e ((16/3)/(-8))/((-2)/39). Let f = -8 + 13. Factor 91*i + j*i + 348*i**2 + 13 - 10*i**2 - f.
2*(13*i + 2)**2
Suppose -5*w + 10 = -15. Let c(b) be the second derivative of -1/6*b**3 - 5*b + 0*b**2 - 1/20*b**w + 1/6*b**4 + 0. Factor c(r).
-r*(r - 1)**2
Let k(t) be the third derivative of 5324*t**7/735 + 121*t**6/70 + 11*t**5/70 + t**4/168 - 4*t**2 - 8*t. Factor k(o).
o*(22*o + 1)**3/7
Let n(i) be the second derivative of i**5/15 + i**4/3 - 32*i**3 + 360*i**2 + 660*i. Find r such that n(r) = 0.
-15, 6
Let j(x) be the third derivative of x**4/24 + 13*x**2. Let c(f) = f**4 + 3*f**3 + 3*f**2. Let t(s) = -c(s) - j(s). Factor t(d).
-d*(d + 1)**3
Let l = 142/3 - 281/6. Let u(h) be the first derivative of l*h**3 + 3/8*h**4 - 2 + 0*h - 1/5*h**5 - 1/2*h**2. Suppose u(f) = 0. What is f?
-1, 0, 1/2, 2
Let s(l) be the third derivative of l**5/120 + 7*l**4/48 + 5*l**3/6 + l**2 - 162*l. Factor s(d).
(d + 2)*(d + 5)/2
Let b = 153 - 149. Let o(m) be the second derivative of 0 + 1/3*m**5 + 4/45*m**6 - 13/36*m**3 + 1/8*m**b + 2*m + 1/6*m**2. Let o(w) = 0. What is w?
-2, -1, 1/4
Let u(p) = -p**3 - 7*p**2 + 8*p - 6. Let t(o) = 5*o**3 + 29*o**2 - 32*o + 25. Suppose -4*b - 8 = -8*b. Let v(f) = b*t(f) + 9*u(f). Solve v(q) = 0 for q.
1, 2
Let u(h) be the second derivative of -h**4/48 + h**3/2 - 11*h**2/8 - 29*h. Let u(s) = 0. Calculate s.
1, 11
Let u(o) be the third derivative of -1/12*o**5 + 0*o + 0 - 5/12*o**4 - 19*o**2 + 0*o**3. Factor u(n).
-5*n*(n + 2)
Let o(s) = -s**3 - 4*s**2 + 2*s - 11. Let f be o(-5). Factor -2*n**5 + 3*n**3 - 3*n**3 - 2*n**3 - 4*n**f.
-2*n**3*(n + 1)**2
Let j(t) be the second derivative of 0 - 4/21*t**3 + 1/42*t**4 - t + 4/7*t**2. Determine k, given that j(k) = 0.
2
Let q(c) be the second derivative of c**4/15 + 4*c**3/5 - 32*c**2/5 + 2*c + 24. Determine o, given that q(o) = 0.
-8, 2
Let b(h) be the second derivative of h**7/336 - h**6/80 + 3*h**5/160 - h**4/96 + 44*h. Suppose b(i) = 0. What is i?
0, 1
Factor -h**4 - 2*h + 7*h**2 - 4*h - h**2 - 4*h**2 + 5*h**2.
-h*(h - 2)*(h - 1)*(h + 3)
Let n = -236 + 236. Let q be 4/(3 - (1 - -1)). Factor 4/9*o**2 + 0 + 2/3*o**3 + n*o + 2/9*o**q.
2*o**2*(o + 1)*(o + 2)/9
Let x(g) be the first derivative of 25/6*g**3 + 8*g - 5 - 10*g**2. Factor x(i).
(5*i - 4)**2/2
Let q(p) = 4*p**2 + 7*p - 24. Let a be q(-14). Suppose 5*c - 662 + a + 5*c**2 = 0. Calculate c.
-1, 0
Let a(f) be the second derivative of -f**6/810 - f**5/540 - 13*f**3/6 - 17*f. Let i(p) be the second derivative of a(p). Suppose i(h) = 0. What is h?
-1/2, 0
Let i(s) = s**3 - 7*s**2 - s + 10. Let v be i(7). Suppose 3*c**3 - 4*c**v + 2*c**2 + 0*c**3 - c**3 = 0. Calculate c.
0, 1
Let j(w) = w - 1. Let k = -34 - -31. Let l(g) = -g**2 - 3*g + 4. Let z(a) = k*l(a) - 12*j(a). Factor z(o).
3*o*(o - 1)
Solve 2*g**3 - 5*g**2 - 40*g + 4*g**3 + 0*g**3 + 60 - g**3 + 0*g**3 = 0.
