4*h**2 - 1/30*h**4 - 1/75*h**5. Factor g(d).
-d*(d + 2)**2/5
Let a(q) = q**3 + 3*q**2 - 2*q - 3. Let v be a(-2). Factor -4*g**3 + 13*g**2 - 5*g + v*g - g**2.
-4*g**2*(g - 3)
Let y(a) be the second derivative of -a**6/6 - a**5/2 + 25*a**4/12 + 5*a**3 - 64*a + 1. What is w in y(w) = 0?
-3, -1, 0, 2
Suppose -2*s - 34 = -102. Let a = s - 31. Factor 1/3*n - 1/3*n**4 - n**2 + n**a + 0.
-n*(n - 1)**3/3
Let 8/5*c - 1/5*c**4 - 12/5 - 2/5*c**3 + 7/5*c**2 = 0. Calculate c.
-3, -2, 1, 2
Let w = -418 - -422. Suppose 2*u - 8 = -2. Factor u*p**3 + 3*p**3 - 6*p**3 + 4*p**2 - w*p**4.
-4*p**2*(p - 1)*(p + 1)
Suppose -34*j = -38*j - 4. Let i(p) = p - 1. Let o(k) = -5*k**2 + 26*k - 41. Let v(q) = j*o(q) - 4*i(q). Factor v(u).
5*(u - 3)**2
Let b be (-4 + 9)/35 + (-8)/56. Find l such that 0*l + b + 2/19*l**4 + 0*l**3 - 2/19*l**2 = 0.
-1, 0, 1
Let x = 31 - 31. Factor -45*j + x*j**2 - 15*j**2 - 4*j**3 - 25 + 7*j**3 + 2*j**3.
5*(j - 5)*(j + 1)**2
Let t be (-76)/((-4)/1)*(-1)/13. Let i = 199/65 + t. Determine a so that 0 + 2/5*a**4 + 2*a**2 + i*a**3 + 4/5*a = 0.
-2, -1, 0
Let x = 1123 + -5612/5. Let b be (-26)/(-8) - 12/48. Factor -6/5*h + x*h**2 + 0 + 3/5*h**b.
3*h*(h - 1)*(h + 2)/5
Let a be 0 - 148/((-20)/5). Suppose 4*t + 17 = a. Determine b, given that 6*b**2 - 2*b**3 - 4*b**2 - 1 + 0*b**5 + 0 + b + b**t - b**4 = 0.
-1, 1
Suppose -10 = -2*r - 2*m, -2*r + 3*r + 4*m = 14. Suppose r - 17 = -5*a. Let -37*d**3 - 12*d + 24*d**a + 3*d**4 + 22*d**3 = 0. What is d?
-2, 0, 1
Suppose -4*k = -3*k - 5, 0 = 4*h + 4*k + 700. Let a = 184 + h. Determine t so that -6*t**3 + 0 - 1/4*t**5 - 4*t - 8*t**2 - 2*t**a = 0.
-2, 0
Let s be (-112)/(-4)*(-2)/(-8). Let z(n) = n**2 - 6*n - 5. Let a be z(s). Factor -5 + 3 - 4*l + 0*l**2 - a*l**2.
-2*(l + 1)**2
Let l(d) be the second derivative of -d**7/2520 - 7*d**6/2160 + d**5/60 - 2*d**4/3 + 5*d. Let i(w) be the third derivative of l(w). Factor i(f).
-(f + 3)*(3*f - 2)/3
Let z(i) = -i + 5. Let s be z(3). Suppose 149 = l + 137. Factor l*h**2 - 9*h**2 - 4*h**s + h.
-h*(h - 1)
Let t = 115 - 103. Let r be t/(-8)*12/(-27). Factor -2/9*g**2 - 4/9*g + r.
-2*(g - 1)*(g + 3)/9
Let g be (108/84)/(-3 - (-162)/42). Factor 3/8*k**4 - 15/8*k**2 + 0*k + g*k**3 + 0.
3*k**2*(k - 1)*(k + 5)/8
Let l be -1 - 4/(-3)*3. Suppose -3*k - 68 = 4. Let i(y) = -y**3 - y**2 + y. Let v(z) = -7*z**3 - 8*z**2 + 7*z. Let b(g) = k*i(g) + l*v(g). Factor b(h).
3*h*(h - 1)*(h + 1)
Let b = 70 - 63. Let g be 2580/525 - (-2)/b. Factor -18/5*c**2 - g*c**3 + 2/5*c + 4/5 - 2*c**4.
-2*(c + 1)**3*(5*c - 2)/5
Let x = 4229 + -12686/3. Factor x*l**2 - 5/3*l + 4/3.
