et t be y(0). Let 5*i - 3*i**2 - t*i - 5*i = 0. Calculate i.
-1, 0
Let d = -158 + 162. Let r be d/30 + 516/180. Factor -1/2*w**4 + w + 0 + 3/2*w**2 + 0*w**r.
-w*(w - 2)*(w + 1)**2/2
Factor 1458*f**2 + 19683 + 3*f**4 - 1145*f + 108*f**3 + 2013*f + 4746*f + 3134*f.
3*(f + 9)**4
Let z = 789 - 786. Factor 1/2*k**z + 0*k + 0 + 0*k**2 + 7/4*k**4.
k**3*(7*k + 2)/4
Suppose -4*b + 15 = 3*r, -3*b + 3 = -b - 3*r. Factor k**4 + 2*k**2 + 0*k - 3*k**2 + 3*k**b + 4*k**2 + k.
k*(k + 1)**3
Let w be (-36)/(-17) + 138/828 + (-29)/102. Factor -2/9*g**w - 200/9 - 40/9*g.
-2*(g + 10)**2/9
Suppose -g - g + 12 = 0. Let -16*h**4 - 35*h**3 - 25*h - 14*h**4 + 115*h**2 - 30 - h**4 + g*h**4 = 0. What is h?
-3, -2/5, 1
Let a(k) be the first derivative of 0*k**2 - 4/5*k + 13 + 1/15*k**3. Solve a(x) = 0.
-2, 2
Let p(g) = -g**5 - 3*g**4 + 20*g**3 + 28*g**2. Let i(z) = -8*z**5 - 24*z**4 + 159*z**3 + 226*z**2. Let h(j) = 6*i(j) - 51*p(j). What is c in h(c) = 0?
-6, -1, 0, 4
Let l(f) = -95*f**2 + 87*f - 18. Let g(a) = -a**2 - a. Let i(c) = c**2 + 5*c - 4. Let p be i(-6). Let x(v) = p*l(v) + 6*g(v). Factor x(t).
-4*(7*t - 3)**2
Let c(v) = v**2 + 7*v + 14. Let d be c(-6). Factor 5*g - 6*g - 2*g**2 + d*g**4 + g**5 - 6*g**4.
g*(g - 1)*(g + 1)**3
Let g(b) = -b**3 + 18*b**2 - 6*b - 585. Let u be g(15). What is t in 4*t**2 + u*t + 2/3*t**3 + 0 = 0?
-6, 0
Let q(y) be the first derivative of 11 + 4/11*y + 3/11*y**2 + 2/33*y**3. Factor q(b).
2*(b + 1)*(b + 2)/11
Suppose -5 - 1 = -3*g. Let a(b) be the second derivative of -6*b + 1/36*b**4 + 0 + 5/18*b**3 + 1/3*b**g - 1/12*b**5 - 1/30*b**6. Solve a(f) = 0 for f.
-1, -2/3, 1
Let h(c) be the second derivative of c**6/90 + c**5/30 - c**4/36 - c**3/9 - 36*c. Suppose h(f) = 0. What is f?
-2, -1, 0, 1
Let n(i) = 3*i**5 - 11*i**4 + 2*i**3 + i**2 + 5*i + 5. Let x(u) = -u**4 + u**3 - u**2 + u + 1. Let l(a) = n(a) - 5*x(a). Factor l(r).
3*r**2*(r - 2)*(r - 1)*(r + 1)
Let w(t) be the third derivative of -t**6/720 + 5*t**5/24 - 19*t**4/2 - 361*t**3/9 - 171*t**2. Factor w(y).
-(y - 38)**2*(y + 1)/6
Let b(g) be the first derivative of 3/5*g**5 + 9/4*g**4 + 0*g**3 + 0*g + 42 - 6*g**2. Solve b(j) = 0.
-2, 0, 1
Let l = 43 + -40. Factor -w - 3*w - w**5 - 10*w**l + 3*w - 10*w**2 - 5*w**4 - 1 - 4*w.
-(w + 1)**5
Let x(h) = h**2 - 88*h - 661. Let u be x(-7). Find p such that -1/2*p**u + 0 - 25/2*p**2 + 5*p**3 + 0*p = 0.
0, 5
Let l(m) be the first derivative of -m**9/6804 + m**7/1890 + m**3/3 - 13. Let n(y) be the third derivative of l(y). Factor n(t).
-4*t**3*(t - 1)*(t + 1)/9
Factor 2/11*q**2 - 38/11*q + 0.
2*q*(q - 19)/11
Let z(v) = v**3 + v**2 + 2*v + 3. Let j be z(0). What is l in -85*l**2 + 2352*l + 4*l**3 - 10976 - 83*l**2 - 2*l**j + 2*l**3 = 0?