-3, 2
Let f(l) = -l**2 - 10*l + 13. Let q be f(-11). Factor -i - 11 + 11 + q*i**2 - i.
2*i*(i - 1)
Let i(b) = b - 8. Let k be i(10). Suppose -o = h, 2*o + k*h + 4 = -h. Find m such that 3*m**4 + m**o - m**4 - 2*m**3 - 4*m**4 = 0.
-2, 0
Let j = 98 + -54. Suppose 0 = -6*z + j - 26. Suppose 2/7*y**4 + 0*y + 0 + 4/7*y**2 + 6/7*y**z = 0. What is y?
-2, -1, 0
Let m(s) be the third derivative of -s**5/60 - s**4/3 + s**2 - 35*s. Solve m(t) = 0.
-8, 0
Let u be (30/(-45))/(3/48) + 11. Factor 5/6*c**2 + 1/3*c - u*c**4 + 0 + 1/6*c**3.
-c*(c - 2)*(c + 1)*(2*c + 1)/6
Let v = -2971 - -2975. Factor 4*j**2 + 10/3*j**3 + 1/3 + 2*j + j**v.
(j + 1)**3*(3*j + 1)/3
Factor -1/3 + 1/3*v**2 + 0*v.
(v - 1)*(v + 1)/3
Let t(b) be the second derivative of -1/252*b**7 + 1/6*b**2 + 0 + 5/36*b**3 + 7*b + 1/36*b**4 - 1/30*b**5 - 1/45*b**6. Factor t(k).
-(k - 1)*(k + 1)**3*(k + 2)/6
Let f(h) be the third derivative of h**8/2520 - 19*h**7/1575 + 17*h**6/300 - 49*h**5/450 + 4*h**4/45 - 870*h**2. Determine c so that f(c) = 0.
0, 1, 16
Let c = -2071 - -132541/64. Let q = 35/64 + c. Factor -q*r + 3/4*r**2 - 1/4*r**3 + 0.
-r*(r - 2)*(r - 1)/4
Let l(d) be the second derivative of 0*d**2 + 4*d + 0*d**3 + 0 + 1/90*d**4. Suppose l(o) = 0. What is o?
0
Let w(t) be the second derivative of -t**4/12 + 19*t**3/6 + t**2 + 34*t. Let a be w(19). Suppose 0 - 1/2*r**a + 0*r = 0. Calculate r.
0
Suppose -2*o + 13*o = 55. Find b such that -9*b**2 + 10*b - o*b**3 - 9*b**2 - 9*b**2 + 22*b**2 = 0.
-2, 0, 1
Let q(m) = m**2 - m + 43. Let l be q(0). Suppose l*z - 48*z = 0. Factor 0*u**4 + z + u**2 - 3/2*u**3 + 0*u + 1/2*u**5.
u**2*(u - 1)**2*(u + 2)/2
Let y(g) = 2*g**2 + g + 1. Let j be y(-2). Suppose -5*s = -j*s. Let 3*q**2 - 27 + s*q + 0*q + 24 = 0. What is q?
-1, 1
Let o = -1459/4 - -4381/12. Factor 1/6*b**4 - 1/3*b**3 + 1/6 + 1/6*b - o*b**2 + 1/6*b**5.
(b - 1)**2*(b + 1)**3/6
Let o = -897/16 + 15345/272. Factor 2/17*w**3 + 4/17*w**2 - o*w + 0.
2*w*(w - 1)*(w + 3)/17
Let w = 131/86 - 44/43. Suppose y - 1/2*y**2 - w = 0. What is y?
1
Let d be (-9)/(468/8) + (-67)/(-13). Let a be d + 3*(-4)/(-4)*-1. Factor 1/4*o**a + 0 + 3/4*o.
o*(o + 3)/4
Factor 0*g**2 + 0 + 8/3*g**3 - 16/9*g**4 + 0*g + 2/9*g**5.
2*g**3*(g - 6)*(g - 2)/9
Let o(r) = -r + 6. Let u be o(3). Suppose -x = u - 6. Find l, given that 31*l**x - 21*l**4 - 26*l**2 - 19*l**4 + 0*l**3 + 25*l**3 + 4*l = 0.
0, 2/5, 1/2
Suppose d = 3*d - 10. Let t = 16 + -11. Factor -2*j**4 + j**2 + j**2 + 4*j**5 + 5*j - d*j**t - 4*j.
-j*(j - 1)*(j + 1)**3
Let s(j) = 135*j**4 - 143*j**3 - j. Let i(f) = -67*f**4 + 71*f**3. Suppose -22 = -4*q - 3*v, 5*v = 5*q - 14 + 4. Let r(l) = q*s(l) + 9*i(l). Solve r(u) = 0.
