54*x**3 - 1/108*x**4 + 0. Factor a(d).
-(d - 1)*(d + 2)/9
Let w(z) be the second derivative of 2/5*z**3 - 5*z - 3/20*z**4 - 3/100*z**5 + 0 + 0*z**2. Factor w(m).
-3*m*(m - 1)*(m + 4)/5
Let o(t) = -t**4 - t**2 + t. Let d = 22 + -19. Let q(m) = -8*m**4 - 25*m**3 - 48*m**2 - 32*m - 10. Let w(s) = d*o(s) - q(s). Suppose w(i) = 0. Calculate i.
-2, -1
Factor -16/5*y**3 + 72/5*y + 0 - 4/5*y**4 + 12/5*y**2.
-4*y*(y - 2)*(y + 3)**2/5
Let b = 29/75 - -1/75. Let n = -1/5 + b. Factor n*q**2 + 0 - 1/5*q**4 + 1/5*q**3 - 1/5*q.
-q*(q - 1)**2*(q + 1)/5
Let z(d) = 45*d**5 - 70*d**4 + 205*d**3 - 180*d**2 + 20*d. Let f(r) = -2*r**5 + r**4 - 2*r**3 - r. Let o(s) = 20*f(s) + z(s). Factor o(c).
5*c**2*(c - 4)*(c - 3)**2
Factor 147*d**4 - 12*d**5 - 430*d**2 - 583*d**2 + 9*d**5 - 1725*d**3 - 862*d**2.
-3*d**2*(d - 25)**2*(d + 1)
Suppose 0 = 3*y - g + 82, 31 = -y + g + 7. Let n be (5 + y/6)/(1/4). Factor n*k**5 + 0 - 4*k**4 + 8*k**3 + 0*k - 16/3*k**2.
2*k**2*(k - 2)**3/3
Suppose -1015*g + 22 = -1004*g. Let t(c) be the third derivative of -4/3*c**5 - 7*c**g + 0 + 7/24*c**6 + 0*c + 55/24*c**4 - 5/3*c**3. Factor t(k).
5*(k - 1)**2*(7*k - 2)
Let z(j) = j**2 - j - 22. Let o be z(5). Let q be 5/(-50) + (-1)/o. Find d, given that 2/5*d**4 - 2/5*d**3 - q*d**2 + 2/5*d + 0 = 0.
-1, 0, 1
Suppose -5/2*r**5 + 15*r**2 + 0 - 10*r**4 - 5/2*r**3 + 0*r = 0. What is r?
-3, -2, 0, 1
Let g = 197 - 139. Let z = g - 55. Find y, given that 0 + 2/7*y**z + 0*y - 2/7*y**4 + 0*y**2 = 0.
0, 1
Let r(v) be the third derivative of -v**8/1176 + v**7/147 - 2*v**6/105 + 2*v**5/105 - 232*v**2. What is g in r(g) = 0?
0, 1, 2
Suppose -2*p = -2*v - 6, 4*p + 3*v - 5*v = 18. Solve 2*q - q**2 - p*q - 2*q**2 - 2*q = 0 for q.
-2, 0
Let m be -3 - (284/(-2))/2. Let z be m/(-34)*(-1)/(0 + 1). Suppose 3*c + 3/2 - 9/2*c**z = 0. Calculate c.
-1/3, 1
Let a = 255001/150 - 1700. Let w(i) be the third derivative of -2*i**2 - a*i**5 + 0 + 0*i - 1/5*i**3 + 1/15*i**4. Let w(v) = 0. What is v?
1, 3
Let q(j) be the third derivative of -1/9*j**4 + 0 - 1/90*j**5 + 0*j - 14*j**2 + 0*j**3. Factor q(a).
-2*a*(a + 4)/3
Let p(f) = 625*f**5 + 1919*f**4 + 2026*f**3 + 778*f**2 + 59*f - 5. Let z(v) = v**4 - v + 1. Let w(r) = -5*p(r) - 30*z(r). Factor w(o).
-5*(o + 1)**3*(25*o + 1)**2
Let y(u) = 7*u**3 + 11*u**2 + 9*u + 5. Suppose -5*b + 3 = -37. Let s(t) = -11*t**3 - 5 - 6*t**2 - 11*t**2 - 3 - 14*t. Let p(f) = b*y(f) + 5*s(f). Factor p(h).
h*(h + 1)*(h + 2)
Suppose -11*j + 60 = -6*j. Let m be ((-2)/(-2))/(-3 - (-39)/j). Solve 0*c**2 + 0 + 1/3*c**m - c**3 + 4/3*c = 0 for c.
-1, 0, 2
Let j(m) = m - 53. Let b be j(56). Let x**2 + 0 - 2/3*x - 1/3*x**b = 0. Calculate x.
0, 1, 2
Suppose 4*g - 13 - 99 = 0. Suppose -8 = 10*f - g. Factor -18/11*c**3 - 12/11*c**f - 2/11*c + 0.
