 + 12/5 + 24/5*i.
3*(i + 1)*(i + 2)**2/5
Factor 611524/3*t**2 + 119552942/9*t**3 + 3128/3*t + 16/9.
2*(391*t + 2)**3/9
Suppose 100 = 23*g + 31. Let c(m) be the second derivative of 0*m**2 + 1/9*m**6 + 7*m + 1/15*m**5 + 0*m**4 + 0*m**g + 1/21*m**7 + 0. Factor c(s).
2*s**3*(s + 1)*(3*s + 2)/3
Let y be (-6)/24 + -2 + 99/28. Let x(s) be the second derivative of y*s**2 + 3*s - 1/70*s**5 - 5/42*s**4 + 0 - 1/7*s**3. Suppose x(h) = 0. What is h?
-3, 1
Let n be -3 + (38 + 0)/(6 + 4). Suppose -4*f = -u + 18, u = -0*u - 3*f - 10. Determine d so that 0 + n*d - u*d**2 = 0.
0, 2/5
Let p(h) = 6 - 97822*h - h**3 + 97828*h + 9*h**2 + 0*h**3. Let b(g) = -5 - 5*g**2 + 2*g**3 - 5*g - 3*g**2 - g**3. Let r(t) = -6*b(t) - 5*p(t). Factor r(m).
-m**2*(m - 3)
Let v(s) be the third derivative of -s**8/42 - 2*s**7/7 - 313*s**6/240 - 109*s**5/40 - 7*s**4/3 - s**3 - s**2 - 8*s. Solve v(w) = 0 for w.
-3, -2, -1/4
Let y = 6 - 0. Factor -15*i**2 + 7*i**2 - 2*i + y*i**2.
-2*i*(i + 1)
Let w(z) = -7*z**3 - 10*z**2 - 45*z - 30. Let r(g) = 5*g**3 + 11*g**2 + 46*g + 31. Let x(v) = 4*r(v) + 3*w(v). Find i, given that x(i) = 0.
-2, -1, 17
Let x(i) be the first derivative of 27*i + 45/2*i**2 + 3/4*i**4 + 7*i**3 - 7. Find m, given that x(m) = 0.
-3, -1
Let u(z) be the first derivative of -z**5/35 + z**4/28 + z**3/3 - 13*z**2/14 + 6*z/7 - 49. Find m such that u(m) = 0.
-3, 1, 2
Determine b, given that 0*b**3 - 9/8*b**2 + 0 + 3/8*b**4 - 3/4*b = 0.
-1, 0, 2
Find a such that 2*a + 1081*a**2 - 1076*a**2 + 68*a = 0.
-14, 0
Factor 108/7 - 2/7*f**2 + 106/7*f.
-2*(f - 54)*(f + 1)/7
Let g = -14/179 + 1639/358. Factor 3/2*y - g*y**2 + 3/2*y**4 + 3 - 3/2*y**3.
3*(y - 2)*(y - 1)*(y + 1)**2/2
Let j be (-6)/(-2) - (8 - -4). Let c(x) = -x**2 - 9*x + 3. Let l be c(j). Factor 1 - l*h**2 - 4 + 0*h**2 - 2*h + 8*h.
-3*(h - 1)**2
Factor 950*d - 1366 + 44314 + 2177 + 5*d**2.
5*(d + 95)**2
Let t be (18/216)/(10/16). Let p(x) be the second derivative of -1/6*x**4 - t*x**3 - 2/25*x**5 - 1/75*x**6 + 0*x**2 - 6*x + 0. Suppose p(o) = 0. Calculate o.
-2, -1, 0
Let q(u) be the first derivative of -5*u**5 - 87*u**4/4 + 23*u**3 - 9*u**2/2 + 37. Let y(i) = -i**3 - i**2 + i. Let z(w) = -3*q(w) + 21*y(w). Factor z(h).
3*h*(h + 4)*(5*h - 2)**2
Let g = 54 - 50. Determine f so that -3*f**3 - 3*f**2 + 3*f - 3*f**g - 2*f**4 + 10*f**4 - 2*f**4 = 0.
-1, 0, 1
Let x(o) be the first derivative of 5*o**4/12 - 10*o**3/3 + 10*o**2 - 15*o - 47. Let g(b) be the first derivative of x(b). Factor g(v).
5*(v - 2)**2
Let m(s) be the first derivative of 4*s**3/3 - 20*s**2 + 36*s - 22. Solve m(r) = 0 for r.
1, 9
Let u be 5/(-15) + (-28)/(-12). Find b such that u*b - 24 + 2*b**2 + 24 = 0.
-1, 0
Let v(r) be the first derivative of 2*r**5/5 - r**4 - 14*r**3/3 - 4*r**2 + 129. Solve v(p) = 0.
