e (8/21 + 6/21)*(-8 + 11). Suppose 14/5*h**n + 0 + 2/5*h**4 - 12/5*h**3 + 1/5*h**5 - h = 0. Calculate h.
-5, 0, 1
Let t(h) be the first derivative of -9/2*h**6 - 4/3*h - 125 - 41/9*h**3 - 16/3*h**2 + 113/12*h**4 + 3*h**5. Suppose t(v) = 0. Calculate v.
-1, -2/9, 1
Let c(p) = -p**2 - 9*p + 126. Let y be c(7). Let m be 14/49*y/10. Factor m*f**2 - 16/5*f + 32/5.
2*(f - 4)**2/5
Let q = -51 + 57. Suppose -q*s + 11 = -13. Factor y - 1 + 2*y**2 + y**2 - s*y**2 + y.
-(y - 1)**2
Find l such that -6*l**3 + 68 + 16*l**3 + 34*l**3 - 108*l**2 - 20 + 16*l = 0.
-6/11, 1, 2
Let z = -125689 - -377083/3. Factor 16/3*u**2 - z + 4/3*u**3 - 4/3*u.
4*(u - 1)*(u + 1)*(u + 4)/3
Let h be (-11 - -10)*(10 + -10). Let r(a) be the third derivative of 1/90*a**5 + h*a + 1/18*a**4 - 1/180*a**6 + 0 + 0*a**3 + 11*a**2. Factor r(s).
-2*s*(s - 2)*(s + 1)/3
Let p(o) be the first derivative of 1/8*o**4 + 0*o + 27/4*o**2 + 2*o**3 - 8. Factor p(i).
i*(i + 3)*(i + 9)/2
Factor 61 + 183939*y**2 + 939*y - 333 - 185133*y**2 + 2 - 3*y**5 - 120*y**4 + 648*y**3.
-3*(y - 2)*(y - 1)**3*(y + 45)
Let y(j) be the first derivative of j**6/27 - 2*j**5/3 - 9*j**4 - 964*j**3/27 - 181*j**2/3 - 46*j - 2058. Solve y(t) = 0 for t.
-3, -1, 23
Let q(d) = -40*d**2 - 4*d - 51. Let n(g) = -56*g + 1. Let u(z) = -3*n(z) - q(z). Factor u(b).
4*(b + 4)*(10*b + 3)
Let x be 47222*(-14)/608 + 446/(-3568). Let j = x + 1088. Factor j*r - 2/19*r**2 - 8/19.
-2*(r - 4)*(r - 1)/19
Factor 1392/5 + 28*g + 2/5*g**2.
2*(g + 12)*(g + 58)/5
Let x(b) = b**3 - 8*b**2 + 3*b - 22. Let l be x(8). Suppose l*k = -0 + 4. Solve s**4 + s**k - 6*s**3 + 12*s**2 - 4*s**2 = 0.
0, 3
Let m be 4/99*-11 + -2 + (-194)/(-72). Suppose -7/4*z**3 + m*z**5 + 13/4*z**2 - 1/4*z**4 - 3/2*z + 0 = 0. What is z?
-3, 0, 1, 2
Let k(l) = -l**2 + 39*l - 138. Let v be k(35). Suppose 2*w + 0*w - 4 = 0. Factor -8*a**2 + 2*a + 4*a**w + 7*a**2 + v*a**3 + a**2.
2*a*(a + 1)**2
Suppose 559 - 487 = 6*t. Factor 917 + t*q**2 + 8*q + 2*q**3 - 36*q**2 - 935 + 31*q + q**3.
3*(q - 6)*(q - 1)**2
Let g(i) be the third derivative of -i**6/1260 - 11*i**5/126 - 3*i**4/14 - 422*i**2. Factor g(t).
-2*t*(t + 1)*(t + 54)/21
Factor -69*c**2 - 60*c**2 - 10852*c - 21738*c + 53105405 - 59*c**2 + 193*c**2.
5*(c - 3259)**2
Let c(h) = -h + 4. Let v be c(-6). Suppose -26 = -3*x - 3*z - 2*z, -3*x = z - v. Determine l, given that 18 + 27*l**2 - 17*l**2 - 13*l**x - 15*l = 0.
-6, 1
Let a(z) be the first derivative of -2*z**3/63 + 418*z**2/7 - 262086*z/7 + 1905. Factor a(o).
-2*(o - 627)**2/21
Let i = 1047999 + -9431983/9. Factor 4/9*m**3 - i*m**2 - 32/9*m + 0.
4*m*(m - 4)*(m + 2)/9
Let u = 9111 + 11339. Factor 51*h**2 - 4*h**3 + 88 + 5*h**2 + u*h - 20590*h.
