et m(t) be the third derivative of -1/90*t**5 + 0*t + 2*t**2 - 1/6*t**4 - t**3 + 0. Find i, given that m(i) = 0.
-3
Suppose h = -3*j + 5, -j = -2*h - 0*h - 11. Let w be 1/(-3) - (-14)/21. Let -1/3*q**4 + 0 + 1/3*q - 1/3*q**j + w*q**2 = 0. Calculate q.
-1, 0, 1
Let x = 43 + -35. Factor x*c**2 + 8/3*c + 6*c**3 + 0.
2*c*(3*c + 2)**2/3
Let r(n) be the third derivative of n**6/40 - n**5/20 + 18*n**2. Factor r(m).
3*m**2*(m - 1)
Let j(d) = 31*d**3 - 53*d**2 - 29*d + 17. Let k(p) = 5*p**3 - 9*p**2 - 5*p + 3. Let h(f) = 6*j(f) - 34*k(f). Let h(l) = 0. Calculate l.
-1/4, 0, 1
Let h(x) be the first derivative of 2*x**3/15 - 3. Factor h(r).
2*r**2/5
Let v(p) be the third derivative of -p**8/168 - p**7/35 - p**6/20 - p**5/30 + 2*p**2. Factor v(i).
-2*i**2*(i + 1)**3
Let y(q) be the first derivative of 5/3*q**2 + 2/3*q**3 + 4/3*q + 2. Factor y(o).
2*(o + 1)*(3*o + 2)/3
Let m(t) = -t**4 + t**2 + 1. Let w(z) = -12*z**4 + 12*z**2 + 8. Let o(b) = 8*m(b) - w(b). Suppose o(j) = 0. What is j?
-1, 0, 1
Let m = 25/2 + -12. Suppose m*z**2 + 2*z + 2 = 0. Calculate z.
-2
Let x(v) = -18*v**5 + 39*v**4 - 9*v**3 - 3*v**2 + 3*v. Let o(f) = 17*f**5 - 40*f**4 + 9*f**3 + 2*f**2 - 4*f. Let q(k) = 3*o(k) + 4*x(k). Solve q(z) = 0.
-2/7, 0, 1
Find w such that 53 - w**2 - 53 + w**4 = 0.
-1, 0, 1
Let f(w) be the first derivative of -5*w**4/4 + 25*w**3 - 375*w**2/2 + 625*w + 36. Factor f(j).
-5*(j - 5)**3
Let j(b) be the second derivative of -b**4/36 + b**3/9 + 39*b. Factor j(q).
-q*(q - 2)/3
Let m(a) be the second derivative of -2*a + 0*a**3 + 3/20*a**5 + 0 - 6*a**2 + 3/4*a**4. Factor m(u).
3*(u - 1)*(u + 2)**2
Suppose -2/9 + 0*z + 2/9*z**2 = 0. What is z?
-1, 1
Let f(i) be the first derivative of -i**8/2520 - i**7/1260 + 4*i**3/3 - 4. Let o(x) be the third derivative of f(x). Factor o(y).
-2*y**3*(y + 1)/3
Let y(v) be the third derivative of -v**8/1680 - v**7/1050 + v**6/600 + v**5/300 - 8*v**2. Determine m, given that y(m) = 0.
-1, 0, 1
Factor 20*o**4 - 2 - o**3 - 19*o**4 + 2.
o**3*(o - 1)
Solve 0 + 4/3*o - 10/3*o**2 - 14/3*o**3 = 0 for o.
-1, 0, 2/7
Factor 0*w**2 - 6/5*w**5 + 0 - 6/5*w**3 + 0*w - 12/5*w**4.
-6*w**3*(w + 1)**2/5
Let t(m) be the second derivative of -m**6/1980 - m**5/220 - m**4/66 - 5*m**3/6 + m. Let s(n) be the second derivative of t(n). Factor s(j).
-2*(j + 1)*(j + 2)/11
Let s(b) be the first derivative of -3/2*b - 3/8*b**4 - 3/2*b**3 - 3 - 9/4*b**2. Solve s(m) = 0.
-1
Let t(c) be the first derivative of -c**9/1344 - c**8/2240 + c**7/560 - c**3 + 7. Let j(v) be the third derivative of t(v). Let j(f) = 0. Calculate f.
-1, 0, 2/3
Let o(i) = -i + 1. Let v(t) = 2*t**3 + 4*t**2 + 3*t - 27. Let m(h) = -22*o(h) - 2*v(h). Find s, given that m(s) = 0.
-2, 2
Let m(j) be the second derivative of 7/20*j**6 - 7/8*j**4 + 3/14*j**7 + j - 1/2*j**3 + 0 + 0*j**2 - 3/10*j**5. Suppose m(s) = 0. What is s?
