4
Let p = 43 - 41. Suppose -3*t**p + 5*t**4 - 3*t - 4*t**4 + t = 0. Calculate t.
-1, 0, 2
Let b(v) be the first derivative of -v**3/24 + 3*v**2/16 - v/4 - 475. Factor b(d).
-(d - 2)*(d - 1)/8
Suppose 12*m = -3*z - 12, -5*m - 17 + 5 = 3*z. Suppose -2/9*j**2 + m*j + 8/9 = 0. What is j?
-2, 2
Let 2*k**3 - 18*k**3 - 33*k - 1540*k**2 + 1468*k**2 - 4 = 0. What is k?
-4, -1/4
Let p = 39860/7 + -5694. Factor 8/7*u**2 + 4/7 - 10/7*u - p*u**3.
-2*(u - 2)*(u - 1)**2/7
Let o(d) be the second derivative of 5*d**4/48 - 35*d**3/2 - 425*d**2/8 - 26*d. Factor o(g).
5*(g - 85)*(g + 1)/4
Factor -106/5*a + 18/5*a**3 + 4 + 68/5*a**2.
2*(a - 1)*(a + 5)*(9*a - 2)/5
Let a(i) be the third derivative of 3/350*i**7 - 3/100*i**5 + 0 + 0*i**3 + 0*i - 12*i**2 - 1/300*i**6 + 1/60*i**4. Factor a(q).
q*(q - 1)*(q + 1)*(9*q - 2)/5
Let n(q) be the second derivative of q**6/6 + 7*q**5/10 + 7*q**4/12 - q**3/3 + 4*q + 22. Factor n(x).
x*(x + 1)*(x + 2)*(5*x - 1)
Let r(d) be the first derivative of d**4/4 - 10*d**3/3 + 5*d + 5. Let q be r(10). Solve 2*n**3 - q*n**3 + 6*n**2 + 0*n**3 = 0.
0, 2
Let a = 1357/1092 - -33/364. Factor 8/3*n - a*n**4 - 8/3*n**3 + 4/3 + 0*n**2.
-4*(n - 1)*(n + 1)**3/3
Let d(g) = -g**3 + 5*g**2 + 4*g + 15. Let y be d(5). Let r be (-28)/y + (-12)/(-15). Determine a so that 0*a**3 + r*a**2 - 3/2*a**5 + 0*a + 0 + 3/2*a**4 = 0.
0, 1
Let n(m) be the first derivative of 4*m**5/5 - 10*m**4 + 48*m**3 - 108*m**2 + 108*m + 292. Solve n(z) = 0.
1, 3
Let 1/3*c**2 + 2 + 5/3*c = 0. Calculate c.
-3, -2
Suppose u = s - 8, -7 - 5 = 3*u. Let p(r) = -18*r - 16. Let a be p(-1). Suppose 2*k**s + 4/5*k**a + 14/5*k**3 + 0*k + 0 = 0. What is k?
-1, -2/5, 0
Factor -33768*a**4 + 16888*a**4 - 2*a**3 + 16882*a**4 - 2*a**2 + 2*a**5.
2*a**2*(a - 1)*(a + 1)**2
Let i(u) be the second derivative of 125/2*u**2 + 25/3*u**3 + 0 + 5/12*u**4 - 12*u. Determine h so that i(h) = 0.
-5
Let u(j) = j**5 + j**4 - j**2 - j. Let a(h) = -33*h**5 - 105*h**4 - 60*h**3 + 6*h**2 - 6*h. Let q(l) = -a(l) + 6*u(l). Find b, given that q(b) = 0.
-2, -1, 0, 2/13
Let i(j) = -3*j**2 + 2*j**2 - 3*j - 21 + 22 + 2*j. Let v(t) = 6*t**2 - 12*t + 28. Let m(f) = 4*i(f) + v(f). Factor m(c).
2*(c - 4)**2
Let r(h) be the third derivative of h**5/30 + 97*h**4/6 + 9409*h**3/3 + 255*h**2. Solve r(s) = 0 for s.
-97
Suppose 0 = 4*v - 9*v - 30. Let f = 10 + v. Factor 15*y - 2 - 3*y**2 + f*y**2 - 1 - 17*y.
(y - 3)*(y + 1)
Let i(c) be the second derivative of -c**7/357 - c**6/255 + 63*c**5/170 - 81*c**4/34 + 90*c**3/17 + c - 127. Solve i(d) = 0 for d.
-10, 0, 3
Let d(h) = 1345*h + 5380. Let i be d(-4). What is c in 0*c**2 - 4/7*c**3 + i - 2/7*c**4 + 0*c = 0?
-2, 0
Let d(i) be the first derivative of i**4/2 + 28*i**3/3 + 13*i**2 + 450. Factor d(r).
