Calculate i.
0, 3
Suppose 0 = 2*x - j + 3, 3*x = -x - 4*j. Let c be x/9*(-180)/15. Factor -2/3*k**3 - 2/9*k - c + 20/9*k**2.
-2*(k - 3)*(k - 1)*(3*k + 2)/9
Let v(z) be the first derivative of -z**6/4 + 6*z**5/5 + 33*z**4/8 - 13*z**3 - 48*z**2 - 48*z + 327. Determine m, given that v(m) = 0.
-2, -1, 4
Let h(t) = 6*t**2 - 24*t - 10. Let m(d) = -2*d - 1. Let f(r) = -h(r) + 10*m(r). Factor f(s).
-2*s*(3*s - 2)
Let o(s) be the second derivative of s**7/840 + s**6/72 - s**3/6 + 9*s. Let j(u) be the second derivative of o(u). Factor j(a).
a**2*(a + 5)
Determine t so that 10*t**2 - 30/7*t**3 + 2/7*t**5 - 48/7 - 22/7*t**4 + 4*t = 0.
-2, -1, 1, 12
Let d(n) = -n**3 - 9*n**2 + 6*n + 4. Let v(r) = 1 - 10*r**2 + 4 + 7*r - 2*r. Let j(p) = 5*d(p) - 4*v(p). Factor j(b).
-5*b*(b - 1)*(b + 2)
Suppose 0 = 4*k + 4*g - 3 + 15, -4*k + 2*g + 6 = 0. Let o(r) be the first derivative of 1/6*r**4 - 1/15*r**5 + 1 + k*r - 1/9*r**3 + 0*r**2. Factor o(s).
-s**2*(s - 1)**2/3
Suppose -14 - 28 = -16*n + 6. Factor 2/3*h - 1/3*h**n - 1/3*h**2 + 0.
-h*(h - 1)*(h + 2)/3
Let g(s) be the second derivative of -s**4/18 - 11*s**3/15 - 28*s**2/15 - s + 21. Factor g(x).
-2*(x + 1)*(5*x + 28)/15
Suppose -5*d - 36 = q, 2*d + 3*d = -5*q - 180. Let a = -32 - q. Solve -3*m**2 + 8*m**a + 4*m - 2 - 5*m**2 + 2 - 4*m**5 = 0 for m.
-1, 0, 1
Let v = 69 - 34. Let a = v + -32. Factor 1 - y**a + 4*y**2 + 3 - 4*y**2 - 3*y**2.
-(y - 1)*(y + 2)**2
Let u(r) be the second derivative of 6*r**3 + 3/20*r**5 - 3/2*r**4 + 0 + 6*r - 12*r**2. Solve u(h) = 0 for h.
2
Let y = -13 + 13. Suppose 4*d = j - 15, 2*d + 3 = -y*j - j. Determine z so that 0*z - 2*z**j + 9*z**2 - 2*z - 5*z**2 = 0.
0, 1
Let v(j) be the second derivative of j**4/42 + 4*j**3/21 + 3*j**2/7 + 56*j. Suppose v(x) = 0. Calculate x.
-3, -1
Factor 44*l + 0*l**2 + 2*l**3 + 22*l - 30 - 34*l**2 - 4*l.
2*(l - 15)*(l - 1)**2
Let i(f) be the third derivative of -f**4/24 + 7*f**3/2 - 11*f**2. Let x be i(21). Suppose x - 1/2*r**2 - 1/4*r**3 - 1/4*r = 0. Calculate r.
-1, 0
Let t be (-50)/(-8)*((-184)/(-1035) + 12/54). Suppose 0 + t*k**3 + 5*k**4 + 0*k**2 + 0*k + 5/2*k**5 = 0. Calculate k.
-1, 0
Let t(i) be the second derivative of -i**4/16 + 9*i**3/8 + 27*i**2/2 + 197*i. Factor t(l).
-3*(l - 12)*(l + 3)/4
Let d(v) be the third derivative of 1/30*v**5 + 5/6*v**4 + 0 + 25/3*v**3 + 5*v**2 + 0*v. Factor d(m).
2*(m + 5)**2
Let q be 8/3 + (-1 + -1)/(-6). Factor 2*w - w + 2 + 2*w**2 - q*w**2.
-(w - 2)*(w + 1)
Suppose 2*v - 11 = 5. Let c be 5 - (-4)/v*2. Factor 3*b**4 + 0*b**2 - c*b**2 + 6*b**3 + 2*b - 5*b**4.
-2*b*(b - 1)**3
Let p be ((-1)/(-2))/((-103)/(-824)). Let c(t) be the third derivative of -1/90*t**6 + 0*t - 1/72*t**p - 10*t**2 + 0 + 0*t**3 + 1/36*t**5. Solve c(r) = 0.