-1, -2/3, -1/2, 0, 1
Determine h, given that -h + h - 3*h**4 + 5*h**4 + 32 - 16*h**2 = 0.
-2, 2
Let k = 61 - 61. Let p(v) be the third derivative of 1/90*v**6 + k*v**4 + 1/45*v**7 + 0*v**3 - 3*v**2 + 0 + 0*v + 0*v**5. Factor p(s).
2*s**3*(7*s + 2)/3
Suppose -1/3 - 1/3*o**2 + 2/3*o = 0. What is o?
1
Let b(c) = -c + 3*c - 9*c - 6*c**3 + c**2. Let z(q) = -5*q**3 + q**2 - 6*q. Let u(s) = -6*b(s) + 7*z(s). Solve u(a) = 0.
-1, 0
Suppose -r + 12 = r. Factor 11*p**3 + p - 4*p**4 - r*p**3 + 0*p - 4*p**2 + 2*p**4.
-p*(p - 1)**2*(2*p - 1)
Let 5/4*s**5 - 1/2*s**2 + 1/2*s**4 + 0*s - 5/4*s**3 + 0 = 0. What is s?
-1, -2/5, 0, 1
Let q(w) be the first derivative of -w**4/30 - 14*w**3/45 - w**2 - 6*w/5 + 11. Factor q(u).
-2*(u + 1)*(u + 3)**2/15
Suppose 3*f = 14 + 1. Let g(z) be the second derivative of 0*z**2 + 1/12*z**3 - 1/8*z**4 - 2*z + 3/40*z**f + 0 - 1/60*z**6. Factor g(h).
-h*(h - 1)**3/2
Let s be ((-3)/15)/((-396)/720). Determine p, given that 0 + 2/11*p**5 - 2/11*p**3 + 0*p - s*p**2 + 4/11*p**4 = 0.
-2, -1, 0, 1
Factor 3*h + 5/2 + 1/2*h**2.
(h + 1)*(h + 5)/2
Let q(n) be the first derivative of n + 1/8*n**3 + 1/48*n**4 + 1/4*n**2 + 4. Let p(u) be the first derivative of q(u). Solve p(x) = 0 for x.
-2, -1
Let m(w) = w**4 + w**3 - w. Let q(z) = 12*z**4 - 3*z**3 - 39*z**2 - 51*z - 12. Let p be -1*1 + 11 + -25. Let s(j) = p*m(j) + q(j). Factor s(g).
-3*(g + 1)**2*(g + 2)**2
Factor 6*r + 15/4*r**2 - 3.
3*(r + 2)*(5*r - 2)/4
Suppose -2/13*q**2 - 4/13 - 6/13*q = 0. Calculate q.
-2, -1
Let v be ((-16)/(-6) - 0)*(-4)/(-16). Factor 8/3 + v*f**2 + 8/3*f.
2*(f + 2)**2/3
Determine a so that -2/9*a**4 - 16/9*a**2 - 4/3*a**3 + 4/3*a + 2 = 0.
-3, -1, 1
Let t be (-2)/6*(-12)/7. Suppose 2/7*s**2 + 0 + t*s = 0. What is s?
-2, 0
Let k(u) be the first derivative of 9 - u**4 + 1/5*u**5 + 2*u**2 + u**3 - 4*u. Solve k(f) = 0.
-1, 1, 2
Let p(w) be the third derivative of -w**9/1134 + w**8/504 - w**7/1260 - 2*w**3/3 - 6*w**2. Let q(a) be the first derivative of p(a). Factor q(f).
-2*f**3*(f - 1)*(4*f - 1)/3
Factor -3*x + 2 + x + 6*x**2 - 6*x.
2*(x - 1)*(3*x - 1)
Let a(i) = 12 - 3 - 5 + 5 + 13*i**2. Let j(u) = 7*u**2 + 5. Let q = 13 + -24. Let b(d) = q*j(d) + 6*a(d). Find n such that b(n) = 0.
-1, 1
Let l = -11 + 13. Let f(h) be the first derivative of 0*h + 2/7*h**2 - l - 2/21*h**3. Let f(u) = 0. Calculate u.
0, 2
Suppose -2/11*o**2 - 32/11 - 2/11*o**4 - 48/11*o + 12/11*o**3 = 0. Calculate o.
-1, 4
Let c(b) = 2*b**3 + b**2 - 2*b + 7. Let j be c(-3). Let y be (-72)/j - (-1)/(-4). Let -3 + 2*k - 1/3*k**y = 0. What is k?
3
Let z(t) be the first derivative of 1/10*t**5 + 0*t**2 + 0*t + 0*t**4 - 3 - 1/6*t**3. Factor z(h).
h**2*(h - 1)*(h + 1)/2
Let r(o) be the second derivative of 2*o - 1/15*o**4 - 1/15*o**3 - 1/50*o**5 + 0 + 0*o**2. Suppose r(u) = 0. Calculate u.
