
Let w(q) = -q**3 - 8*q**2 - 3*q + 55. Let r be w(-4). Determine a so that -9*a**r - 3/2*a + 15/4*a**4 + 0 + 27/4*a**2 = 0.
0, 2/5, 1
Let t(x) = -x + 1. Let g(l) = 5*l**3 - 24*l**2 + l - 6. Let z(k) = -5*g(k) - 30*t(k). Factor z(v).
-5*v*(v - 5)*(5*v + 1)
Suppose 2/7*i**2 - 10/7 - 8/7*i = 0. Calculate i.
-1, 5
Let n = 947 - 947. Let f(x) be the first derivative of -2/13*x**3 + 2 + 0*x**4 + 2/13*x**2 + 2/65*x**5 + n*x. Factor f(y).
2*y*(y - 1)**2*(y + 2)/13
Suppose 2*s - 21 = 3*o - 6, 2*o + 10 = s. Factor 0*k - 2/9*k**2 + s.
-2*k**2/9
Let b(c) be the first derivative of c**3 - 27*c**2/2 + 60*c + 119. Suppose b(n) = 0. Calculate n.
4, 5
Suppose 0 = 4*r + q - 4, 5*r + 62*q = 64*q + 18. Solve 5/2*g + r + 1/2*g**2 = 0 for g.
-4, -1
Let i = -153 + 467/3. Let d = i + -13/6. Factor -2/3*v**3 - 2/3*v**4 + 1/6*v + d*v**5 + v**2 - 1/3.
(v - 1)**3*(v + 1)*(3*v + 2)/6
Let g = -508/13 - -4624/117. Factor -2/9*b**2 + 2/3 + g*b.
-2*(b - 3)*(b + 1)/9
Let d(l) be the second derivative of l**8/336 - l**7/168 - 5*l**3/6 - 13*l. Let o(j) be the second derivative of d(j). Find c such that o(c) = 0.
0, 1
Determine w so that 0 - 12/17*w**4 - 20/17*w**2 + 2/17*w**5 + 6/17*w + 24/17*w**3 = 0.
0, 1, 3
Let h(z) be the third derivative of z**8/672 - z**7/105 - z**6/120 + z**5/10 + 3*z**4/16 - z**2 + 75. Factor h(a).
a*(a - 3)**2*(a + 1)**2/2
Let v(n) be the first derivative of 9/16*n**2 + 1 - 3/8*n**4 + 3/8*n + 0*n**3. Factor v(j).
-3*(j - 1)*(2*j + 1)**2/8
Suppose -3*i + 7 - 28 = 0. Let x = -9 - i. Let g(q) = -5*q**3 + 7*q - 2. Let u(h) = 11*h**3 - h**2 - 14*h + 4. Let y(r) = x*u(r) - 5*g(r). Factor y(w).
(w - 1)*(w + 2)*(3*w - 1)
Let c be 3*1 - 940/900. Let p(x) be the first derivative of -c*x**3 + 6/5*x**4 - 4/15*x + 6 + 17/15*x**2. Factor p(r).
2*(2*r - 1)**2*(9*r - 2)/15
Find x such that -54*x + 86*x**2 - 59*x**3 + 25*x**2 - 4 + 9*x**2 - 3*x**3 = 0.
-2/31, 1
Let r = -1796/3 - -89801/150. Let p(i) be the third derivative of 1/600*i**6 + 0*i + 1/120*i**4 + 0 + 0*i**3 - r*i**5 - 10*i**2. Factor p(a).
a*(a - 1)**2/5
Let g(q) be the second derivative of 32*q**7/147 - 48*q**6/35 + 97*q**5/35 - 12*q**4/7 + 8*q**3/21 - 301*q. Factor g(i).
4*i*(i - 2)**2*(4*i - 1)**2/7
Let p = 4511/75 + -37/25. Let t = p + -58. Suppose 4/3*k**2 + 0*k + 0 - 2/3*k**4 + t*k**3 = 0. What is k?
-1, 0, 2
Determine p, given that -38/7*p + 37/7 + 1/7*p**2 = 0.
1, 37
Let p(a) = 3*a**5 + a**4 + 10*a**3 - a**2 - 3*a - 5. Let f(s) = -2*s**5 - 5*s**3 + s + 3. Let b(y) = 5*f(y) + 3*p(y). Determine u so that b(u) = 0.
-1, 0, 1, 4
Let b(w) be the first derivative of 2*w**3/21 + 27*w**2/7 - 8*w + 185. Factor b(m).
2*(m - 1)*(m + 28)/7
Let c be 3 - 0 - 2 - 5/((-15)/1). Find s such that -2/3*s**2 - c*s + 2/3*s**4 + 0 + 4/3*s**3 = 0.
