 + 0*h - 4/3*h**3. Determine c so that s(c) = 0.
-4, 0
Find j such that -126*j - 193 + 4*j**2 - 141 - 6*j**2 + 0*j**2 + 462*j = 0.
1, 167
Suppose u + 14 = -0. Let n(x) = -8*x - 19. Let v be n(u). Find p, given that v - 14*p - 12*p**3 - 2*p - 93 + 64*p**4 + 28*p**5 - 64*p**2 = 0.
-2, -1, -2/7, 0, 1
Let z = -4 - -6. Let d be (-33)/6*-24*8/264. Factor -d*p + 29*p**2 - 37*p**z + 18*p**2.
2*p*(5*p - 2)
Suppose 3*t + 19*v + 11 = 14*v, -3*t - v = -5. Let -33*w - 6*w**t - 379 + 228 + 187 - 75*w**2 = 0. What is w?
-12, -1, 1/2
Let s(u) = u**3 - 3168*u**2 - 1115128*u - 130842622. Let n(b) = 18*b**3 - 50688*b**2 - 17842044*b - 2093481951. Let h(j) = 2*n(j) - 33*s(j). Factor h(y).
3*(y + 352)**3
Let h = 56360 + -56357. Suppose 1/4*m**h - 2*m + 3 - 1/4*m**2 = 0. What is m?
-3, 2
Let b(m) be the third derivative of m**7/195 + m**6/260 - 11*m**5/390 - m**4/52 + 4*m**3/39 - 10544*m**2. Let b(u) = 0. What is u?
-1, 4/7, 1
Let d(r) be the first derivative of -r**3/5 + 99*r**2/10 - 648*r/5 + 5720. Factor d(t).
-3*(t - 24)*(t - 9)/5
Let f = -26 + 36. Let k = 11 - f. Let l(d) = -176*d**3 + 294*d**2 - 140*d + 19. Let m(z) = z**3 + z**2 + 1. Let b(v) = k*l(v) + m(v). Factor b(j).
-5*(j - 1)*(5*j - 2)*(7*j - 2)
Let j(t) be the second derivative of t**5/160 + t**4/96 + 437*t - 1. Factor j(l).
l**2*(l + 1)/8
Let p(o) be the third derivative of o**6/20 - o**5/15 + o**4/12 + 3*o**3 + 67*o**2. Let i(q) = q**3 + q. Let t(b) = -5*i(b) + p(b). Factor t(k).
(k - 3)**2*(k + 2)
Let j = 6348 - 6345. Let b(i) be the third derivative of 1/60*i**5 + 27*i**2 + 0*i - 5/12*i**4 + 25/6*i**j + 0. Determine s, given that b(s) = 0.
5
Suppose 0 = -2*r - 47 + 51. Factor 2*g**r - 3 + 0 + 3.
2*g**2
Let t = -109 + 110. Suppose 3*n = w + 2*n - t, 4*n = 3*w. What is y in 15*y**2 + 2*y - 28*y**5 - 821*y**4 + 806*y**w + 0*y**2 + 26*y**3 = 0?
-1, -2/7, -1/4, 0, 1
Solve 0 - 3*y**4 + 759/2*y**2 + 663/4*y**3 - 9/4*y**5 + 108*y = 0 for y.
-8, -2, -1/3, 0, 9
Suppose -l + 65 = 4*w, w - 5 - 10 = l. Suppose 31 = 2*g + 5*v, 2*g + 7*v = 5*v + w. Factor 25 - 15*i - 1/5*i**3 + g*i**2.
-(i - 5)**3/5
Let a(c) be the first derivative of -c**6/12 + 13*c**5/10 + 25*c**4/4 - 87*c**3 - 2673*c**2/4 - 3267*c/2 - 204. Factor a(b).
-(b - 11)**2*(b + 3)**3/2
Suppose -u**5 - 3594*u**2 - 1323 + 4*u**5 - 1107*u**4 + 1224*u**4 + 954*u**3 + 3843*u = 0. What is u?
