5. Determine d so that p*d**2 + 0 - 2/7*d**3 + 2/7*d**4 + 0*d = 0.
0, 1
Factor 41*z**3 - 43*z**3 - 30*z**2 - 2420*z + 144*z**2 + 854*z - 1682.
-2*(z - 29)**2*(z + 1)
Determine x so that -3/2*x**4 - 3/2*x**2 + 0 + 0*x - 3*x**3 = 0.
-1, 0
Let l(n) be the first derivative of n**5/20 - n**3/6 - 8*n - 9. Let i(c) be the first derivative of l(c). Let i(x) = 0. What is x?
-1, 0, 1
Find n such that 81*n**2 + 80*n**2 + 42*n + 12*n - 158*n**2 + 231 = 0.
-11, -7
Let x(h) = 5*h**3 - 12*h**2 - 54*h - 128. Let r(q) = -4*q**3 + 13*q**2 + 61*q + 128. Let k(s) = 6*r(s) + 5*x(s). Factor k(j).
(j + 2)*(j + 8)**2
Let l(d) be the second derivative of 4/3*d**3 + 1/15*d**6 + 14*d + 1/2*d**5 + 4/3*d**4 + 0 + 0*d**2. Factor l(u).
2*u*(u + 1)*(u + 2)**2
Factor 20*v**2 + 20*v**2 - 63*v**3 - v**4 + 2*v**4 - 40*v**2.
v**3*(v - 63)
Suppose -5*k - 11 + 56 = 0. Suppose 4*b - 21 + k = 0. Let 22*y**4 - 28*y**4 - 4*y - 11*y**2 - b*y**2 + 20*y**3 + 8 - 4*y = 0. What is y?
-2/3, 1, 2
Let w(f) be the second derivative of f**4/42 + 4*f**3/21 + 3*f**2/7 - 2*f - 10. Factor w(s).
2*(s + 1)*(s + 3)/7
Factor 5*r**3 - r**5 + 3*r**2 - 6*r + r**5 + 4*r - 4*r**3 + r**5 - 3*r**4.
r*(r - 2)*(r - 1)**2*(r + 1)
Let d(s) be the second derivative of 4*s**5/45 - 11*s**4/36 + s**3/3 + 5*s**2/2 + 8*s. Let w(x) be the first derivative of d(x). What is n in w(n) = 0?
3/8, 1
Find i, given that -10/11 - 28/11*i - 24/11*i**2 - 4/11*i**3 + 2/11*i**4 = 0.
-1, 5
Suppose 4/5*l - 14/15 + 2/15*l**2 = 0. Calculate l.
-7, 1
Let f = -761 - -766. Let m(v) be the second derivative of -2/9*v**3 + f*v + 0 - 1/9*v**4 - 1/60*v**5 + 0*v**2. Factor m(r).
-r*(r + 2)**2/3
Let x be -22 + 196/16 + 10. Factor -1/4*o**2 + x*o**4 + 1/2*o - 1/2*o**3 + 0.
o*(o - 2)*(o - 1)*(o + 1)/4
Let r be 1 - -2 - (-3 - -3). Let h be (-28)/(-12) + r/(-9). Factor 2 + t + 4*t - 8*t**3 + 2*t**4 - 13*t + 12*t**h.
2*(t - 1)**4
Let 6/5 + 3/5*s**4 + 3/5*s**3 - 3/5*s - 9/5*s**2 = 0. Calculate s.
-2, -1, 1
Suppose 1541*r = 1535*r. Let i(v) be the third derivative of 0*v**3 + r*v**6 + 0 + 0*v**4 + 0*v - 1/735*v**7 + 1/210*v**5 - v**2. Factor i(g).
-2*g**2*(g - 1)*(g + 1)/7
Find c, given that -82*c**4 - 59*c**2 + 24*c**5 + 12*c + 113*c**3 + 6*c**4 - 9*c**5 - 5*c**2 = 0.
0, 2/5, 2/3, 1, 3
Let l(i) be the third derivative of -i**7/42 + 13*i**6/12 + 7*i**5 + 215*i**4/12 + 145*i**3/6 + 199*i**2 - 1. Find c, given that l(c) = 0.
-1, 29
Suppose -w + 37*v - 41*v = 14, -14 = -w + 3*v. Factor -9/4*l + 1/2 + 7/4*l**w.
(l - 1)*(7*l - 2)/4
Let w(j) be the first derivative of 2*j**3/51 + 92*j**2/17 + 4232*j/17 - 442. Factor w(b).
2*(b + 46)**2/17
Let n be 148/(-14) - (-8)/14. Let a = 12 + n. Factor -h**a + 3*h**4 - 2*h**3 - 2*h**5 + h**2 + h**4.