-2, -1, 0, 1
Let b = 9 + 21. Find t, given that 33*t**2 + 28*t**2 + 2*t**3 + b*t**2 - 97*t**2 + 4*t = 0.
0, 1, 2
Let n = -12227/17 - -719. Let c = n + 49/136. Factor 0*h + 1/8*h**3 + 0 + c*h**2.
h**2*(h + 1)/8
Suppose 0 = -2*j - 3*h + 2, -5*h = 3*j + 1 - 3. Factor -7*k + k**2 - 4*k**2 + j*k.
-3*k*(k + 1)
Let i(a) be the third derivative of 2*a**7/105 + a**6/30 - 2*a**5/5 + 209*a**2. Factor i(s).
4*s**2*(s - 2)*(s + 3)
Let q(a) be the second derivative of -19*a + 7/3*a**3 + 1/6*a**4 + 6*a**2 - 1. Factor q(i).
2*(i + 1)*(i + 6)
Let f(h) be the second derivative of -h**6/30 + 21*h**5/20 - 17*h**4/3 - 9*h + 1. Determine z, given that f(z) = 0.
0, 4, 17
Let q(y) be the third derivative of 0 - 5/18*y**4 + 0*y + 1/9*y**5 - 3*y**2 + 1/24*y**6 + 0*y**3. Solve q(c) = 0 for c.
-2, 0, 2/3
Find m such that 0*m + 9/4*m**3 + 0 + 15/8*m**4 + 0*m**2 - 3/8*m**5 = 0.
-1, 0, 6
Suppose -2*k = 3*u - 15, -8*k + 6 = -10*k + 4*u. Let i be (-152)/(-48) + k*(-1 - 0). Factor 0 - 2/3*l - 5/6*l**3 + 4/3*l**2 + i*l**4.
l*(l - 2)**2*(l - 1)/6
Let g(x) = 7*x**2 + 71*x + 8. Let d(b) = 72*b**2 + 708*b + 84. Let y(l) = -2*d(l) + 21*g(l). Factor y(w).
3*w*(w + 25)
Suppose -5*v = a - 31, -5*v + 3*a - 2*a = -29. Suppose -3*o + 1 + v = -u, 2*u - 8 = -5*o. Factor 22*z**2 - o*z**3 + 6*z**3 - 30*z**2.
4*z**2*(z - 2)
Let s be 5*(2 - 3)*-1. Suppose 0*k - 115 = -s*k. Factor -45*g + k*g + 2*g**2 + 28*g + 4.
2*(g + 1)*(g + 2)
Let f(d) be the first derivative of 0*d + 1/27*d**6 + 1/9*d**2 + 0*d**5 + 44 - 1/9*d**4 + 0*d**3. Suppose f(w) = 0. Calculate w.
-1, 0, 1
Factor 18*m + 68*m - 350 - 5*m**3 + 171*m**2 - 10 + 104*m + 4*m**2.
-5*(m - 36)*(m - 1)*(m + 2)
Let o(y) be the third derivative of y**6/24 + y**5 + 145*y**4/24 + 15*y**3 - 3*y**2 - 4*y. Factor o(m).
5*(m + 1)*(m + 2)*(m + 9)
Let o be -2 - (-4)/2 - (-5)/(-235). Let w = o + 99/235. Factor -w + 4/5*u - 2/5*u**2.
-2*(u - 1)**2/5
Let c be 0 + (-7)/(21/(-6)) + -1. Suppose -2*j + c - 5 = v, -4*v - 4*j = 4. Suppose 0*s + 2/3 - 2/3*s**v = 0. What is s?
-1, 1
Let w(u) be the first derivative of u**4/14 + 200*u**3/21 - 101*u**2/7 - 873. Factor w(k).
2*k*(k - 1)*(k + 101)/7
Let m(j) be the second derivative of -5*j**4/48 - 115*j**3/24 - 75*j**2/2 + 140*j. Factor m(z).
-5*(z + 3)*(z + 20)/4
Let f(g) be the third derivative of 0*g + 1/180*g**6 - g**3 + 0*g**5 + 0*g**4 - 1/420*g**7 + 0 - g**2. Let s(m) be the first derivative of f(m). Factor s(d).
-2*d**2*(d - 1)
Suppose 0 = -4*g - 24*g. Let z(d) be the second derivative of 0 + g*d**2 + 1/12*d**3 - 1/120*d**6 + 0*d**5 - 5*d + 1/16*d**4. Suppose z(f) = 0. What is f?
-1, 0, 2
Let m = 21312 - 63935/3. Let -m*z**2 + 0 + 0*z = 0. What is z?
0
Suppose 13*p + 36 = 62. Let t(q) be the second derivative of 0 + 1/70*q**5 + 2/7*q**p + q + 1/105*q**6 - 1/14*q**4 - 1/21*q**3. Factor t(k).