-1, 0, 4
Suppose 4*g = -3*a + 12, -g = -2*a - 0*g - 3. Let o = 292/5 + -58. Factor 0*d**2 + 0 + a*d**4 + 4/5*d**3 - 2/5*d - o*d**5.
-2*d*(d - 1)**2*(d + 1)**2/5
Let p(b) be the first derivative of 2/3*b**4 + 1/10*b**5 - 8 - 1/3*b**3 + 0*b**2 - 4/15*b**6 - 7*b. Let h(a) be the first derivative of p(a). Factor h(f).
-2*f*(f - 1)*(f + 1)*(4*f - 1)
Let f(z) = z**3 + z**2 - 2*z + 2164. Let d be f(0). Find q such that -12*q + 2148 + 2*q**2 - d + 0*q**2 + 2*q**2 = 0.
-1, 4
Let s(u) be the first derivative of -u**5/15 + 5*u**4/6 - u**3 - 60. Factor s(o).
-o**2*(o - 9)*(o - 1)/3
Let s = 42693029527/2093 + -20398008. Let r = -3/299 - s. Let -2/7*x**4 - r*x + 2/7 + 0*x**2 + 4/7*x**3 = 0. Calculate x.
-1, 1
Let o(t) = -t**3 + 20*t**2 - 19*t + 5. Let v be o(19). Factor 5*k**2 - 7*k + 22*k - v + 8*k**3 - 3*k**3 - 20*k**2.
5*(k - 1)**3
Let g = -5/1508 - 489331/4524. Let t = -108 - g. Factor 4/3*c - t*c**2 - 8/3.
-(c - 4)**2/6
Let l(y) be the third derivative of -y**7/735 - y**6/105 - y**5/70 + 53*y**2. Factor l(a).
-2*a**2*(a + 1)*(a + 3)/7
Let n be 1/3*(-2964)/(-228)*(-1)/(-13). Factor -2/3 + l - n*l**2.
-(l - 2)*(l - 1)/3
Suppose -3*a + 22 = 4*s, s = a + 7 - 5. Solve 3*f**3 - f**3 + 24*f - 13*f**3 - 13*f**3 + 4*f**2 - 4*f**s = 0.
-6, -1, 0, 1
Let z(r) be the third derivative of 1/270*r**6 - 2/27*r**4 + 0 + 2/135*r**5 - 16/27*r**3 + 14*r**2 + 0*r. Find i, given that z(i) = 0.
-2, 2
Factor 296/9*b + 80/9*b**2 + 32 + 2/9*b**3.
2*(b + 2)**2*(b + 36)/9
Factor -1180 + 860 - 7*y**2 - 507*y + 3*y**2 + 183*y.
-4*(y + 1)*(y + 80)
Suppose 5*w + c = 39, 9*w + 5*c - 35 = 4*w. Suppose -f = f + w*f. Factor 1/3*d**2 - 2/3*d**3 + 0*d + f - d**4.
-d**2*(d + 1)*(3*d - 1)/3
Let c(a) = -5*a**3 - 15*a**2 + 46*a. Let r(z) = -45*z**3 - 135*z**2 + 415*z. Let p(i) = -35*c(i) + 4*r(i). Solve p(g) = 0.
-5, 0, 2
Let y(p) be the second derivative of p**5/70 + 2*p**4/21 + 4*p**3/21 - 115*p. Factor y(r).
2*r*(r + 2)**2/7
Solve -112/15 + 2/15*f**2 + 22/3*f = 0 for f.
-56, 1
Find v, given that -2/3*v**4 - 2/3*v**2 + 2*v - 2*v**3 + 4/3 = 0.
-2, -1, 1
Let y(g) be the first derivative of 7/8*g**2 + 11 - 1/12*g**3 - 3/2*g. Factor y(q).
-(q - 6)*(q - 1)/4
Let i(j) = 3*j**3 + j**2. Let a be i(1). Let q(r) = -r**2 + 4*r + 3. Let z be q(a). Suppose 2*c**2 - 4*c**3 + c**2 + 3*c + 2*c**z + 1 + 3*c**3 = 0. Calculate c.
-1
Let c(f) be the third derivative of 7*f**8/16 - 16*f**7/5 - 227*f**6/40 + 67*f**5/2 - 77*f**4/2 + 20*f**3 - 89*f**2. What is j in c(j) = 0?
-2, 2/7, 1, 5
Let s(n) be the third derivative of -n**8/840 + n**7/75 - n**6/20 + 3*n**5/50 - 2*n**2 + 37. Factor s(h).
-2*h**2*(h - 3)**2*(h - 1)/5
Let j = 256/105 + 8/35. Solve -16/3 - 1/3*z**2 + j*z = 0 for z.