0, 1/4, 1
Let t(b) = -b**2 + b + 3. Let s be t(3). Let q be ((-4)/s)/(-2 - (-80)/15). Factor 0*n - 1/5*n**4 + 0 + q*n**2 + 1/5*n**3.
-n**2*(n - 2)*(n + 1)/5
Let v(t) = -t**2 + 4*t + 26*t**3 + 6*t**2 + 15*t**4 + 2*t. Let d(b) = -60*b**4 - 105*b**3 - 20*b**2 - 25*b. Let c(x) = 6*d(x) + 25*v(x). Solve c(q) = 0.
-1, -1/3, 0
Let p = 140/73 - 487/292. Determine y, given that -3/4*y**3 - 1/4*y**4 + 0 + 3/4*y + p*y**2 = 0.
-3, -1, 0, 1
Let p(x) = -2*x**2 + 13*x - 4. Let r be p(6). Let v(q) be the first derivative of 0*q**3 - 1/6*q**4 + 1/3*q**r + 1/15*q**5 - 1/3*q - 4. Factor v(a).
(a - 1)**3*(a + 1)/3
Suppose 7*s + 4 - 32 = 0. Find p, given that 8 + 5*p**2 - s*p - 10*p**2 + p**2 = 0.
-2, 1
Let m be (-60)/(-24)*6*(0 - -1). What is k in 13 + 13*k**2 + m*k - 10*k**2 + 5 = 0?
-3, -2
Factor 476680*p**2 - 476700*p**2 - 125*p - 36 + 6.
-5*(p + 6)*(4*p + 1)
Suppose 2 = -2*d + 4*p + 22, -3*d + 5*p + 32 = 0. What is n in -16*n - d*n**2 + 2*n**3 + 22*n + 26*n - 24 = 0?
2, 3
Let r = -427/18 + -101/18. Let y = 30 + r. Factor -y*c + 2/9*c**2 + 0.
2*c*(c - 3)/9
Suppose 324 = -81*x + 869 - 302. What is l in -1/3*l**5 + 0*l + 0 - 2/3*l**4 + 0*l**2 - 1/3*l**x = 0?
-1, 0
Let k(d) = 9*d**2 + 67*d + 138. Let j(i) = -125*i**2 - 940*i - 1930. Let g(y) = -4*j(y) - 55*k(y). Factor g(b).
5*(b + 2)*(b + 13)
Suppose 4*n - 5 = 39. Suppose 2*k + 2*k + 2*v + 2 = 0, 0 = -2*k - 3*v - n. Find o, given that 2*o**k - 6*o + 8*o + 0*o**2 = 0.
-1, 0
Let k(i) = 9*i**4 + 25*i**3 + 54*i**2 - 89*i - 161. Let s(x) = x**4 + 3*x**3 + 7*x**2 - 11*x - 20. Let w(u) = -6*k(u) + 51*s(u). Suppose w(y) = 0. Calculate y.
-3, -1, 2, 3
Let w be 3922/2960 - (-45)/(-40). Let 0*o + 0 + 1/5*o**3 - 1/5*o**4 - 1/5*o**5 + w*o**2 = 0. Calculate o.
-1, 0, 1
Let m(c) be the second derivative of 5/2*c**2 - 10*c - 5/48*c**4 - 5/8*c**3 - 1. Factor m(x).
-5*(x - 1)*(x + 4)/4
Let c(a) be the third derivative of a**7/70 + 3*a**6/20 - 27*a**5/20 + a**4/2 + 18*a**3 + a**2 - 4. Determine f, given that c(f) = 0.
-9, -1, 2
Let i(k) = 1. Let b(h) be the second derivative of -h**4/12 - 2*h**3/3 + 3*h**2 + 10*h. Let s(u) = -b(u) + 6*i(u). Factor s(j).
j*(j + 4)
Let t(n) = 10*n**5 - 6*n**4 - 14*n**3 - 66*n**2 - 20*n - 16. Let s(y) = 2*y**5 - y**4 - 3*y**3 - 13*y**2 - 4*y - 3. Let v(b) = -16*s(b) + 3*t(b). Factor v(h).
-2*h*(h - 2)*(h + 1)**3
Let n(p) be the second derivative of p**5/90 + p**4/27 - p**3/27 - 2*p**2/9 - 164*p. Factor n(a).
2*(a - 1)*(a + 1)*(a + 2)/9
Suppose 0 = 5*o - 3*z + 12, -3*z = -15 + 3. Factor 0*i**4 - 4/7*i**3 + 2/7*i + o*i**2 + 0 + 2/7*i**5.
2*i*(i - 1)**2*(i + 1)**2/7
Let a = -317 + 2857/9. Solve 10/9*u - 10/9*u**3 + 4/9*u**2 - a = 0 for u.