-4*(h - 11)*(h - 2)*(h - 1)
Let u = -1233 - -1465. Let t = u - 2551/11. Factor -7/11*h + 0 + t*h**2.
h*(h - 7)/11
Find f, given that 2/7*f**4 + 0 - 200/7*f + 50/7*f**3 - 8/7*f**2 = 0.
-25, -2, 0, 2
Let v(n) be the second derivative of n**6/90 - n**5/12 - n**4/36 + 5*n**3/18 + 447*n. Determine h, given that v(h) = 0.
-1, 0, 1, 5
Let t = -5212 - -3059445/587. Let a = t + 579/4696. Factor 0*v**2 + 0 + a*v**3 - 1/8*v.
v*(v - 1)*(v + 1)/8
Let 9*y**2 - 586*y**3 + 1 + 12*y + 583*y**3 - 1 = 0. Calculate y.
-1, 0, 4
Let r(n) be the third derivative of 0*n**3 + 0*n**4 + 0*n + 1/70*n**6 - 1/147*n**7 + 2*n**2 + 1/1176*n**8 + 0 + 0*n**5. Factor r(z).
2*z**3*(z - 3)*(z - 2)/7
Let j = 1703 + -737. Factor 6*k**3 + 966*k - j*k - 3*k**4 - 3*k**2.
-3*k**2*(k - 1)**2
Let q(k) be the second derivative of 0 - 7/9*k**2 + 70*k + 2/27*k**4 - k**3. What is b in q(b) = 0?
-1/4, 7
Suppose 168*y = 32*y + 272. Let c(n) be the second derivative of 3/80*n**5 - 1/16*n**4 - 35*n + 0 + 0*n**3 + 0*n**y. Solve c(f) = 0.
0, 1
Let d(j) be the third derivative of j**8/168 - j**7/21 + j**6/12 + j**5/6 - j**4/2 + 327*j**2 - 1. Let d(g) = 0. What is g?
-1, 0, 1, 2, 3
Suppose 159*h - 162*h - 5*o + 14 = 0, -3*o + 12 = 0. Let r be -8 + h/(-6)*24. Solve 0*n**2 + 0*n + r + 1/4*n**3 = 0.
0
Let q(a) be the second derivative of a**5/130 - 55*a**4/78 - 56*a**3/39 - 441*a. Suppose q(v) = 0. Calculate v.
-1, 0, 56
Let q = 1033/1848 + 13/168. Let o(y) be the first derivative of 16/11*y**2 - 46/33*y**3 - 8/11*y + q*y**4 + 33 - 6/55*y**5. Find m, given that o(m) = 0.
2/3, 1, 2
Let b(c) be the second derivative of 13*c**7/168 + 23*c**6/60 + 3*c**5/16 - 3*c**4/8 - 1047*c. Solve b(i) = 0.
-3, -1, 0, 6/13
Let s(h) be the second derivative of 3*h**5/20 + 17*h**4/12 - 9*h**2 + 14*h. Let y(l) = -65*l**3 - 375*l**2 + 395. Let f(z) = 45*s(z) + 2*y(z). Factor f(p).
5*(p - 1)*(p + 2)**2
Let b(m) be the first derivative of -4/9*m**2 + 0*m + 2/27*m**3 - 46. Solve b(f) = 0.
0, 4
Factor 440/3 - 72*k - 2/3*k**2.
-2*(k - 2)*(k + 110)/3
Suppose 11 = 5*x - 22*a + 23*a, -4*x + 4 = 2*a. Let y = -3/484 + 6307/2420. Factor 0 - y*j**2 - j**4 + 4/5*j + 14/5*j**x.
-j*(j - 1)**2*(5*j - 4)/5
Let r = 32238 + -161187/5. What is v in -r*v**4 + 3/5*v**5 + 0 + 3/5*v**2 + 0*v - 3/5*v**3 = 0?
-1, 0, 1
Let q(d) = -d**4 + d**2 + d - 2. Let n(u) = 23*u**4 + 25*u**3 - 38*u**2 - 13*u + 6. Let j(f) = n(f) + 3*q(f). Let j(w) = 0. What is w?
-2, -1/4, 0, 1
Let q = 4595875/3 - 1531945. Factor -30*v - 5*v**3 - q + 85/3*v**2.
-5*(v - 4)*(v - 2)*(3*v + 1)/3
Let u be (37 + (32 - 69))/19. Factor -5/3*h**2 + u - 10/3*h.
-5*h*(h + 2)/3
Let j(m) = m**3 + 16*m**2 - 35*m + 20. Let t be j(-18). Suppose 3*y + a = -5, -5*y + t*y + a + 5 = 0. Factor 2/5*i + y - 8/5*i**2 - 2*i**3.