-2*h**3*(h - 1)**2
Suppose -2*r = 6*s - 4*s - 4, 2*s + 5*r + 2 = 0. Let q(i) be the second derivative of -3/14*i**2 + 0*i**s - 1/6*i**3 + 1/35*i**5 + 0 - 4*i. Factor q(n).
(n + 1)*(2*n - 3)*(2*n + 1)/7
Let n(v) be the second derivative of v**10/24192 + v**9/2016 - 7*v**4/2 + 41*v. Let s(k) be the third derivative of n(k). Factor s(z).
5*z**4*(z + 6)/4
Suppose -8*m + 5*m + 18 = 0. Let t be (-1 - -1)/(m/3). Let -1/2*i**4 - i - 2*i**3 + t - 5/2*i**2 = 0. Calculate i.
-2, -1, 0
Factor 1/2*y**3 - 2*y + 2 - 1/2*y**2.
(y - 2)*(y - 1)*(y + 2)/2
Let j(a) = 2*a**4 - 7*a**3 - 18*a**2 + 3*a + 10. Let h(q) = 3*q**4 - 10*q**3 - 26*q**2 + 5*q + 14. Let b(p) = 5*h(p) - 7*j(p). Determine s, given that b(s) = 0.
-2, 0, 1, 2
Let a = 4 + -2. What is z in -4 - 2*z**3 - 8*z**a - 6*z**2 + 15 + 13 - 8*z = 0?
-6, -2, 1
Let j(p) be the first derivative of -5*p**3/3 - 5*p**2 + 40*p - 149. Factor j(q).
-5*(q - 2)*(q + 4)
Determine g, given that -2*g**3 + 5/2*g**2 - 6 + 47/2*g = 0.
-3, 1/4, 4
Suppose 5*y = -2*y + 21. Factor 3*o**2 + 229 - 6*o - 229 + 15*o**4 + 24*o**y.
3*o*(o + 1)**2*(5*o - 2)
Suppose -4*a + 3*a = -14. Let x = a + -9. Factor 26*j**2 - 6*j - 5*j**3 - 2*j - 8 - x*j**3.
-2*(j - 2)*(j - 1)*(5*j + 2)
Let z = -35394/5 - -7079. Suppose 1/5 + z*g**2 - 2/5*g = 0. What is g?
1
Let l(j) be the second derivative of -12769*j**4/90 - 452*j**3/45 - 4*j**2/15 - 177*j. Find m such that l(m) = 0.
-2/113
Let l(s) = -s**3 + 4*s**2 + 3. Let g be (2 + -2)/(-3) + 4. Let u be l(g). Factor -6*a**2 + 0*a - 10*a**3 - u*a + 7*a**3.
-3*a*(a + 1)**2
Let w be (-2)/(-30)*9/2. Let l(b) be the first derivative of w*b**2 - 2 + 0*b + 1/5*b**3. Factor l(r).
3*r*(r + 1)/5
Let u(j) be the second derivative of 4 - 1/60*j**6 + 0*j**5 + 0*j**3 - 1/4*j**2 - 2*j + 1/12*j**4. Determine g so that u(g) = 0.
-1, 1
Let h = 63 - 58. Let b(q) be the second derivative of -1/30*q**6 + 1/10*q**h + 0 - 1/42*q**7 + 1/6*q**4 - 1/2*q**2 - 1/6*q**3 + 4*q. Let b(g) = 0. What is g?
-1, 1
Let o(h) be the second derivative of 0 + 0*h**2 + 1/9*h**3 - 23*h + 1/18*h**4. Solve o(v) = 0 for v.
-1, 0
Let y(d) = -d**3 - 12*d**2 + 11*d - 24. Let k be y(-13). Factor -19*t**2 - 2*t**3 + 6*t**2 + 14*t - 20 + 21*t**k.
-2*(t - 5)*(t - 1)*(t + 2)
Let f(k) be the second derivative of -5*k**4/12 + k**3/3 - 4*k - 7. Factor f(t).
-t*(5*t - 2)
Let y(s) be the third derivative of -s**8/3192 - 4*s**7/665 + 29*s**6/570 - 46*s**5/285 + 21*s**4/76 - 16*s**3/57 + 66*s**2 + 2*s. Factor y(k).
-2*(k - 1)**4*(k + 16)/19
Let z be (-2 - 13)/(7/(-3) - -2). Let l be 141/45 + (-6)/z. Factor 0*k**2 - 2/3*k**4 + 0*k - 2/3*k**l + 0.
-2*k**3*(k + 1)/3
Suppose -8*v + 13*v = -1180. Let n = v + 236. Factor n - 2/3*i**2 + 8/3*i**3 + 2*i**4 - 4/3*i.
2*i*(i + 1)**2*(3*i - 2)/3
Let c(p) be the second derivative of -p**2 + 2*p + 0 + 1/6*p**4 + 0*p**3. Factor c(f).