2*r*(r + 1)*(r + 13)
Let c(z) = -6*z**2 - 3*z + 4. Let a(j) = -7*j**2 - 2*j + 3. Let s(l) = 5*a(l) - 6*c(l). Find n, given that s(n) = 0.
-9, 1
Let l(z) = 5*z**3 - 67*z**2 + 170*z. Let r be l(10). Factor 0*y**3 + 8/15*y**4 + 0*y + 2/15*y**5 + 0 + r*y**2.
2*y**4*(y + 4)/15
Let o(h) be the third derivative of 0*h**3 + 0*h - 1/20*h**5 + 0*h**4 - 1/40*h**6 + 1/112*h**8 + h**2 + 1/70*h**7 + 0. Suppose o(d) = 0. What is d?
-1, 0, 1
Let h(j) be the third derivative of -j**7/840 + 47*j**6/480 - 11*j**5/15 + 43*j**4/24 - j**2 + 406*j. Determine f, given that h(f) = 0.
0, 2, 43
Let p(x) = -12*x**5 + 16*x**4 + 28*x**3 - 256*x**2 + 452*x - 252. Let f(k) = 2*k**5 + k**3 - k - 1. Let y(l) = 4*f(l) + p(l). Determine n so that y(n) = 0.
-4, 2
Suppose 16*b - 4*b - 36 = 0. Let h(l) be the first derivative of -32*l - 8*l**2 + 6 - 2/3*l**b. Factor h(s).
-2*(s + 4)**2
Let w = -1165 + 1167. Factor 2/5*k + 2/5*k**3 - 4/5*k**w + 0.
2*k*(k - 1)**2/5
Suppose 0 = 3*g, 7 - 3 = 2*p + g. Suppose -2*k + 2*s = -3*k, -k + p*s = 0. Suppose k*x - 3*x + 52*x**3 - 49*x**3 = 0. Calculate x.
-1, 0, 1
Let w(h) = -2*h**2 + 3*h**2 - h**2 + h**2 - 3*h - 2. Let y be w(4). Factor -21 - 3*c**y - 10 + 12*c + 12*c - 17.
-3*(c - 4)**2
Let h(v) be the first derivative of -2*v**7/21 + 4*v**6/15 - v**5/5 - 13*v - 20. Let x(a) be the first derivative of h(a). Determine s, given that x(s) = 0.
0, 1
Suppose 183*f = 246 + 486. Solve 1/2*z**5 + z**2 - 1/2*z + 0*z**3 + 0 - z**f = 0.
-1, 0, 1
Let 1/6*f**5 - 31/6*f**2 + 0*f + 0 - 61/6*f**3 - 29/6*f**4 = 0. What is f?
-1, 0, 31
Let o(n) be the third derivative of n**6/360 - n**5/120 + 2*n**3/3 - 17*n**2. Let l(v) be the first derivative of o(v). Let l(a) = 0. What is a?
0, 1
Suppose -36*y = -23*y - 39. Let 9/5*r**2 + 9/5*r**y + 0 + 3/5*r**4 + 3/5*r = 0. What is r?
-1, 0
Factor 6/5 + 3/5*m**3 + 4/5*m**2 - 13/5*m.
(m - 1)*(m + 3)*(3*m - 2)/5
Let o(a) be the third derivative of a**6/200 + 3*a**5/25 + 11*a**4/40 - 39*a**2 - 4*a. What is x in o(x) = 0?
-11, -1, 0
Suppose h - 17 = -3*v, 0 = h - 2*v + 3*v - 19. Let 4*z**2 - h + 19*z - 12*z + 0*z + 9*z = 0. Calculate z.
-5, 1
Let m(b) be the third derivative of 1/6*b**4 + 0*b**5 + b + 0 + 0*b**7 - 1/15*b**6 + 11*b**2 + 0*b**3 + 1/84*b**8. Factor m(d).
4*d*(d - 1)**2*(d + 1)**2
Let k(h) be the third derivative of 1/140*h**5 - 1/14*h**3 - 10*h**2 + 0*h**4 + 0*h + 0. Factor k(z).
3*(z - 1)*(z + 1)/7
Let p(s) be the first derivative of s**6/120 + s**5/20 + s**4/8 - 22*s**3/3 - 26. Let r(u) be the third derivative of p(u). Factor r(i).
3*(i + 1)**2
Let j(c) be the first derivative of -c**4/16 - 5*c**3/12 + 71. Factor j(h).
-h**2*(h + 5)/4
Let c(b) be the second derivative of b**5/4 + 35*b**4/12 - 5*b**3/6 - 45*b**2/2 + 17*b. Let q(j) = -j**3 + j + 1. Let k(z) = c(z) + 10*q(z). Factor k(x).