-2*c*(3*c + 1)**2/11
Factor -37845*b**4 - 642*b**2 - 59 + 460*b - 263*b**2 + 39 - 25855*b**3 + 5845*b**3.
-5*(3*b + 1)**2*(29*b - 2)**2
Let u be 5/(35/212) + 4/(-14). Factor -81*l**2 + 26*l + 12*l + u + 5*l**3 + 121*l**2 + 27*l.
5*(l + 1)**2*(l + 6)
Let p(j) = -2*j**3 + j**2 + j + 1. Let n(b) = 14*b**2 - 10*b**3 - b - 265 + 263 + 5*b. Let m(c) = -2*n(c) + 12*p(c). Factor m(t).
-4*(t - 1)*(t + 1)*(t + 4)
Solve 5/6*g + 1/6*g**2 - 7/3 = 0.
-7, 2
Let f be 1837/3006 - (-1 + 20/18). Factor -1/4*q**2 - f*q + 0.
-q*(q + 2)/4
Factor -t**4 + t**5 - t + 0*t + t - 14*t**3 - 4*t**4.
t**3*(t - 7)*(t + 2)
Let a(m) = 8*m + 58. Let t be a(-7). Let q(b) be the first derivative of -2*b**3 - 3/2*b**t + 6/5*b**5 + 1/2*b**6 + 0*b**4 - 1 + 0*b. Factor q(i).
3*i*(i - 1)*(i + 1)**3
Let m(o) = 2*o**2 - 3*o - 28. Let p be m(-4). Let n be p/(-12) - -5 - (1 - 2). Suppose -4/3*q**3 - n*q**4 + 0 + 4/3*q + 14/3*q**2 = 0. Calculate q.
-1, -2/7, 0, 1
Let v be 7015/(-17871) + 6/14. Let c = v - -91/555. Factor -1/5*u**3 + 0 + 2/5*u - c*u**2.
-u*(u - 1)*(u + 2)/5
Let w(z) be the third derivative of 0*z**4 + 1/30*z**6 + 0*z**3 - 18*z**2 + 0 + 1/15*z**5 + 0*z. Factor w(j).
4*j**2*(j + 1)
Let i(a) = 5*a**2 + 153*a + 1122. Let f(o) = -5*o**2 - 152*o - 1123. Let d(l) = 3*f(l) + 2*i(l). Factor d(w).
-5*(w + 15)**2
Let y(l) = l - 3. Let d(n) = -n**2 - 6*n + 20. Let i(r) = 3*d(r) + 12*y(r). Factor i(m).
-3*(m - 2)*(m + 4)
Let m be 6 + 6/((-4)/2). Factor -5*y**2 - 4*y**3 + 9*y**4 - 9*y**3 + 16*y**m + y.
y*(y + 1)*(3*y - 1)**2
Let n(g) be the second derivative of -g**9/30240 - g**8/4480 - g**7/1680 - g**6/1440 - 5*g**4/6 + 10*g. Let v(w) be the third derivative of n(w). Factor v(q).
-q*(q + 1)**3/2
Let u(i) = 14*i**3 + 12*i**2 + 3*i - 7. Let j(m) = 5*m**3 + 4*m**2 + m - 2. Let g(v) = -11*j(v) + 4*u(v). Suppose g(z) = 0. What is z?
-3, -2, 1
Factor -6*g - 26*g + 8*g + 23*g**2 - 63 + 27 - g**5 - 3*g**4 + 9*g**3.
-(g - 2)**2*(g + 1)*(g + 3)**2
Let f = 360/581 + -4/83. Let g(i) = -i**2 - 4*i - 2. Let d be g(-2). Factor -2/7*t - f + 2/7*t**d.
2*(t - 2)*(t + 1)/7
Let w = 53 + -53. Suppose -f + 2*r + 2*r + 4 = 0, w = 2*f + 2*r - 8. Factor 0 + 0*y**2 + 0*y**f + 3/2*y**3 + 0*y - 3/2*y**5.
-3*y**3*(y - 1)*(y + 1)/2
Let o(l) be the third derivative of l**6/360 + l**5/60 - 5*l**4/36 - 4*l**3/3 + 445*l**2. Solve o(p) = 0 for p.
-4, -2, 3
Suppose -4*h**2 - 100 - 68 + 48*h + 44*h = 0. Calculate h.
2, 21
Let n be 3 - 4 - ((-2)/(-25) - 102/25). What is s in 2*s + 9/5*s**2 - 3/5 - 4/5*s**n = 0?
-1, 1/4, 3
Let r = -1129 - -1132. Let k(p) be the second derivative of 11*p + 0 + 0*p**2 - 4/21*p**r + 1/21*p**4. Factor k(l).
4*l*(l - 2)/7
Let z = -54 + 57. Factor 4*l**2 - 153 - 4*l**z + 4*l**2 + 153.