-2*i*(i + 1)*(5*i - 1)/5
Let h(y) be the third derivative of 1/120*y**6 + 81*y**2 - 1/3*y**3 + 0 - 1/24*y**4 + 1/30*y**5 + 0*y. Solve h(b) = 0 for b.
-2, -1, 1
Let x(q) = 4*q - 5. Let y be x(2). Let c be (-6 - -1)*8/(-20). Factor -12 - 6*b**2 + 3*b**2 + 3*b**2 + y*b**c.
3*(b - 2)*(b + 2)
Factor 21780 + 1/5*u**2 + 132*u.
(u + 330)**2/5
Let w(m) be the second derivative of -m**5/130 - m**4/26 + 4*m**2/13 - 1084*m - 1. Let w(l) = 0. What is l?
-2, 1
Let s(r) be the second derivative of r**4/60 - 5*r**3/3 - 159*r**2/10 + 4*r + 25. Factor s(u).
(u - 53)*(u + 3)/5
Let s(u) be the first derivative of 15 + 1/4*u**6 + 57/8*u**4 + 12*u**2 - 25/2*u**3 - 21/10*u**5 - 6*u. Factor s(x).
3*(x - 2)**2*(x - 1)**3/2
Let s(g) = g**3 - 4*g**2 + g - 3. Let d(n) = 6*n**3 - 97*n**2 + 79*n + 119. Let y(a) = d(a) - 7*s(a). Find m such that y(m) = 0.
-70, -1, 2
Let y(f) be the second derivative of -f**6/225 + f**5/10 - f**4/9 - 4*f**3/3 + 56*f**2/15 - 4*f - 1. Solve y(k) = 0.
-2, 1, 2, 14
Suppose 0 = -5*s - w, 3*w = -s - s. Factor 8*b**3 + 12*b**2 + 8*b**3 + 18*b**2 + 0*b**4 + s*b**3 + 2*b**4.
2*b**2*(b + 3)*(b + 5)
Let x(h) be the third derivative of -h**5/12 + 65*h**4/24 + 75*h**3 + 10*h**2 + 67*h. Find g, given that x(g) = 0.
-5, 18
Determine a so that 1/3*a**2 + 1265/3*a + 842 = 0.
-1263, -2
Let v(i) be the third derivative of 1/105*i**7 + 0 + 165*i**2 + 289/3*i**3 + 136/3*i**4 + 37/5*i**5 - 8/15*i**6 + 0*i. Factor v(d).
2*(d - 17)**2*(d + 1)**2
Determine w, given that 4*w**3 - 1796*w + 766*w**2 + 365*w**2 + 900 - 239*w**2 = 0.
-225, 1
Let q(j) be the third derivative of -j**6/720 - 11*j**5/180 + 119*j**4/144 + 289*j**3/3 - 156*j**2 + j + 5. Suppose q(n) = 0. Calculate n.
-17, 12
Let a(j) be the first derivative of -3*j - 1/8*j**4 - 183 + 5/4*j**2 + 1/3*j**3. Solve a(l) = 0.
-2, 1, 3
Let v(u) be the third derivative of 0 - 121*u**2 + 1/9*u**4 - 1/504*u**8 + 2/315*u**7 + 0*u + 1/60*u**6 - 4/45*u**5 + 0*u**3. Determine d, given that v(d) = 0.
-2, 0, 1, 2
Let a = 18 - 16. Suppose 0 = -2*n - 5*x + 114, -a*n - 157 = -5*n - 4*x. Let t + 5*t - n*t**2 + 45*t**2 = 0. What is t?
0, 3
Let i be 0/(-24 - -27 - 16). Let c = 1169/970 + -1/194. Factor -2/5*b**2 - c*b + i.
-2*b*(b + 3)/5
Let j = 5841 + -81773/14. Let k(h) be the third derivative of 0 + 23*h**2 - j*h**4 - 1/210*h**5 - 5/21*h**3 + 0*h. Let k(l) = 0. What is l?
-5, -1
Let y = -1445/1191 + 1011/397. Factor 5/6*r**3 + 0 + 2/3*r + y*r**2 + 1/6*r**4.
r*(r + 1)*(r + 2)**2/6
Let t(y) be the second derivative of 3/2*y**6 + 0 - 650/3*y**3 + 545/12*y**4 - 43*y + 39/2*y**5 + 250*y**2. Factor t(q).
5*(q + 5)**2*(3*q - 2)**2
Let j(d) be the first derivative of -7 + 2/3*d**3 - 74*d**2 + 2738*d. Let j(o) = 0. What is o?
37
Let i(f) be the second derivative of f**6/30 + 46*f**5/5 - 739*f**4/48 + 185*f**3/24 + 3*f + 851. Let i(b) = 0. Calculate b.
-185, 0, 1/2
Let 