14
Let f(s) = s**2 - s - 1. Let o(m) = -m**3 - 5*m**2 + 5. Let a(b) = 5*f(b) - 5*o(b). Determine q, given that a(q) = 0.
-6, -1, 1
Let p(l) be the third derivative of l**8/168 + 2*l**7/105 - l**6/60 - l**5/15 - l**2 + 5*l. Find w, given that p(w) = 0.
-2, -1, 0, 1
Let k = -1329/35 + 192/5. Solve 0 + 15/7*m + k*m**2 = 0.
-5, 0
Let f(t) be the third derivative of 0*t - 1/20*t**6 + 0*t**3 + 0 + 2/15*t**5 + 9*t**2 + 1/3*t**4. Factor f(v).
-2*v*(v - 2)*(3*v + 2)
Let b = 4/27 - 23/216. Let k(d) be the first derivative of 3 + 1/8*d**4 + 3/20*d**5 - 1/4*d - 1/6*d**3 + b*d**6 - 3/8*d**2. What is u in k(u) = 0?
-1, 1
Let h(y) be the first derivative of y**6/18 - 163*y**5/15 + 2241*y**4/4 - 729*y**3 + 160. Factor h(f).
f**2*(f - 81)**2*(f - 1)/3
Let q(d) be the third derivative of -d**6/30 + 8*d**5/15 - 2*d**4 + 89*d**2. Factor q(v).
-4*v*(v - 6)*(v - 2)
Suppose -12*w + 3 = -13*w. Let k be (-4 + 5 - -4) + w. Determine f so that 4*f**2 - 5*f**3 - k*f**2 - 3*f**4 - 5*f**2 - f**3 = 0.
-1, 0
Suppose -5*a = -57*a. Let t(k) be the second derivative of 0 - 10*k - 2*k**2 + a*k**3 + 1/12*k**4. Factor t(w).
(w - 2)*(w + 2)
Let i = 2213 - 8851/4. Let -1/4*w**4 + 0*w**3 + 0 + 0*w + i*w**2 = 0. What is w?
-1, 0, 1
Let t = 112202/165 - 680. Let s(z) be the third derivative of 0*z**3 + 3*z**2 - 1/660*z**6 + t*z**5 + 0*z + 0 - 1/33*z**4. Determine u so that s(u) = 0.
0, 2
Let o = -47 + 49. Let l(d) be the second derivative of -2*d + 1/8*d**o + 0*d**3 + 0 - 1/48*d**4. Factor l(a).
-(a - 1)*(a + 1)/4
Factor 58*o**3 - 33*o**4 + 3*o**5 + 172*o - 4*o - 219*o**2 + 71*o**3 - 48.
3*(o - 4)**2*(o - 1)**3
Let v(d) be the second derivative of -d**4/36 - d**3/18 + d**2 - 27*d. Factor v(m).
-(m - 2)*(m + 3)/3
Let 8 + 0*w**2 + 2/3*w**3 - 26/3*w = 0. Calculate w.
-4, 1, 3
Let z(v) be the second derivative of v**4/6 - 13*v**3/3 + 22*v**2 + 146*v + 1. Factor z(i).
2*(i - 11)*(i - 2)
Let z(w) be the third derivative of -w**9/393120 - w**8/131040 + w**7/16380 - 8*w**5/15 + 36*w**2. Let i(c) be the third derivative of z(c). Factor i(j).
-2*j*(j - 1)*(j + 2)/13
Let m(t) = 7*t**2 - 19*t + 25. Let j(s) = -3*s**2 + 9*s - 12. Suppose 0*p + 30 = 5*p. Let i(z) = p*m(z) + 13*j(z). Factor i(d).
3*(d - 1)*(d + 2)
Suppose -4*a - 5*h + 22 = 0, -5*h + 0*h = -4*a + 2. Suppose -2*p - i = -11, a*p - i = -5*i + 19. Solve 14 - 8*y**2 - 4*y**4 - 8*y**p + 20*y**3 - 14 = 0 for y.
-2, 0, 1/2, 1
Let n(f) be the second derivative of -5*f**7/112 + f**6/10 + 3*f**5/40 - 2*f + 138. Solve n(a) = 0.
-2/5, 0, 2
Suppose 5*o + 5*w - 20 = 0, 4*o = 2*w + 3 + 7. Solve 3/8*g**2 + 0*g + 0 - 3/8*g**o = 0.
0, 1
Factor -4*r**3 + 5/2 - 8*r + 9*r**2 + 1/2*r**4.
(r - 5)*(r - 1)**3/2
Let s be ((-87)/(-15) - 2) + (-8)/(-40). Solve 10*h**2 - 5*h**5 + 5*h**s - 15*h**4 + 3 - 3 + 5*h = 0 for h.