4
Let i(q) be the second derivative of -q**7/126 - 7*q**6/90 - 3*q**5/20 + 7*q**4/36 + 5*q**3/9 + 2*q + 35. Suppose i(v) = 0. What is v?
-5, -2, -1, 0, 1
Find t, given that -5/6*t - 1/6*t**3 - t**2 + 0 = 0.
-5, -1, 0
Let q = 25 + -20. Let b(u) be the first derivative of u**4 + 3*u**2 - 7 + 9 + q - 5*u**2. What is h in b(h) = 0?
-1, 0, 1
Factor -4/9*p**2 + 2/9*p**3 - 2/3*p + 0.
2*p*(p - 3)*(p + 1)/9
Let o(w) = w**3 - 12*w**2 + 31*w + 30. Let u be o(7). Let y be -1 - (0 - (-2 - -3)). Solve -2/3 + y*p + 2/3*p**u = 0.
-1, 1
Let b(j) be the second derivative of -j**4/30 + j**3/15 + 6*j**2/5 + 95*j. Factor b(s).
-2*(s - 3)*(s + 2)/5
Let c(t) be the first derivative of t**6/27 - 4*t**5/15 + 18. Factor c(s).
2*s**4*(s - 6)/9
Let i(n) = n**2 - 357*n + 743. Let f(d) = -3*d**2 + 356*d - 744. Let z(t) = 3*f(t) + 4*i(t). Find r such that z(r) = 0.
-74, 2
Let p(h) be the third derivative of -h**6/30 - 22*h**5/15 - 70*h**4/3 - 400*h**3/3 + 4*h**2 - 35. Factor p(u).
-4*(u + 2)*(u + 10)**2
Let m(a) = -5*a**3 + 16*a**2 - 17*a + 14. Let j(n) = 5*n**3 - 15*n**2 + 15*n - 15. Let k(v) = -4*j(v) - 5*m(v). Factor k(c).
5*(c - 2)*(c - 1)**2
Let u(q) = q**2 + q - 1. Let d(t) = -t + 1. Let f be d(2). Let s(l) = -l**2 - l**2 + 6 - 247503*l + 247509*l. Let w(k) = f*s(k) + 2*u(k). Factor w(h).
4*(h - 2)*(h + 1)
Let -17*p**2 + 20 - 11*p - 5*p + 20 + 21*p**2 - 12*p = 0. Calculate p.
2, 5
Suppose 3*n + 3 = 0, 5*k + 4*n - 3*n - 14 = 0. Solve -3*m**5 + 2*m**5 + m**3 - 3*m**2 + k*m**2 = 0 for m.
-1, 0, 1
Let z(n) be the first derivative of 2*n**5/85 + 9*n**4/34 + 16*n**3/17 + 16*n**2/17 - 9. Determine f so that z(f) = 0.
-4, -1, 0
Let s(z) be the third derivative of -5*z**8/112 + 4*z**7/21 - 7*z**6/24 + z**5/6 + 52*z**2 - 1. Determine u so that s(u) = 0.
0, 2/3, 1
Let o = 9 - 27. Let l be 5/(-3)*o/6. Suppose 2*i**2 + 2*i**4 - 3*i**4 - 4*i + i**l - i**4 + 3*i = 0. Calculate i.
-1, 0, 1
Suppose 0 = 44*u - 57 - 31. Let f(r) be the first derivative of 0*r + 1/18*r**6 + 0*r**u - 7 + 1/12*r**4 + 0*r**3 + 2/15*r**5. Factor f(d).
d**3*(d + 1)**2/3
Let p(q) be the second derivative of q**6/45 + q**5/15 - q**4/2 - 2*q**3/9 + 8*q**2/3 + 3*q - 3. Solve p(t) = 0.
-4, -1, 1, 2
What is z in 40 - 71 - 260*z - 33 - 16*z**2 = 0?
-16, -1/4
Suppose 31*w - 10*w = -47*w. Let z(t) be the second derivative of 9*t + 2/5*t**5 + 2/15*t**6 + 0*t**3 + 0 + 0*t**4 + w*t**2. Factor z(k).
4*k**3*(k + 2)
Let j(o) = -36*o**2 - 23*o + 24. Let m(s) = -21*s**2 - 12*s + 12. Let c(x) = -3*j(x) + 5*m(x). Factor c(t).
3*(t - 1)*(t + 4)
Suppose -5*t + 7 = -3. Factor -3*y**3 + y**t - 12*y + 5*y**2 + 3*y + 6*y**3.
3*y*(y - 1)*(y + 3)
Let g(i) be the third derivative of -i**6/180 - 11*i**5/45 - 8*i**4/3 + 32*i**3 - 25*i**2 - i. Factor g(y).
-2*(y - 2)*(y + 12)**2/3
Let n(p) be the second derivative of 4/11*p**2 + 0 + 5/33*p**3 