
Solve -1/5*m**3 - 3/5*m**2 + 9/5*m - 1 = 0.
-5, 1
Let t(d) be the third derivative of d**5/90 + 17*d**4/108 + 10*d**3/27 - 61*d**2. Suppose t(z) = 0. What is z?
-5, -2/3
Let r(y) be the first derivative of 3*y**4/20 - y**3/5 - 3*y**2/2 - 9*y/5 + 340. Factor r(n).
3*(n - 3)*(n + 1)**2/5
Let b(l) be the first derivative of 3*l**4/7 + 124*l**3/21 + 170*l**2/7 + 100*l/7 + 198. Determine j so that b(j) = 0.
-5, -1/3
Let b(o) be the third derivative of 2*o**7/105 + 7*o**6/18 + 139*o**5/45 + 71*o**4/6 + 20*o**3 - 229*o**2. Find v, given that b(v) = 0.
-5, -3, -2/3
Let j = -194 - -188. Let u be (-5 + 2)/(j/4). Factor 0 + 36/7*s**3 + 9/7*s**u - 6/7*s + 3*s**4.
3*s*(s + 1)**2*(7*s - 2)/7
Let p = -5/819 + 278/819. Factor 1/3*j**2 + p - 2/3*j.
(j - 1)**2/3
Let i(n) be the third derivative of n**8/560 - n**6/120 - n**3/3 - 4*n**2. Let g(y) be the first derivative of i(y). Find l such that g(l) = 0.
-1, 0, 1
Let j(s) be the first derivative of -s**4/14 + 4*s**3/7 - 9*s**2/7 - 50. Let j(u) = 0. What is u?
0, 3
Let y(k) = k + 5. Let o be y(4). Let h be 45/o - (3 - 1). Factor 5*d**2 + d**5 - 5*d + 3*d**4 - 11*d**2 + h*d + d**3 + 3*d**2.
d*(d - 1)*(d + 1)**2*(d + 2)
Let n be 0 + (-3)/(-3 - -2). Suppose 0 = z + n*z - 2*u - 26, 2*z - 11 = 3*u. Factor z*g + 2*g - 3*g - 6*g**3 + 8*g**3 + 2 + 6*g**2.
2*(g + 1)**3
Let k(n) = 7*n**2 + 5*n - 2. Let s(r) = -7 + 6 - r**2 + 2*r**2. Let d(u) = -4*k(u) + 12*s(u). Factor d(w).
-4*(w + 1)*(4*w + 1)
Let c(g) = g**3 + 6*g**2 - 16*g. Let a(j) = 4*j**2 - 8*j. Let h(v) = 9*a(v) - 4*c(v). Solve h(k) = 0 for k.
0, 1, 2
Let z(h) be the third derivative of h**7/10080 - h**6/2880 - h**5/240 - 5*h**4/12 + 5*h**2. Let m(f) be the second derivative of z(f). Factor m(s).
(s - 2)*(s + 1)/4
Factor 17*i**2 - 290*i - i**2 + 9*i**2 - 120.
5*(i - 12)*(5*i + 2)
Let l = 46 - 51. Let f be 2 - (l + (-20)/(-5)). Let -4/9*o - 2*o**f - 14/9*o**2 - 2/9*o**5 - 10/9*o**4 + 0 = 0. Calculate o.
-2, -1, 0
Let v(u) be the second derivative of u**5/20 + 5*u**4/12 + 2*u**3/3 - u**2 + 2*u. Let n be v(-2). What is i in i**2 - 1 + 3*i**2 - i**n - 2*i - 4*i**2 = 0?
-1
Suppose 4*g + s = 32, -27*g - s = -25*g - 18. Let j be 2/g + (-1253)/(-245) + -5. Solve j + 2/5*d**2 - 4/5*d = 0 for d.
1
Let v(f) be the third derivative of f**7/210 - f**6/20 + f**5/60 + f**4 + 8*f**3/3 + f**2 - 35*f. Factor v(b).
(b - 4)**2*(b + 1)**2
Let g(r) be the first derivative of -3*r**5/5 + 9*r**4/2 - 8*r**3 - 628. Factor g(m).
-3*m**2*(m - 4)*(m - 2)
Let t(w) be the second derivative of -2/5*w**2 - 11*w + 2/15*w**3 - 1/150*w**6 + 1/20*w**4 + 0 - 1/50*w**5. Factor t(n).
-(n - 1)**2*(n + 2)**2/5
Let r be ((-3)/(-6))/((-2)/(-12)) + 0. Let d be ((-2)/12)/(r/(-27)). Factor d*j**2 - 1/4*j + j**4 + 0 - 9/4*j**3.
j*(j - 1)**2*(4*j - 1)/4
Factor 1/4*l**4 + 0*l**2 - 1/4*l**3 + 0 + 0*l.
l**3*(l - 1)/4
Suppose -21 = -2*v + 3*k, 5*k - 1 + 11 = -5*v. Determine x so that -x**v + 4*x**4 - 1 - 4*x + 3*x**3 + 3*x**5 - 6*x**2 - x + 3*x**4 = 0.
