54*i**2. Solve q(z) = 0.
-11/4, 0
Let c(b) = 5*b**3 + 38*b**2 + 70*b + 43. Let t(q) = -15*q**3 - 113*q**2 - 210*q - 128. Let g(s) = -8*c(s) - 3*t(s). Solve g(r) = 0.
-4, -2, -1
Let u(y) be the second derivative of y**6/90 - 2*y**5/15 + 5*y**4/12 + 4*y**3/9 - 8*y**2/3 + 21*y - 4. Find p such that u(p) = 0.
-1, 1, 4
Let v = 47/250 + 671/1750. Find y such that 0 - 20/7*y - 16/7*y**2 + v*y**3 = 0.
-1, 0, 5
Let t(l) be the second derivative of -l**4/12 + 5*l**3/6 - 3*l**2 + 495*l. Determine u so that t(u) = 0.
2, 3
Let j be -1*(5 + -7)*5. Factor 9*b**3 + 25*b**2 + 5*b**4 + 6*b**3 + j*b + 5*b**3.
5*b*(b + 1)**2*(b + 2)
Let x(g) = g**4. Let v(l) = 7 - 2 - 1 - 1. Let a(q) = -q**4 + 1. Let y(f) = 6*a(f) - 2*v(f). Let i(d) = 5*x(d) + y(d). Find u, given that i(u) = 0.
0
Suppose -5*l - 15 = -2*o, -4*o + 13 = -2*o - 3*l. Factor -5*b**2 - 30*b**3 - 14*b + 5*b**4 - 15*b**2 + 54*b + o*b**5.
5*b*(b - 2)*(b - 1)*(b + 2)**2
Find i, given that -42/5 - 3/5*i**2 - 27/5*i = 0.
-7, -2
Let b = 14461 - 72291/5. Suppose 0*n = -n + 4, n - 14 = -5*f. Factor 2/5*m**4 + b*m + 2*m**3 + 18/5*m**f + 4/5.
2*(m + 1)**3*(m + 2)/5
Let k(l) be the second derivative of 0*l**4 + 0*l**5 - 1/30*l**6 + 0 - l - 1/42*l**7 + 0*l**3 + 0*l**2. Solve k(r) = 0.
-1, 0
Let n(g) be the second derivative of -7*g**4/48 + 4*g**3/3 - 9*g**2/2 - 751*g. Let n(o) = 0. Calculate o.
2, 18/7
Factor 15/2*p - 1/2*p**2 + 50.
-(p - 20)*(p + 5)/2
Let w(o) be the first derivative of -3/14*o**4 - 3/35*o**5 + 3/7*o - 4 + 3/7*o**2 + 0*o**3. What is r in w(r) = 0?
-1, 1
Factor -16/3*l**4 + 8/3*l**2 - 4/3*l**3 + 4*l**5 + 0*l + 0.
4*l**2*(l - 1)**2*(3*l + 2)/3
Let c = -22154 - -66464/3. Factor 5/3*p - 2/3*p**2 - c.
-(p - 2)*(2*p - 1)/3
Let a(m) = -9*m**4 + 13*m**3 - 11*m**2 - 25*m - 2. Let p(u) = -3*u**4 - u**3 - u**2 + u - 1. Let b(t) = a(t) - 2*p(t). Let b(x) = 0. What is x?
-1, 0, 3
Let c(z) be the second derivative of 3*z**5/40 - z**4/8 - 11*z**3/2 + 30*z**2 - 29*z + 3. Determine l so that c(l) = 0.
-5, 2, 4
Let r(g) be the third derivative of g**6/60 - 13*g**5/30 + 8*g**4/3 - 20*g**3/3 - 138*g**2. Factor r(v).
2*(v - 10)*(v - 2)*(v - 1)
Let m(w) be the first derivative of 5*w**3/3 - 15*w**2/2 + 58. Factor m(o).
5*o*(o - 3)
Let c(g) be the first derivative of 2*g**5/25 - 3*g**4/5 + 6*g**3/5 - 79. Factor c(v).
2*v**2*(v - 3)**2/5
Let j(m) be the first derivative of m**7/105 - 2*m**5/15 - 9*m**2 + 9. Let x(r) be the second derivative of j(r). Factor x(g).
2*g**2*(g - 2)*(g + 2)
Suppose -45*p - 10 - 17 = -27. Factor 0*d**4 - 1/5*d**5 + 0*d**2 + p - 16/5*d + 8/5*d**3.
-d*(d - 2)**2*(d + 2)**2/5
Let m(w) be the third derivative of w**8/112 + 4*w**7/35 + 21*w**6/40 + 7*w**5/10 - 5*w**4/2 - 12*w**3 - 78*w**2. Determine r, given that m(r) = 0.
-3, -2, 1
Let z be (-470)/(-25) + -24 - -7. Find h such that -18/5 + z*h**2 - 21/5*h = 0.