(l - 4)*(l - 1)/3
Let x(m) be the second derivative of 5/72*m**4 + 0 - 1/18*m**3 + 11*m + 0*m**2. Factor x(r).
r*(5*r - 2)/6
Let z(o) be the second derivative of 4/9*o**4 + 1/45*o**6 + 0 - 4/9*o**3 + 0*o**2 - 13*o - 1/6*o**5. Suppose z(g) = 0. What is g?
0, 1, 2
Let w(g) be the second derivative of g**6/300 - 7*g**5/50 + 13*g**4/20 - 19*g**3/15 + 5*g**2/4 - 7*g + 13. Factor w(z).
(z - 25)*(z - 1)**3/10
Let b(s) be the first derivative of s**4/16 + s**3/6 - 5*s**2/2 + 6*s + 193. Factor b(w).
(w - 2)**2*(w + 6)/4
Let m = -85 - -85. Factor 59*w + 2*w**3 + 51*w + m*w**3 - 112*w.
2*w*(w - 1)*(w + 1)
Let h = 6 + -3. Suppose -3*x - 9 + 30 = 3*p, 25 = h*x + 5*p. Factor -5*r**3 - 2*r**3 - 2*r**4 + 8*r**3 + x*r**3 - 4*r**2.
-2*r**2*(r - 2)*(r - 1)
Let s(t) be the third derivative of 0*t + 17/30*t**4 - 121/525*t**7 + 0 - 1/10*t**5 + 17*t**2 - 4/15*t**3 - 517/600*t**6. Suppose s(n) = 0. What is n?
-2, -1/2, 2/11
Suppose 4*t = 6*t + g, -5*t + 6*g = g. Factor 1/2*f**4 + 1/2*f**2 - f**3 + t*f + 0.
f**2*(f - 1)**2/2
Find y such that 32/9*y**4 + 0*y + 20/3*y**3 + 16/9*y**2 - 4/3*y**5 + 0 = 0.
-1, -1/3, 0, 4
Let a(s) be the first derivative of 21 + 2*s**2 - 11/3*s - 1/9*s**3. Factor a(j).
-(j - 11)*(j - 1)/3
Let w(s) be the first derivative of s**6/60 + 3*s**5/20 - s**4/24 - s**3/2 - 18*s + 17. Let u(d) be the first derivative of w(d). Factor u(x).
x*(x - 1)*(x + 1)*(x + 6)/2
Let c = -781/3 + 261. Let z(b) be the first derivative of c*b**6 - 8/3*b**3 - 3*b**2 - b + 1/2*b**4 + 9/5*b**5 + 3. Solve z(i) = 0 for i.
-1, -1/4, 1
Let v = -67 + 66. Let c(f) = f**5 + f**3 + f - 1. Let n(l) = -8*l**5 + 3*l**4 + l**3 - 6*l**2 - 8*l + 8. Let w(y) = v*n(y) - 5*c(y). Factor w(q).
3*(q - 1)**3*(q + 1)**2
Let z = 110 - 101. What is d in -d**2 - 17*d + 12*d + z*d + 5 + 0 = 0?
-1, 5
Suppose 2*z - 48 = -44. Let b be ((0 + z)/16)/((-31)/(-62)). What is t in b*t + 0 - 1/4*t**2 = 0?
0, 1
Let t(x) be the first derivative of -11 + 0*x**2 - 1/900*x**6 + 0*x**4 + 2/3*x**3 + 0*x + 1/300*x**5. Let f(k) be the third derivative of t(k). Factor f(o).
-2*o*(o - 1)/5
Let l(a) = 5*a**5 + 73*a**4 + 313*a**3 + 7. Let c(u) = 5*u**5 + 74*u**4 + 314*u**3 + 6. Let s(r) = -7*c(r) + 6*l(r). Find p, given that s(p) = 0.
-8, 0
Let l(n) be the first derivative of -5/4*n**4 - 50/3*n**3 - 32 - 45/2*n**2 + 0*n. Factor l(p).
-5*p*(p + 1)*(p + 9)
Let b(z) be the second derivative of z**4/30 - 38*z**3/5 + 3249*z**2/5 - 598*z. Factor b(g).
2*(g - 57)**2/5
Let j(o) = o**3 + o**2 - o - 1. Let y(v) = -4*v**3 + 7*v**2 - 22*v + 3. Suppose 0 = -75*i + 78*i + 9. Let l(a) = i*j(a) - y(a). Factor l(s).
s*(s - 5)**2
Suppose 8 = -5*m + 13. Let c be 2*m - 200/110. Solve 2/11*s**3 - c*s**2 + 0 + 10/11*s**4 + 0*s + 6/11*s**5 = 0.
-1, 0, 1/3
Suppose 4*d + 2*p = 0, 0 = d - 281*p + 276*p. Factor 4/7*i**4 - 4/7*i**2 + d*i**3 + 2/7*i**5 - 2/7*i + 0.