-1, 0
Suppose 0 + 0*k + 0*k**2 - 2/3*k**3 = 0. What is k?
0
Let p(b) be the third derivative of 0 + 0*b**5 - 8*b**2 + 0*b**7 + 0*b**4 + 0*b**6 + 0*b + 0*b**3 - 1/84*b**8. Factor p(k).
-4*k**5
Factor 102*v - 24 - 144*v**2 + 135/2*v**3.
3*(3*v - 2)**2*(5*v - 4)/2
Factor -25*t**4 + 2*t + 5*t**3 + 26*t**4 + t + 7*t**2.
t*(t + 1)**2*(t + 3)
Factor 8*j**4 + j**3 + 48*j - 14*j**2 + 66*j**2 + 23*j**3 + 16 - 4*j**4.
4*(j + 1)**2*(j + 2)**2
Let h = 98 - 96. Factor -2/7*b**4 + 0*b**h + 2/7 + 4/7*b**3 - 4/7*b.
-2*(b - 1)**3*(b + 1)/7
Let o(h) = -10*h**4 - 8*h**3 + 18*h**2 + 16*h - 10. Let p(x) = -x**4 + x**2 + 1. Let q(v) = -o(v) + 6*p(v). Let q(s) = 0. Calculate s.
-2, 1
Let y(n) = -n**2 - 9*n - 5. Let k be y(-8). Suppose -k*w = -0*w. Solve 0*z**2 + w*z**4 + 0 + 0*z - 1/2*z**5 + 1/2*z**3 = 0.
-1, 0, 1
Let x be 4/(-28)*(-6)/9. Let r(j) be the first derivative of 0*j + 0*j**2 - 2/35*j**5 - 1/7*j**4 + 2 - x*j**3. Factor r(h).
-2*h**2*(h + 1)**2/7
Let q(t) = -t**3 + t**2 + 1. Let v(h) = -57*h**2 + 111*h - 51. Let u(y) = 3*q(y) - v(y). Let u(a) = 0. Calculate a.
1, 18
Let a be 1 + (-8 - 330/(-42)). Factor a - 2/7*j**2 + 4/7*j.
-2*(j - 3)*(j + 1)/7
Find h, given that -1/5*h**2 + 3/5 + 2/5*h = 0.
-1, 3
Let v = -50 - -30. Let w = 23 + v. Factor 0 + f**w - 1/5*f + 4/5*f**2.
f*(f + 1)*(5*f - 1)/5
Factor 1/3*m - 1/3*m**4 - 1/3*m**3 + m**2 - 2/3.
-(m - 1)**2*(m + 1)*(m + 2)/3
Let n be 1/(-4) - 3/(-12). Suppose n = -11*x + 5*x. Determine k, given that -2/3*k**5 + 0*k - 2/9*k**2 + 2/3*k**3 + x + 2/9*k**4 = 0.
-1, 0, 1/3, 1
Let x be 1/(-2) - (-26)/48. Let g(z) be the second derivative of 2*z - x*z**4 - 1/80*z**5 + 0*z**2 + 0*z**3 + 0. Factor g(v).
-v**2*(v + 2)/4
Let l = 76 - 71. Factor 10/3*u**3 + 4/3*u**2 + 0 + 2/3*u**l + 0*u + 8/3*u**4.
2*u**2*(u + 1)**2*(u + 2)/3
Let t(f) = 9*f**4 + 34*f**3 - 5*f**2 + 3*f + 3. Let a(l) = -18*l**4 - 68*l**3 + 11*l**2 - 5*l - 5. Let q(x) = 3*a(x) + 5*t(x). Factor q(y).
-y**2*(y + 4)*(9*y - 2)
Let z(w) be the second derivative of -w**5/60 + w**4/12 - w**3/9 - 9*w. Find q, given that z(q) = 0.
0, 1, 2
Let h(s) be the first derivative of -3 + 1/60*s**5 - s**2 + 0*s - 1/24*s**4 + 0*s**3. Let c(l) be the second derivative of h(l). Factor c(x).
x*(x - 1)
Let a = 145/3528 - 4/147. Let k(s) be the third derivative of s**2 + 0*s**3 + 0*s + 1/360*s**6 + 0 + 1/90*s**5 + a*s**4. Solve k(j) = 0.
-1, 0
Let h be (4 + -1)*40/12. Suppose -3*v + h - 4 = 0. Find j, given that -2 - 6*j - 5*j**3 - j**3 + 4*j**3 - 6*j**v = 0.
-1
Let x(s) be the first derivative of -s**6/36 + s**4/8 + s**3/9 + 16. Factor x(i).
-i**2*(i - 2)*(i + 1)**2/6
Let a(g) be the second derivati