-1, 0, 1
Let k(z) be the second derivative of z**7/1400 - z**6/300 - z**5/200 + z**4/20 + z**3/3 - z. Let o(l) be the second derivative of k(l). Factor o(i).
3*(i - 2)*(i - 1)*(i + 1)/5
Suppose 0*x + 15 = 3*x. Suppose 3*k + h - 3 = -4, 0 = 4*k + 5*h + x. Factor 2/7*v**3 - 2/7*v + k + 2/7*v**2 - 2/7*v**4.
-2*v*(v - 1)**2*(v + 1)/7
Determine z, given that 19*z**2 - 11*z + 36*z**2 + 32*z**2 - 86*z**2 - 80 = 0.
-5, 16
Let q(s) = -2*s**2 - 512*s + 16381. Let u(g) = -12*g**2 - 2560*g + 81904. Let b(j) = -16*q(j) + 3*u(j). Factor b(h).
-4*(h - 64)**2
Suppose 4 = -3*i + 7*i. Let m be (i + (3 - 3))*(1 + -1). Factor m + 9/4*g**4 - 9/4*g**3 + 3/4*g**2 - 3/4*g**5 + 0*g.
-3*g**2*(g - 1)**3/4
Let s(i) be the first derivative of -i**7/420 + i**6/60 + i**5/60 - i**4/4 - i**3/3 + 4*i + 31. Let l(m) be the third derivative of s(m). Factor l(a).
-2*(a - 3)*(a - 1)*(a + 1)
Let o(j) be the second derivative of -1/4*j**4 + 0*j**3 + 3/2*j**2 + 0 + 21*j. Let o(c) = 0. Calculate c.
-1, 1
Suppose -135*q = 111*q. Factor 0*r + q + 0*r**2 - 1/5*r**3.
-r**3/5
Let d = 19 - 9. Let f = -6 + d. Let 3*s**2 + s**f + s**4 + s**4 - 2*s**3 - 4*s**3 = 0. Calculate s.
0, 1
Let w be 48/(-20)*((-12)/(-16))/((-9)/20). Suppose 4/3*n**3 - 6*n**2 - 3*n**5 + 5/3*n + 16/3*n**w + 2/3 = 0. What is n?
-1, -2/9, 1
Let d(p) = p. Let g be d(2). Suppose g*b = -2*b. Factor 6/11*s + b - 2/11*s**2.
-2*s*(s - 3)/11
Let k(s) be the third derivative of -s**6/60 - 4*s**5/15 + s**4/12 + 8*s**3/3 + 3*s**2 + s. Factor k(z).
-2*(z - 1)*(z + 1)*(z + 8)
Let w be (6/18)/(5/30). Let -4/11*n + 2/11*n**3 + 2/11*n**w + 0 = 0. What is n?
-2, 0, 1
Let q(a) = a + 13. Let y be q(-11). Factor -3 + y*s**2 - 3*s**2 + 4*s + 0*s**2.
-(s - 3)*(s - 1)
Factor o + 54*o**4 + 81*o**4 - 11*o - 260460*o**2 + 260325*o**2 + 10*o**3.
5*o*(o - 1)*(o + 1)*(27*o + 2)
Find u such that 0*u + 11*u**3 - 1/4*u**4 + 0 - 121*u**2 = 0.
0, 22
Let m = 4 + -12. Let w = 20 + m. Factor -9 - 9*q + 4*q**2 + w - 16*q**2.
-3*(q + 1)*(4*q - 1)
Let d(w) be the second derivative of 0 + 0*w**2 + 15*w + 1/5*w**5 - 1/30*w**6 - 5/12*w**4 + 1/3*w**3. Factor d(n).
-n*(n - 2)*(n - 1)**2
Solve -8/7 + 0*z + 10/7*z**2 - 2/7*z**4 + 0*z**3 = 0 for z.
-2, -1, 1, 2
Let f(r) be the second derivative of 3/2*r**3 + 1/4*r**4 + 0 + 3*r**2 + r. Suppose f(x) = 0. Calculate x.
-2, -1
Let q be (-2)/3 - 900/(-270). Let o(r) be the first derivative of q*r + 1/6*r**4 + 10/9*r**3 + 8/3*r**2 + 3. Let o(i) = 0. What is i?
-2, -1
Let b(m) = -m**2 + 8*m - 6. Let a be b(6). Factor 15*o**3 + 0*o**4 + 27*o**2 + 192*o + 3*o**4 - 171*o + a.
3*(o + 1)**3*(o + 2)
Let f = 81/2 + -39. Let i be 5/(-3)*(-13 - 944/(-80)). Find n such that 3/4*n - f + 3/2*n**i - 3/4*n**3 = 0.
-1, 1, 2
Let q(g) be the third derivative of -g**8/840 - g**7/21 - g**6/30 + 57*g**5/5 - 459*g**4