-2/3, 3
Suppose 6*z = 5*z + 1, -5*z = -3*l + 10. Solve -2*k**2 - k - 1/2*k**l + 0 + 5/4*k**4 + 3/4*k**3 = 0 for k.
-1, -1/2, 0, 2
Factor 2/3*v**2 + 2/9*v + 0 + 2/9*v**4 + 2/3*v**3.
2*v*(v + 1)**3/9
Solve 1/5*r**4 + 4/5*r - r**3 + 4/5 - r**2 + 1/5*r**5 = 0 for r.
-2, -1, 1, 2
Let f(a) be the first derivative of 2*a**5/95 + a**4/38 - 20*a**3/57 + 8*a**2/19 + 10. Factor f(z).
2*z*(z - 2)*(z - 1)*(z + 4)/19
Let f(a) be the second derivative of 1083*a**5/20 + 1273*a**4/16 + 93*a**3/2 + 27*a**2/2 + 193*a. Factor f(s).
3*(4*s + 1)*(19*s + 6)**2/4
Factor -23*b**2 - 44*b + 19*b**2 + 119 - 159.
-4*(b + 1)*(b + 10)
Let s(u) be the second derivative of -3*u**5/20 - u**4/2 + 29*u**3/2 + 45*u**2 - 4*u + 10. Solve s(y) = 0 for y.
-6, -1, 5
Let b be (-54)/729 + 2/27. Let w(h) be the first derivative of b*h**3 + 0*h - 10*h**2 + h**5 - 11 + 15/4*h**4. Factor w(s).
5*s*(s - 1)*(s + 2)**2
Determine q so that -16/9*q**2 + 0*q - 2/9*q**4 + 4/3*q**3 + 0 = 0.
0, 2, 4
Let v = -23 + 26. Let 2*z**2 - 4*z**v + 0*z**3 + 2*z**3 + 4*z = 0. What is z?
-1, 0, 2
Let c(r) be the first derivative of 3*r**5/10 + 195*r**4/8 + 693*r**3 + 6897*r**2 - 15972*r + 187. Factor c(t).
3*(t - 1)*(t + 22)**3/2
Let i be 6*(-3)/27*-6. Suppose -2*r - 4 = 4*o, -i*r = -o - 7 - 3. Factor 2/3*c**r + 0 + 2/9*c + 2/3*c**3 + 2/9*c**4.
2*c*(c + 1)**3/9
Factor -16*g**2 + 17 - 15*g - 107 + 21*g**2.
5*(g - 6)*(g + 3)
Let n(o) = o**3 - o + 4. Let i be n(0). Solve -63*p - 4*p**2 + 3*p**i + p**2 + 65*p + 0*p**2 - 2*p**3 = 0.
-1, 0, 2/3, 1
Let s = -66 + 92. Suppose s*t**2 - 50*t**4 - 2 + 40*t + 8 + 2 - 40*t**3 + 16*t**2 = 0. Calculate t.
-1, -2/5, 1
Let h = 33 + -21. Suppose 0 = -10*q + h*q - 4. Factor -2*j - q*j - 7*j**3 + 5*j**4 - 14*j**4 - 4 + 11*j**2 + 13*j**3.
-(j - 1)**2*(3*j + 2)**2
Suppose -2*i = -3 - 3. Let a(z) be the first derivative of 0*z - 1/5*z**2 - 2 - 1/10*z**4 + 4/15*z**i. Factor a(p).
-2*p*(p - 1)**2/5
Let t be (-10242)/(-7588) - 3*2/12. Let y = t - -2/271. Solve 6/7*i**2 + y*i + 2/7 + 2/7*i**3 = 0 for i.
-1
Solve 27*i**2 + 6*i**4 + i - 96*i**3 - 5*i**2 + 129*i**3 + 11*i + 17*i**2 = 0.
-4, -1, -1/2, 0
Suppose 0 = -3*w + 343 + 221. Let u = w - 188. Find i such that 2/11*i**5 + u*i**3 + 0*i + 8/11*i**2 + 0 - 6/11*i**4 = 0.
-1, 0, 2
Suppose 3*h = -2*d + 17, -202*d + 198*d = 2*h - 22. Factor 12/5*i**2 + 1/5*i**5 + 0 - 2/5*i**3 - 4/5*i**d + 9/5*i.
i*(i - 3)**2*(i + 1)**2/5
Let m(t) be the third derivative of t**8/50400 + t**7/3150 + t**6/450 - t**5/20 + t**2. Let f(d) be the third derivative of m(d). Factor f(z).
2*(z + 2)**2/5
Let c = -2 + 6. Suppose -2*t = -5*k + 256, -c*k = 4*t - 3*t - 210. Determine v, given that -k*v**4 + 4*v**3 - 2*v - 2*v**5 + 52*v**4 = 0.