-1, -1/3, 1
Let a(n) = 4*n - 70. Let y be a(18). Suppose 2*c + y*f - 10 = -0*f, 2*f = 6. Suppose -1/2*g**c + 0 + 1/2*g**3 + 0*g = 0. What is g?
0, 1
Let d be (-3388)/(-1078) + (-24)/21. Let 22/9*q**3 - 26/9*q**d + 4/9*q + 0 = 0. What is q?
0, 2/11, 1
Let 4/5*q**4 + 0*q - 2/5*q**3 - 4/5*q**2 + 2/5*q**5 + 0 = 0. Calculate q.
-2, -1, 0, 1
Let v(q) be the second derivative of -16/33*q**3 - 14*q - 7/165*q**6 + 0 - 4/11*q**2 - 1/231*q**7 - 19/110*q**5 - 25/66*q**4. Factor v(h).
-2*(h + 1)**3*(h + 2)**2/11
Let h(o) be the third derivative of 3/100*o**5 + 1/560*o**8 + 0 + 0*o**3 + 0*o - 3/350*o**7 - 1/20*o**4 + 1/200*o**6 + 12*o**2. Find r, given that h(r) = 0.
-1, 0, 1, 2
Let f(y) = -y**3 - 2*y**2 + 2*y + 1. Let q be f(-3). Suppose -10 = -q*d + 6. Solve u**4 - u**d - 8*u**3 + 4*u**5 + u**4 + 3*u**4 = 0 for u.
-2, 0, 1
Let f(i) = 2*i**3 - 14*i - 12. Let l(p) be the third derivative of -p**6/20 + 7*p**4/4 + 6*p**3 + 5*p**2. Let q(x) = 8*f(x) + 3*l(x). Factor q(h).
-2*(h - 3)*(h + 1)*(h + 2)
Let g(d) be the second derivative of -d**7/105 - d**6/75 + d**5/10 + d**4/30 - 8*d**3/15 + 4*d**2/5 - 107*d + 1. Factor g(m).
-2*(m - 1)**3*(m + 2)**2/5
Solve -3/8*q**5 + 3/4*q**4 - 3*q**2 + 9/8*q**3 + 3/2*q + 0 = 0.
-2, 0, 1, 2
Let b(q) be the second derivative of -9*q**5/160 + 29*q**4/32 - 39*q**3/8 + 15*q**2/2 - 612*q. Suppose b(m) = 0. What is m?
2/3, 4, 5
Let t = 44519 + -133552/3. Solve t*a**2 + 0*a - 10/3*a**3 + 0 + 5/3*a**4 = 0 for a.
0, 1
Let g(o) be the first derivative of -o**3/3 - 13*o**2 - 18*o + 10. Let x be g(-19). Factor 21*t + 29*t + 5*t**2 + 10 + x.
5*(t + 5)**2
Let 27/7*t**3 - 60/7*t**2 - 3/7*t**4 + 36/7*t + 0 = 0. What is t?
0, 1, 2, 6
Let b(x) = -8*x**3 + 174*x**2 + 47*x - 62. Let s be b(22). Solve 28/15*m - 2/5*m**s + 2/5 + 32/15*m**2 + 4/15*m**3 = 0.
-1, -1/3, 3
Let u(i) = -5*i**2 - 13*i + 11. Let m(s) = -4*s**2 - 8*s + 3. Let f(x) = -x**2 - x - 1. Let n(j) = -2*f(j) + m(j). Let y(p) = 7*n(p) - 3*u(p). Factor y(l).
(l - 2)*(l - 1)
Let h be (8/(-2))/(-1) + 1. Let i(m) = -8*m**4 + 10*m**2 - 8. Let z(v) = -4 - 1 - 2 - 7*v**4 - 22*v**2 + 31*v**2. Let f(k) = h*i(k) - 6*z(k). Factor f(x).
2*(x - 1)**2*(x + 1)**2
Let w(q) be the first derivative of -q**5 - 6*q**4 - 10*q**3/3 + 24*q**2 - 9*q - 46. Let w(l) = 0. Calculate l.
-3, 1/5, 1
Let o(v) be the first derivative of 5/12*v**4 - 10/3*v**3 - 40/3*v + 27 - 25/2*v**2. Find c, given that o(c) = 0.
-1, 8
Let s = -641 - -641. What is m in -4/5*m**2 + 6/5*m + 2/5*m**5 - 8/5*m**3 + s*m**4 + 4/5 = 0?