-21, 1
Let s = -84 + 87. Find v such that -23*v**3 - 12*v + 15*v**4 - 16*v**2 + v**2 + 32*v**s + 3*v**5 = 0.
-4, -1, 0, 1
Let r(n) be the first derivative of -n**4/66 + 31*n**3/33 - 49*n + 36. Let p(j) be the first derivative of r(j). What is y in p(y) = 0?
0, 31
Let z be 278/(-20) - (-22)/(-220). Let s(v) = -8*v - 112. Let w be s(z). Let 1/7*k**2 - 4/7 + w*k = 0. What is k?
-2, 2
Let w(c) be the third derivative of -1/60*c**5 + 1/600*c**6 - 8/15*c**3 - 11/60*c**4 + 0 + 14*c + c**2. Factor w(h).
(h - 8)*(h + 1)*(h + 2)/5
Let o = -3147/580 + 3/116. Let k = -49/10 - o. Determine j so that -1/2 + k*j - 1/8*j**2 = 0.
2
Let n(y) = 3*y**2 + 169*y - 3435. Let k(m) = 2*m**2 + 170*m - 3396. Let a(u) = 5*k(u) - 4*n(u). Factor a(r).
-2*(r - 60)*(r - 27)
Let x be (12/4 - 2)*(19 - 12). Suppose 0 = 9*m - 13*m - 3*g + x, m = -4*g - 8. Find u, given that m*u**2 + 2*u + 1/4 = 0.
-1/4
Let a(z) = -3*z**2 + 1049*z + 1040. Let k(d) = -2*d + 1. Let b(p) = -a(p) - 4*k(p). Solve b(x) = 0 for x.
-1, 348
Let d be 1 - 49 - (-3 + 0). Let k = d + 51. Determine r, given that -14*r - 8*r**2 + 0 + k - 2 = 0.
-2, 1/4
Let k(r) be the second derivative of r**6/90 + 7*r**5/30 + r**3/3 - 22*r**2 + r + 34. Let v(c) be the second derivative of k(c). Factor v(o).
4*o*(o + 7)
Let x = 1352/105 - 1322/105. Solve 48/7*j - x*j**2 + 0 = 0 for j.
0, 24
Let p(q) be the third derivative of 0 + 1/210*q**6 - 4/3*q**3 + 0*q**4 + 3/280*q**5 + 0*q - 7*q**2. Let c(w) be the first derivative of p(w). Factor c(b).
3*b*(4*b + 3)/7
Let m = -47 + 49. Determine d so that 14*d + 0 + 3*d**3 + 5 + 34*d - 51*d**m - 5 = 0.
0, 1, 16
Let z be -12 + -5 + 4 - -16. Suppose -4/3*o + 5/3*o**4 + 4/3 - o**5 - z*o**2 + 7/3*o**3 = 0. What is o?
-1, 2/3, 1, 2
Let h(v) be the first derivative of v**5/12 - 5*v**4/3 + 10*v**3 + v**2/2 + 17*v + 33. Let g(d) be the second derivative of h(d). Factor g(j).
5*(j - 6)*(j - 2)
Factor 112*b - 110*b + 298*b + 5*b**2.
5*b*(b + 60)
Determine f so that 876*f**2 - 6272 - 4*f**5 - 1624*f**3 - 210*f**2 - 1479*f**2 - 176*f**4 - 1667*f**2 + 10556*f = 0.
-32, -7, 1
Let p = -11549 - -11555. Let c(d) be the third derivative of 0 + 0*d + 1/2*d**3 + 15*d**2 + 7/180*d**5 + 5/24*d**4 + 1/360*d**p. Factor c(k).
(k + 1)*(k + 3)**2/3
Suppose 78*h**2 - 59*h + 48*h**2 - 128*h - 110*h - 3*h**3 + 174*h = 0. What is h?
0, 1, 41
Let f(z) be the third derivative of -z**6/30 - 289*z**5/3 - 261364*z**4/3 - 1042568*z**3/3 + 6*z**2 + 23*z + 3. Factor f(t).