-1, 0, 1
Let s = 14/13 + -9/13. Let q = 38/65 - s. What is y in 2/5*y**2 + q*y - 1/5*y**3 - 2/5 = 0?
-1, 1, 2
Factor 12/5 + 3*d**3 + 37/5*d + 1/5*d**4 + 39/5*d**2.
(d + 1)**3*(d + 12)/5
Let k(v) = -11*v**2 + 12*v - 15. Let b(t) = 29*t - 6*t - 10*t**2 - 14 - t - 10*t. Let c(u) = -7*b(u) + 6*k(u). Suppose c(j) = 0. What is j?
1, 2
Let h(o) = 27*o**2 + 5*o + 10. Let k be h(-2). Let u be (k/18*2/15)/2. Factor -2/5*n**5 + 2/5 + u*n**4 - 4/5*n**2 + 4/5*n**3 - 2/5*n.
-2*(n - 1)**3*(n + 1)**2/5
Let o be 2/((-1 - 2) + 4) - 5. Let k be (-3)/((-63)/(-2))*o. Factor -k*q**2 + 0 + 8/7*q.
-2*q*(q - 4)/7
Suppose -217 = -8*t - 201. Factor 1/2*n**4 - 3*n**t - 4*n + 0*n**3 - 3/2.
(n - 3)*(n + 1)**3/2
Let d(a) be the first derivative of -4*a**3/21 - 12*a**2/7 + 220. Let d(p) = 0. Calculate p.
-6, 0
Let m(r) be the first derivative of r**3/18 - r**2/4 + 152. Factor m(h).
h*(h - 3)/6
Let x(v) be the second derivative of -v**6/120 + 9*v**5/20 - 81*v**4/8 - 4*v**3 - 13*v. Let d(u) be the second derivative of x(u). Find j, given that d(j) = 0.
9
Let 4/9*m**3 + 2/9*m**4 - 2/3*m**2 - 8/9 - 16/9*m = 0. What is m?
-2, -1, 2
Let q(a) = -a**2 + 1. Let i(y) = 7*y**2 + 4*y - 20. Let t(j) = -i(j) - 6*q(j). Let f be t(-6). Factor 3*s**f - 14*s - 6 + 4*s + 7*s + 0*s**2.
3*(s - 2)*(s + 1)
Suppose 12*q = 11*q + 12. What is r in 8*r**3 - 5*r - 9*r**3 - 12*r + q - 3*r + 9*r**2 = 0?
1, 2, 6
Let c(q) = -334*q - 8 - 127 + 135*q**4 + 64*q + 55*q**2 + 270*q**3. Let w(m) = 5*m**4 + 10*m**3 + 2*m**2 - 10*m - 5. Let a(f) = 2*c(f) - 55*w(f). Factor a(n).
-5*(n - 1)*(n + 1)**3
Factor 56/5 - 4/5*y**2 + 52/5*y.
-4*(y - 14)*(y + 1)/5
Suppose 117*y - 48 = 101*y. Let c(s) be the first derivative of 9/10*s**4 + 8*s**2 - 9 - 26/5*s**y - 24/5*s. Let c(z) = 0. Calculate z.
2/3, 3
Let m(o) be the first derivative of 0*o**2 + 0*o + 19 + 1/5*o**5 - 1/3*o**3 - 1/6*o**6 + 1/4*o**4. Solve m(w) = 0 for w.
-1, 0, 1
Let v(c) be the second derivative of c**6/150 - 17*c**5/100 + 8*c**4/5 - 104*c**3/15 + 64*c**2/5 + 2*c + 6. Factor v(q).
(q - 8)*(q - 4)**2*(q - 1)/5
Let i = -131 - 16. Let u = i + 1032/7. Factor -66/7*a**2 - 24/7*a**3 - 72/7*a - u*a**4 - 27/7.
-3*(a + 1)**2*(a + 3)**2/7
Let n(m) = 2*m**2 + 2*m. Let s = -6 + 1. Let d(a) = a**2 + a. Let q(w) = s*d(w) + 4*n(w). Factor q(r).
3*r*(r + 1)
Let z(x) = x**3 - 9*x**2 + 7*x + 10. Let u be z(8). What is r in 3*r**u - 12*r**2 + 4*r**2 + 10*r = 0?
0, 2
Let f(o) = o**4 + o**3 + o + 1. Let p(m) = -6*m**4 + 37*m**3 - 5 - 5*m + 47*m**3 - m**2 - 87*m**3. Let j(i) = -10*f(i) - 2*p(i). Factor j(t).
2*t**2*(t - 1)**2
Let r be -4 - (5 - 405/(-5)). Let l be (-12)/(-90) + 57/r + 2. What is z in -1/2*z**3 - l*z**2 - 1/2 - 3/2*z = 0?
-1
Let q(w) be the third derivative of -w**5/360 + w**4/72 + 5*w**3/12 + 19*w**