2*i*(i - 1)*(i + 1)**3/7
Let j(t) be the third derivative of -5*t**5/36 + 5*t**4/24 - 39*t**2 + 2. Factor j(n).
-5*n*(5*n - 3)/3
Let w = -2501 + 2506. Let 0*i**4 + 0 + 2/9*i**w + 0*i + 0*i**2 - 2/9*i**3 = 0. Calculate i.
-1, 0, 1
Let z(j) be the first derivative of 4*j**5/15 + 2*j**4 + 16*j**3/3 + 20*j**2/3 + 4*j - 61. Factor z(f).
4*(f + 1)**3*(f + 3)/3
Let t(y) be the second derivative of y**4/20 + 3*y**3/10 + 3*y**2/5 - 142*y. Factor t(n).
3*(n + 1)*(n + 2)/5
Let v = 156 + -152. Let j be ((-10)/(-6) + (3 - v))*1. Determine r so that -r + j + 1/3*r**2 = 0.
1, 2
Let k be 10 + (4 + -3)*-6. Let o(d) be the first derivative of 0*d + 5/12*d**k - 2/15*d**5 + 2 - 2/9*d**3 + 0*d**2. Factor o(m).
-m**2*(m - 2)*(2*m - 1)/3
Let l(m) be the third derivative of -m**5/60 + 23*m**4/6 - 1058*m**3/3 + 36*m**2. Find x, given that l(x) = 0.
46
Suppose -2*h - 7*y + 9*y = -2, h + 2 = 2*y. Suppose 4*x**2 + h*x**3 + 11*x + 10*x - 29*x = 0. Calculate x.
-2, 0, 1
Let l(m) be the third derivative of -m**6/24 - 19*m**5/12 - 85*m**4/12 - 778*m**2. Factor l(q).
-5*q*(q + 2)*(q + 17)
Let f(s) be the first derivative of -6*s**4/7 + 148*s**3/21 - 72*s**2/7 + 20*s/7 + 108. Solve f(y) = 0.
1/6, 1, 5
Factor 1/2*d + 0 - 5/4*d**2 - 1/4*d**4 + d**3.
-d*(d - 2)*(d - 1)**2/4
Let w(h) be the second derivative of -h**7/126 + h**6/20 - 11*h**5/120 - h**4/24 + 13*h**3/36 - h**2/2 - 6*h. Solve w(l) = 0.
-1, 1, 3/2, 2
Let s = 29 - 27. Let -9*j**s - 18*j + 11*j**2 + 32*j = 0. Calculate j.
-7, 0
Let k be 4/(-18) + 5910/5940. Let n = -3/11 + k. Factor 1/2*f**3 + n*f**2 + 0 - f.
f*(f - 1)*(f + 2)/2
Let r = 569 + -569. Factor 3*s**5 + 0*s + r + 9/2*s**4 + 0*s**2 + 3/2*s**3.
3*s**3*(s + 1)*(2*s + 1)/2
Let w(r) be the first derivative of -19 + 30*r - 25/2*r**2 + 5/3*r**3. Solve w(n) = 0.
2, 3
Let a(i) = 7*i**3 + 2*i**2 - 7*i + 2. Let b(z) = -155*z**3 - 45*z**2 + 155*z - 45. Let p(y) = -45*a(y) - 2*b(y). Factor p(q).
-5*q*(q - 1)*(q + 1)
Let q(p) be the first derivative of p**8/336 - p**7/168 - 5*p**6/72 - p**5/8 - 19*p**3/3 - 29. Let n(k) be the third derivative of q(k). Factor n(t).
5*t*(t - 3)*(t + 1)**2
Let s(x) be the first derivative of x**5/90 - 2*x**4/27 + 5*x**3/27 - 2*x**2/9 + 7*x + 13. Let j(q) be the first derivative of s(q). Factor j(a).
2*(a - 2)*(a - 1)**2/9
Let s(u) be the second derivative of u**6/65 + 2*u**5/65 - 2*u**4/39 - 4*u. Factor s(j).
2*j**2*(j + 2)*(3*j - 2)/13
Let s(y) = 5*y**3 + 4*y**2 - 9*y. Let o(v) = -15*v**3 - 15*v**2 - 9*v + 35*v + 4*v**2. Let a(k) = -4*o(k) - 11*s(k). Solve a(d) = 0 for d.
-1, 0, 1
Let t(g) be the second derivative of 2/3*g**4 + 5/3*g**3 + 0 + 1/10*g**5 - 14*g + 2*g**2. Determine f so that t(f) = 0.
-2, -1
Let t(b) be the third derivative of b**6/40 + 13*b**5/20 - b**4/8 - 13*b**3/2 + b**2 - 25. Solve t(w) = 0.
-13, -1, 1
Suppose -7*z + 2*z + 15 = 0. Suppose -z*w + 12 = 