-4*l**2*(l - 2)
Let x = -9 - -12. Solve -3 - j + j + 3*j**2 + j - 5*j**x + 4*j**3 = 0 for j.
-1, 1, 3
Suppose -s - 5 = 4*z, 2*s + 3*z - 1 = 6*z. Let c(p) = -219*p**3 - 2*p - 1. Let f be c(s). Factor -f + 15*x**2 + 220 - 6*x.
3*x*(5*x - 2)
Let q(n) be the third derivative of -n**5/20 - 57*n**4/2 - 6498*n**3 - 378*n**2. Factor q(z).
-3*(z + 114)**2
Suppose 0 = -4*z - 184 - 156. Let n = z + 89. Factor 0 + 0*p + 2/9*p**n + 0*p**2 - 2/9*p**3.
2*p**3*(p - 1)/9
Let b(f) be the second derivative of -f**6/20 - 15*f**5/8 - 27*f**4 - 176*f**3 - 384*f**2 - 545*f. Factor b(d).
-3*(d + 1)*(d + 8)**3/2
Factor -11*o - 4*o**2 + 34*o - 60 - 17*o - 38*o.
-4*(o + 3)*(o + 5)
Let t(d) be the first derivative of d**3/5 - 48*d**2 + 477*d/5 - 662. Factor t(z).
3*(z - 159)*(z - 1)/5
Suppose -p + 2*p = -15. Let m be (p/(-20) - 1) + (-2)/(-8). Suppose -4/3*z**3 - 8/9*z**2 - 2/9*z - 8/9*z**4 - 2/9*z**5 + m = 0. What is z?
-1, 0
Let p = 182 + -175. Let s(a) be the first derivative of -12/11*a - 13/11*a**2 + p + 10/33*a**3. Solve s(j) = 0.
-2/5, 3
Suppose 39*k - 15*k + 11*k = 0. Let k*j + 4/9*j**4 + 0*j**3 + 0 - 4/9*j**2 = 0. Calculate j.
-1, 0, 1
Let r(g) = -3*g**2 + 6*g + 9. Let i(t) = -6*t**2 + 11*t + 17. Let l(q) = -3*i(q) + 5*r(q). Suppose l(x) = 0. What is x?
-1, 2
Let i(v) be the third derivative of v**7/490 + 3*v**6/280 - 9*v**5/70 + v**4/14 + 12*v**3/7 - 549*v**2. Suppose i(t) = 0. Calculate t.
-6, -1, 2
Let k(v) be the first derivative of -4*v**3/3 + 36*v**2 - 324*v - 177. Find p, given that k(p) = 0.
9
Suppose z = 2*z - 5*a - 10, 0 = 5*z + 2*a - 50. Let v be 15/(-6)*(-8)/z. Factor 0*f**2 - 3*f**4 - 5*f**3 + 5*f + 2 - 2*f**v + 3*f**2.
-(f - 1)*(f + 1)**2*(3*f + 2)
Let q(v) be the third derivative of v**6/12 + 165*v**5/4 + 6355*v**4 - 38440*v**3/3 + 3*v**2 + 27. Factor q(a).
5*(a + 124)**2*(2*a - 1)
Let q(u) be the first derivative of -5 - u**2 + 5/12*u**3 - 8*u - 1/24*u**4. Let s(r) be the first derivative of q(r). Factor s(v).
-(v - 4)*(v - 1)/2
Suppose 4*r - 10 = b, -3*r - 14*b + 3 = -17*b. Let q(y) be the third derivative of 1/150*y**5 + 0 + 0*y + 0*y**r - 5*y**2 - 1/30*y**4. Factor q(v).
2*v*(v - 2)/5
Let v(f) be the third derivative of f**6/1020 + f**5/255 - f**4/204 - 2*f**3/51 - 2*f**2 - 23. Determine u so that v(u) = 0.
-2, -1, 1
Factor -70/3*h - 2/3*h**3 - 22/3*h**2 - 50/3.
-2*(h + 1)*(h + 5)**2/3
Suppose 62*c = -65*c + 49*c. Factor c*i + 3/7*i**3 + 3/7*i**5 - 6/7*i**4 + 0*i**2 + 0.
3*i**3*(i - 1)**2/7
Suppose 26*m = -2*f + 37 + 55, m - 3*f = -18. Let 12/5*k - 24/5*k**2 - 3/5*k**4 + 0 + 3*k**m = 0. What is k?
0, 1, 2
Factor 1/6*w**2 + 19/3*w + 361/6.
(w + 19)**2/6
Let c(s) be the third derivative of -s**7/105 - 7*s**6/60 + 17*s**5/30 - 3*s**4/4 + s**2 - 36. Factor c(k).
-2*k*(k - 1)**2*(k + 9)
Let m be (-8)/12*(-58 + 55). Suppose 10/9*i**3 + 0*i + 2/9*i*