2*(f - 1)*(f + 1)
Let c(x) be the second derivative of -x**5/90 + x**3/27 + 98*x + 1. Factor c(g).
-2*g*(g - 1)*(g + 1)/9
Factor 33*u - 5*u**3 + 181 + 7*u - 241 + 5*u**2.
-5*(u - 2)**2*(u + 3)
Let j(y) be the first derivative of -y**3/21 - 17*y**2/7 - 64*y/7 + 7. Suppose j(u) = 0. Calculate u.
-32, -2
Let u(y) be the first derivative of y**7/126 - y**6/20 + 17*y**5/180 - 2*y**3/9 - 6*y**2 + 38. Let f(w) be the second derivative of u(w). Factor f(s).
(s - 2)*(s - 1)**2*(5*s + 2)/3
Factor -337*s**2 - 9*s**3 + 3*s**5 + 12*s**4 - 51*s + 295*s**2 + 27*s.
3*s*(s - 2)*(s + 1)**2*(s + 4)
Let w(f) be the third derivative of f**7/35 - 119*f**6/180 + 13*f**5/45 + 21*f**2 + 3. Factor w(x).
2*x**2*(x - 13)*(9*x - 2)/3
Let i = 2 + 82. Let p = i - 1258/15. Determine b, given that 4/15*b**2 + 8/15*b - 16/15 - p*b**3 = 0.
-2, 2
Let w(n) be the first derivative of -n**7/42 - n**6/12 + 31*n**2/2 - 1. Let u(p) be the second derivative of w(p). Factor u(c).
-5*c**3*(c + 2)
Let m be (5 - 4)*(-5)/1. Let w = m - -8. Factor -w + 7 + 4*v + 4 + 2*v**2 + 4*v.
2*(v + 2)**2
Factor -1/9*b**3 - 1/9*b**2 + 0*b + 0.
-b**2*(b + 1)/9
Suppose 0*l - g = -3*l + 33, l - 2*g = 16. Let a be (-4)/l - (-216)/90. Factor -3*i + 0*i + 3*i**3 + 0*i**2 - 9 + 9*i**a.
3*(i - 1)*(i + 1)*(i + 3)
Let p(c) be the first derivative of -2*c**4 - 12 + 4*c**2 - 12/5*c**5 + 4*c**3 + 0*c. Let p(w) = 0. Calculate w.
-1, -2/3, 0, 1
Let j(v) be the first derivative of -v**6/540 + v**5/18 - 25*v**4/36 + 14*v**3/3 + 31. Let c(t) be the third derivative of j(t). Determine i so that c(i) = 0.
5
Let g(o) be the first derivative of o**4/26 - 2*o**3/13 - o**2/13 + 6*o/13 + 82. Factor g(x).
2*(x - 3)*(x - 1)*(x + 1)/13
Let u(z) = z**2 + 111*z + 218. Let w be u(-109). Let t = -2040/7 - -292. Factor 0*i + t*i**3 + 0 + 2/7*i**4 - 2/7*i**5 + w*i**2.
-2*i**3*(i - 2)*(i + 1)/7
Let b(a) = -3*a + 10. Let z be b(4). Let q be (-4)/((-40)/25) + 4/z. Suppose -5/8*d - q*d**2 - 1/8*d**3 - 1/4 = 0. What is d?
-2, -1
Let i = 1418 - 1416. Factor -1/2*l**5 - 3*l**4 - 2*l + 0 - 13/2*l**3 - 6*l**i.
-l*(l + 1)**2*(l + 2)**2/2
Let v(s) = 16*s**4 + 8*s**3 + 6*s**2 - 28*s + 16. Let m(l) = -l**4 - l**2 + 2*l - 1. Let u(o) = 36*m(o) + 2*v(o). Find z, given that u(z) = 0.
1
Let z(b) be the third derivative of 0*b + 0*b**3 - 25/84*b**4 - 1/21*b**5 + 5*b**2 - 1/420*b**6 + 0. Factor z(n).
-2*n*(n + 5)**2/7
Let q(b) be the third derivative of -b**8/504 - b**7/63 - b**6/60 + b**5/18 + b**4/9 - 2*b**2 + 3*b. Suppose q(f) = 0. Calculate f.
-4, -1, 0, 1
Let h = -99 - -102. Suppose -3*f - 20 = 5*s, -h*f = -2*s + 3*s + 4. Determine j, given that 4/7*j**4 + 2/7*j**5 - 2/7*j + f + 0*j**3 - 4/7*j**2 = 0.
-1, 0, 1
Let r = 24193/34 + -12054/17. Let 15/4*h**2 + r*h**3 - 5/4*h**4 + 0*h + 0 = 0.