-4*(t + 1)*(t + 722)**2
Suppose 8*p - 13*p + 20 = -4*i, 0 = -5*p + 5*i + 15. Let 6*d - 8*d - 7*d**3 + p*d**3 - d**2 = 0. What is d?
-1, 0, 2
Let h = 63 + -21. Let j = 44 - h. Solve 42*d**2 + 22*d**4 - 12*d + 6*d**j - 51*d**3 - 7*d**4 = 0 for d.
0, 2/5, 1, 2
Suppose 0 = -106*w - 10 + 10. Let j(a) be the second derivative of w + 5/6*a**3 + 35/2*a**2 - 35/12*a**4 - 1/4*a**5 + 18*a. Factor j(m).
-5*(m - 1)*(m + 1)*(m + 7)
Let j(v) be the second derivative of 0*v**2 + 1/70*v**5 + 2 - 10/21*v**3 + 1/14*v**4 + 20*v. Find x such that j(x) = 0.
-5, 0, 2
Let a(m) = 10*m**4 - 68*m**3 + 72*m**2 + 1042*m. Let t(l) = 3*l**4 - 23*l**3 + 25*l**2 + 347*l. Let c(h) = 2*a(h) - 7*t(h). Solve c(q) = 0.
-3, 0, 5, 23
Let t(j) be the second derivative of -j**5/50 + 152*j**4/15 + 1228*j**3/15 + 1232*j**2/5 + 2166*j - 1. Factor t(f).
-2*(f - 308)*(f + 2)**2/5
Factor 205*s**3 + 619*s + 1/2*s**4 - 618*s**2 - 413/2.
(s - 1)**3*(s + 413)/2
Factor 0*c**2 - 11078*c - 6725*c - 17007483 + 1959*c - 3*c**2 + 1558*c.
-3*(c + 2381)**2
Let u(a) be the first derivative of 0*a + 3/20*a**5 + 77/4*a**3 + 147/4*a**2 - 27 + 3*a**4. Factor u(d).
3*d*(d + 2)*(d + 7)**2/4
Let w(a) be the first derivative of -392/5*a + 28/5*a**2 - 2/15*a**3 + 31. Factor w(o).
-2*(o - 14)**2/5
Suppose -14*f + 112 = -16*f. Let s be (-1)/((-21)/(-18))*f/36. Suppose -4/3 + 4/3*y**3 + 4/3*y**2 - s*y = 0. Calculate y.
-1, 1
Let r(z) be the third derivative of -z**5/10 - 2*z**4/3 - 11*z**3/2 - 9*z**2 + 2*z. Let q(n) = -n**2 - 1. Let p(y) = 5*q(y) - r(y). Factor p(f).
(f + 2)*(f + 14)
Let 41063625 + 4040*p**4 + 3950*p**5 + 5167755*p**2 - 31065525*p + 70238*p**3 - 3930*p**5 + 194847*p**3 = 0. Calculate p.
-69, 5/2
Let d(b) = b**3 + 11*b**2 + 27*b - 4. Let p be d(-7). Factor r + r**5 + 7*r**p - 11*r**4 + 2*r**4 + 9*r**2 - 19*r + 10*r.
r*(r - 8)*(r - 1)**2*(r + 1)
Let c = 6461/294795 - -2/6551. Let b(v) be the second derivative of -2/9*v**4 - 1/15*v**5 + c*v**6 + 2/9*v**3 + v**2 + 0 - 11*v. Factor b(k).
2*(k - 3)*(k - 1)*(k + 1)**2/3
Suppose 5*u - 56 = 2*f, 4*f - 8 = 3*u - 50. Let q = 223 + -220. Factor 2*s**q - 6*s + s**4 - 1 + 0 + u*s - 6*s.
(s - 1)*(s + 1)**3
Let q(z) = z**2 + 3*z - 1. Let p(v) = -8*v**2 - 38*v + 10. Let g(y) = p(y) + 10*q(y). Factor g(h).
2*h*(h - 4)
Let d be (-9 + 2 - -4)/(31 - 