2*(k - 1)**2*(k + 1)*(k + 2)/7
Let f be -11 + (5 - -7) - 12/(-88)*-2. Determine x, given that -f - 2/11*x**3 - 12/11*x**2 - 18/11*x = 0.
-4, -1
Let w(h) = 3*h**3 + 0*h + 3 - 2*h - 1 - h**2. Let n(l) = -9 + 13*l**2 + 4*l - 4*l**2 + 5*l - l**4 - 5*l**2 - 12*l**3. Let r(x) = 2*n(x) + 9*w(x). Factor r(q).
-q**2*(q - 1)*(2*q - 1)
Let k(m) be the third derivative of 0*m + 0*m**3 + 0*m**5 + 0 + 1/1155*m**7 - 1/220*m**6 - 16*m**2 + 0*m**4. Factor k(h).
2*h**3*(h - 3)/11
Let y = 1517/908 - -18/227. Suppose 0 = 4*h, 3*p - 2*h + 0*h - 3 = 0. Suppose y*s**2 + 4*s + p = 0. Calculate s.
-2, -2/7
Let n(s) = 4*s**2 + s - 1. Let l be n(1). Suppose -2*b + 5*b = -2*t + 12, -2*t - l*b + 14 = 0. Factor -j - 2*j**2 - 3*j**2 + 4*j**2 - j**t - j**2.
-j*(j + 1)**2
Let m(i) be the second derivative of -i**7/21 - 2*i**6/15 + 9*i**5/10 + 7*i**4/3 - 20*i**3/3 - 24*i**2 - 2*i + 21. Let m(a) = 0. What is a?
-3, -2, -1, 2
Let c(o) be the second derivative of -o**6/840 + 3*o**3/2 - 6*o. Let g(j) be the second derivative of c(j). Find h such that g(h) = 0.
0
Let s(r) = -r**3 + 16*r**2 + 10*r + 32. Let l be s(17). Let q be (l/42 - -2)/(4/(-80)). Factor -2/7*u**3 - 8/7 - 16/7*u - q*u**2.
-2*(u + 1)*(u + 2)**2/7
Factor -424 - 10*r**2 + 5*r**2 + 439 + 10*r.
-5*(r - 3)*(r + 1)
Factor -5*j**4 - 55*j + 30*j**3 + 0*j**4 + 25*j**3 - 59 - 45*j**2 + 109.
-5*(j - 10)*(j - 1)**2*(j + 1)
Let a(x) be the second derivative of -9*x**5/20 - 125*x**4/4 - 101*x**3 - 120*x**2 + 128*x. Factor a(r).
-3*(r + 1)*(r + 40)*(3*r + 2)
Let y(x) = -4*x**2 + 8*x + 6. Let c be y(3). Let r be 5 - (-39)/c - -2. Factor -r*o + 1/2*o**2 + 1/2*o**3 - 1/2.
(o - 1)*(o + 1)**2/2
Let u be (32/(-56))/((-6)/21). Let j(v) = 4*v**u + 10*v - 6 - 5*v**2 - 3*v. Let i(b) = 12*b**2 - 90*b + 78. Let r(a) = -2*i(a) - 27*j(a). Factor r(o).
3*(o - 2)*(o - 1)
Let q(g) be the first derivative of 2*g**7/21 + 8*g**6/15 + 2*g**5/5 - 4*g**4/3 - 2*g**3 + 22*g + 43. Let x(y) be the first derivative of q(y). Factor x(o).
4*o*(o - 1)*(o + 1)**2*(o + 3)
Let w(z) be the second derivative of z**5/130 - 5*z**4/78 + 4*z**3/39 + 2*z + 115. Factor w(l).
2*l*(l - 4)*(l - 1)/13
Let a(q) = -q**2 + 2. Let x be a(0). Factor -5*b + 17*b + 0*b**2 + 4*b**x + 7 + 1.
4*(b + 1)*(b + 2)
Suppose -1/3*o**3 - 2/3*o + 0 + o**2 = 0. What is o?
0, 1, 2
Let b be 12/(-24) - 1084/(-2160). Let o(w) be the third derivative of b*w**6 + 0*w**4 - 1/945*w**7 + 1/135*w**5 + 0*w + 0 + 0*w**3 + w**2. Factor o(r).
-2*r**2*(r - 2)*(r + 1)/9
Let i(p) = 2*p**2 - p - 1. Let d(m) = 16*m**2 + 38*m + 90. Let r(s) = d(s) - 6*i(s). Factor r(o).
4*(o + 3)*(o + 8)
Let t(u) be the second derivative of u**4/12 - 4*u**3/3 + 9*u**2 - 24*u. Let j be t(4). Factor -2/11*h**j + 0 + 2/11*h.
-2*h*(h - 1)/11
Let z be