-2/9, 0, 2/7, 1
Let f(s) be the second derivative of 1/42*s**4 + 0 - 8/21*s**3 - 44*s + s**2. Let f(n) = 0. What is n?
1, 7
Let y(g) be the first derivative of -2*g**5/105 + 11*g**4/21 - 94*g**3/21 + 220*g**2/21 - 200*g/21 - 287. Solve y(o) = 0.
1, 10
Find z, given that -4/5*z**3 + 0 - 1/5*z**4 + 11/5*z**2 - 6/5*z = 0.
-6, 0, 1
Let o(v) = -2*v**4 - 2*v**3 + 2*v**2 - 20*v. Let a(w) = -w + 4 + 10 - 14. Let m(u) = -44*a(u) + 2*o(u). Find l, given that m(l) = 0.
-1, 0, 1
Let w(b) be the second derivative of b**8/840 - b**6/180 + 11*b**3/6 - 4*b. Let s(n) be the second derivative of w(n). Factor s(t).
2*t**2*(t - 1)*(t + 1)
Factor 643147 + 28*q**2 + 24*q - 4*q**4 - 643147.
-4*q*(q - 3)*(q + 1)*(q + 2)
Suppose -5 = -5*d + 10. Let x = 550 - 547. Suppose -w**3 + 0*w - d*w + w**3 + 3*w**x = 0. What is w?
-1, 0, 1
Let b(t) be the second derivative of t**4/16 - 6*t**3 + 216*t**2 + 3*t + 25. Let b(s) = 0. What is s?
24
What is y in 5*y**2 + 2 + 23*y**2 - 10 - 62*y + 2*y**3 + 20 + 20 = 0?
-16, 1
What is b in 1/4*b**3 + 1 - b**2 - 1/4*b = 0?
-1, 1, 4
Let 98 - 96*r + 46 + 36*r + 4*r**3 - 8*r**2 = 0. What is r?
-4, 3
Let j(g) = g**3 + 10*g**2 - 13*g - 20. Let h be j(-11). Factor h*c**2 - 4387 + 4387 + 3*c - c**3.
-c*(c - 3)*(c + 1)
Let j(s) be the second derivative of 0*s**6 + 0 + 0*s**4 + 1/20*s**5 + 0*s**3 + 0*s**2 - 10*s - 1/42*s**7. Factor j(c).
-c**3*(c - 1)*(c + 1)
Let a = -198 - -198. Let m(h) be the second derivative of 23/48*h**4 + 1/2*h**2 - 2*h + a + 2/3*h**3 + 1/40*h**6 + 7/40*h**5. Solve m(j) = 0.
-2, -1, -2/3
Let a(l) be the third derivative of -5*l**6/12 + 10*l**5/3 + l**4/12 - 4*l**3/3 + 14*l**2 - 8*l. Solve a(m) = 0 for m.
-1/5, 1/5, 4
Let f = 9/2 - 5. Let u = f + 3/4. Factor -1/4*x**5 + 1/2*x**4 + 0 + 0*x**3 - 1/2*x**2 + u*x.
-x*(x - 1)**3*(x + 1)/4
Let q(n) be the third derivative of n**5/100 - 9*n**4/2 + 810*n**3 + 10*n**2 + 11. Let q(l) = 0. What is l?
90
Let o(z) be the first derivative of -3993*z**5/35 - 9801*z**4/28 + 2046*z**3/7 - 582*z**2/7 + 72*z/7 + 78. Find h, given that o(h) = 0.
-3, 2/11
Let b(c) = -2*c**2 + 20*c + 26. Let q be b(11). Let s be ((-2)/q)/(3*1/(-4)). Factor 0 + 0*o + 0*o**2 + s*o**4 + 1/3*o**3 + 1/3*o**5.
o**3*(o + 1)**2/3
Let u(r) = 5*r**2 + r + 6. Let d(p) = -6*p**2 - 2*p - 6. Let q be (-68)/(-11) + (-12)/66. Let z(g) = q*d(g) + 7*u(g). Solve z(l) = 0 for l.
-6, 1
Solve -177/2*x - 171 + 9/2*x**3 + 255*x**2 = 0 for x.
-57, -2/3, 1
Let d be 20*(96/(-50) - -2). Let t(n) be the first derivative of -10*n**3 + 7*n**2 - 2*n - 5 + 13/2*n**4 - d*n**5. What is b in t(b) = 0?
1/4, 1
Suppose 4*r - 16 = 8. Let o be (-50)/(-18) + r/27. Factor 0*p**3 - p + 4*p**2 + 2*p**5 + 2*p**o - 3*p**5 - 2*p**4 - 2.
-(p - 1)**2*(p + 1)**2*(p + 2)
Let q be ((0/(-5))/((-2)/2))/(-2). Let s(h) be the