-1, 2/5, 1
Let c = -33 - 42. Let x be -4 + (-5)/(c/85). Find z, given that 4/3*z**2 - 1/3*z**3 + 2/3 - x*z = 0.
1, 2
Let s(w) be the second derivative of w**6/6 - 31*w**5/4 - 40*w**4/3 + w - 10. Let s(q) = 0. Calculate q.
-1, 0, 32
Let o = 214 + -214. Suppose 23*h - 37 - 9 = o. Find j, given that -20/13*j - 2/13*j**h - 50/13 = 0.
-5
Factor 4*p**2 - 34*p - 22*p + 3*p**2 - 9*p**2 + 4*p**2.
2*p*(p - 28)
Let n(o) be the third derivative of o**6/240 - 2*o**2. Determine h, given that n(h) = 0.
0
Let o(s) be the third derivative of -1/16*s**4 + 0*s - 1/120*s**5 + 20*s**2 + 0*s**3 + 0. Factor o(r).
-r*(r + 3)/2
Let d(n) be the second derivative of 1/8*n**3 + 1/8*n**2 + 1/16*n**4 - 17*n + 1/80*n**5 + 0. Determine t so that d(t) = 0.
-1
Let a(y) = -81*y**2 + 1089*y + 1203. Let k(t) = -5*t**2 + 68*t + 75. Let m(u) = 2*a(u) - 33*k(u). Find n, given that m(n) = 0.
-1, 23
Let i(t) be the second derivative of -4/15*t**3 + 3/2*t**2 + 0 - 1/600*t**6 + t - 1/50*t**5 - 1/10*t**4. Let a(u) be the first derivative of i(u). Factor a(q).
-(q + 2)**3/5
Let r(n) = -337*n + 8090. Let v be r(24). Factor 0*d + 2/9*d**v - 2/9.
2*(d - 1)*(d + 1)/9
Let a(l) be the first derivative of 3*l**4/32 - 11*l**3/4 + 171*l**2/16 + 176. Let a(t) = 0. Calculate t.
0, 3, 19
Let x(v) be the second derivative of 3/100*v**5 - 9/10*v**2 + 25*v + 0 - 1/2*v**3 - 1/20*v**4. What is t in x(t) = 0?
-1, 3
Suppose 0 = 3*d, -3*d + 0*d = -2*p + 18. Suppose -p*j + 8 = -7*j. Factor -s**j - 2*s**3 - 4*s**2 + 3*s**2 + 0*s**3.
-s**2*(s + 1)**2
Let a(m) be the first derivative of -3*m**3/5 + 6*m**2 - 36*m/5 + 100. Suppose a(x) = 0. Calculate x.
2/3, 6
Suppose -2*b - 5*s + 7 = 2*b, 5*b - s = -13. Let x be (12/15)/b*6/(-4). Factor 3/5 - 6/5*n + x*n**2.
3*(n - 1)**2/5
Factor -13/2 - 1/4*h**2 - 15/4*h.
-(h + 2)*(h + 13)/4
Let s(r) be the third derivative of r**6/540 + 2*r**5/135 + r**4/108 - 2*r**3/9 - 147*r**2. Factor s(x).
2*(x - 1)*(x + 2)*(x + 3)/9
Factor -112*p**2 - 920/7*p**3 + 0 - 160/7*p + 100/7*p**4.
4*p*(p - 10)*(5*p + 2)**2/7
Let o(d) be the third derivative of 12*d**2 + 0*d - 5/168*d**4 - 1/7*d**3 + 1/420*d**5 + 0. Factor o(z).
(z - 6)*(z + 1)/7
Let c(m) be the second derivative of 8/15*m**3 - 1/30*m**4 - 39*m + 0 - 16/5*m**2. Factor c(g).
-2*(g - 4)**2/5
Suppose -4*b - 10 = -6*b. Solve 404 - 404 - k**3 + k**b = 0.
-1, 0, 1
Let n(w) be the third derivative of -w**8/26880 + w**6/960 + w**5/240 + 3*w**4/4 - 3*w**2. Let r(h) be the second derivative of n(h). Factor r(u).
-(u - 2)*(u + 1)**2/4
Find a, given that -2/9*a**3 + 8/9*a + 0 - 2/9*a**4 + 8/9*a**2 = 0.
-2, -1, 0, 2
Let p be (-3116)/(-13325) - (44/(-75) - (-10)/15). Factor -4/13*b + 2/13 + p*b**2.
2*(b - 1)**2/13
Let q(z) = z - 23 + 23. Let a(r) = -r**3 + 2*r**2 + 5*r - 2. Let s(x) = -a(x) + 4*q(x). Find l such that s(l) = 0.
-1, 1, 2
Let r = 10146 - 10142. Factor -3/4*z**5 + 0*z - 9/4*z**3 + 9/4*z**r + 3/4*z**2 + 0.