-5*(x - 7)*(x - 1)*(x + 1)
Let v(o) be the second derivative of -o**4/42 - 2*o**3/21 + 20*o + 3. Factor v(s).
-2*s*(s + 2)/7
Let l(g) be the third derivative of g**6/120 - 2*g**5/15 + 17*g**4/24 - 5*g**3/3 + 447*g**2. Factor l(d).
(d - 5)*(d - 2)*(d - 1)
Suppose -u = -4*u - 51. Let o(x) = -23*x**3 - 43*x**2 - 89*x + 432. Let f(s) = 8*s**3 + 14*s**2 + 30*s - 144. Let d(k) = u*f(k) - 6*o(k). Factor d(v).
2*(v - 2)*(v + 6)**2
Let s = 98/185 + -24/185. Factor 1/5*l + 1/5*l**3 + 0 - s*l**2.
l*(l - 1)**2/5
Let a = -48092/3 - -16031. Let 1/6*h**3 - 1/6*h - 1/3*h**2 + a = 0. What is h?
-1, 1, 2
Let v be (1/95)/(439/223890). Factor 28/19 + 14/19*n**2 - v*n.
2*(n - 7)*(7*n - 2)/19
Let u(h) = 2*h**3 - h**2 + 3. Let v(w) = w**2 - 1. Let g(o) = 2*o + 2. Let d be g(-2). Let p(q) = d*u(q) - 6*v(q). Factor p(m).
-4*m**2*(m + 1)
Let s(k) be the second derivative of 8/9*k**4 + 77/9*k**3 + 1/30*k**5 + 98/3*k**2 + 23*k + 0. Let s(b) = 0. Calculate b.
-7, -2
Let x = -12 - -16. Find s such that -3*s**3 + 9*s**3 + 0*s**x - 13*s**2 - 6*s - 2*s**4 + 11*s**2 + 4 = 0.
-1, 1, 2
Let c(s) be the second derivative of -s**6/135 - 11*s**5/90 - 4*s**4/9 + 4*s**3/3 + 2*s - 30. Determine u so that c(u) = 0.
-6, 0, 1
Let k(r) = 386*r - 18422. Let n(x) = -x**2 - 1545*x + 73683. Let j(t) = -9*k(t) - 2*n(t). Factor j(i).
2*(i - 96)**2
Let i be (-8)/(-1) + (-11 - -5). Solve 0 - 1/8*o**i + o = 0 for o.
0, 8
Let w(n) be the first derivative of -n**4/6 - 28*n**3/9 + 5*n**2 + 450. Factor w(s).
-2*s*(s - 1)*(s + 15)/3
Suppose 16*j - 14 = 9*j. Suppose -4*i = -126 + 18. Determine y, given that y**2 - 6*y**2 + j*y**2 - 18*y - i = 0.
-3
Let v be (-10)/2 - ((-1023)/77 - -8). Factor 0*q**3 + v*q**4 - 6/7*q**2 + 4/7*q + 0.
2*q*(q - 1)**2*(q + 2)/7
Let i(k) be the first derivative of -k**5/210 + k**3/21 - 16*k**2 - 44. Let b(u) be the second derivative of i(u). Factor b(w).
-2*(w - 1)*(w + 1)/7
Let z(h) = 2*h + 5. Let l(j) = j**2 + 3*j + 6. Let x(y) = -5*l(y) + 6*z(y). Let q(k) = k**3 - 11*k**2 - 7*k. Let r(s) = 3*q(s) - 7*x(s). Factor r(t).
t**2*(3*t + 2)
Let a(h) be the third derivative of -h**8/16 - 6*h**7/35 + h**6/10 + 7*h**5/10 + 3*h**4/8 - h**3 - 69*h**2. What is q in a(q) = 0?
-1, 2/7, 1
Suppose -129*r**2 - 3*r**3 - 54 + 162*r**2 - r**4 + 27*r - 2*r**4 = 0. Calculate r.
-3, -2, 1, 3
Let s(v) be the second derivative of 0*v**2 + 0*v**3 + 0*v**5 - 12*v - 1/40*v**6 + 0 + 1/48*v**4 - 1/84*v**7. Factor s(o).
-o**2*(o + 1)**2*(2*o - 1)/4
Let o(x) be the second derivative of -x**6/6 - 3*x**5/4 + 5*x**4/2 + 20*x**3/3 + x + 6. Factor o(r).
-5*r*(r - 2)*(r + 1)*(r + 4)
Let n(t) be the first derivative of t**6/27 - 2*t**5/45 - t**4/18 + 2*t**3/27 - 53. Factor n(h).
2*h**2*(h - 1)**2*(h + 1)/9
Let u = 1033 + -1028. Let c(v) be the