-1, 1, 2
Let r(z) be the second derivative of 0 + 1/70*z**6 - 26*z - 6/35*z**5 + 15/28*z**4 - 24/7*z**2 + 4/7*z**3. Find v such that r(v) = 0.
-1, 1, 4
Let q be 3/14*9/((-90)/(-16)). Let c = 524/105 + q. Factor c*p**2 + 0 + 2/3*p + 44/3*p**3 + 6*p**5 + 16*p**4.
2*p*(p + 1)**2*(3*p + 1)**2/3
Let s(o) = -32*o**3 + 40*o**2 - 8*o. Let z(w) = 15*w**2 + 57*w**2 - 65*w**3 + 19*w - 35*w + 9*w**2. Let d(m) = 9*s(m) - 4*z(m). Factor d(j).
-4*j*(j - 1)*(7*j - 2)
Let h(v) be the third derivative of v**5/90 + 29*v**4/36 - 62*v**3/9 - 184*v**2. Factor h(z).
2*(z - 2)*(z + 31)/3
Let v(k) be the first derivative of k**5/30 - 5*k**4/8 + 11*k**3/3 - 29*k**2/3 + 12*k + 63. Factor v(x).
(x - 9)*(x - 2)**3/6
Let c(k) be the third derivative of k**7/210 - k**6/30 + k**5/20 - 129*k**2. Find z, given that c(z) = 0.
0, 1, 3
Let -x**5 - 78*x**2 + 6*x**3 - 2*x**5 + 39*x**4 - 293 - 3*x + 332 = 0. Calculate x.
-1, 1, 13
Let v be 20/(-30) - (-2)/3. Solve v*b**2 + 1 + 2*b**2 + 3*b + 2*b + 2*b**2 = 0.
-1, -1/4
Let x(j) = j**3 + j + 1. Let r(b) = -3*b**3 + b**3 + 2*b**3 + 4 - 6*b**2 + 2*b**3. Let q(i) = -r(i) + 4*x(i). Factor q(y).
2*y*(y + 1)*(y + 2)
Let w be ((-28)/(-5))/(16/120). Determine a so that -w*a - 23*a + 6*a**2 - 5*a**3 - a**2 + 75*a = 0.
-1, 0, 2
Let i be 2 - (2 - (-4)/(-2)). Suppose -2*o + i = -4. Solve -4*j**5 + j**2 - 1 - j**4 + 3*j**3 + j**2 + 3*j**5 - j**o - j = 0 for j.
-1, 1
Factor -30*z**2 + 144*z**3 + 154*z**2 - 65*z**2 + 108*z + 157*z**2 + 4*z**5 + 40*z**4.
4*z*(z + 1)*(z + 3)**3
Let z be 148/259 - 25/56. Factor -1/2*p**2 - 5/8*p - z*p**3 - 1/4.
-(p + 1)**2*(p + 2)/8
Determine b, given that -3*b - 99*b**4 - 15*b**2 + 98*b**4 + 7*b**3 + 18 + 2*b**2 = 0.
-1, 2, 3
Let t(d) be the third derivative of d**7/490 + d**6/280 - d**5/140 - d**4/56 + 36*d**2 - d. What is n in t(n) = 0?
-1, 0, 1
Let j = -601/21 - -201/7. Let a(f) be the first derivative of -2 + j*f**3 + 0*f**2 + 0*f + 1/7*f**4. Factor a(q).
2*q**2*(2*q + 1)/7
Let x(c) be the third derivative of c**8/224 - 51*c**7/560 - 17*c**6/320 + 51*c**5/160 + 13*c**4/64 + 64*c**2. Let x(d) = 0. What is d?
-1, -1/4, 0, 1, 13
Let d(y) be the third derivative of 1/45*y**5 + 0 - 7/180*y**6 - 2/9*y**3 + 0*y - 6*y**2 + 7/36*y**4. Factor d(j).
-2*(j - 1)*(j + 1)*(7*j - 2)/3
Let c(f) = f**3 - 4*f**2 + 4*f - 1. Let l be c(3). Let a = -72 + 75. Factor 3*k + k**3 - k**3 - k**a - l*k**3.
-3*k*(k - 1)*(k + 1)
Let q(i) be the third derivative of 5*i**8/1344 - i**7/42 + i**6/36 + 5*i**4/12 + 2*i**2. Let a(h) be the second derivative of q(h). Let a(v) = 0. What is v?
0, 2/5, 2
Let d(j) = 61*j**2 - 158*j + 5770. Let p(f) = -112*f**2 + 315*f - 11541. Let l(v) = -11*d(v) - 6*p(v). Factor l(u).
(u - 76)**2
Let b(c) = -5*c**2 - 46*c + 45. Let d(q) = 2*q**2 + 15*q - 15. Let u(h) = -3*b(h) - 8*d(h). Let m be u(17). Factor