
-4, 1
Factor 0 + 1/2*x**3 + 1/6*x**5 + 1/6*x**2 + 0*x + 1/2*x**4.
x**2*(x + 1)**3/6
Let n(x) be the second derivative of -7*x**5/60 - 2*x**4/3 - 2*x**3/3 - x**2/2 - x. Let i(d) be the first derivative of n(d). Factor i(y).
-(y + 2)*(7*y + 2)
Solve -4/3*h**3 + 2/3 - 2*h**4 - 2/3*h**5 + 2*h + 4/3*h**2 = 0 for h.
-1, 1
Let v(t) be the second derivative of 0 - 1/50*t**5 - 3*t + 0*t**2 + 0*t**3 + 1/30*t**4. Factor v(z).
-2*z**2*(z - 1)/5
Let m(z) be the third derivative of 2/5*z**5 + 3/40*z**6 - 2*z**2 + 0 + 0*z + 7/8*z**4 + z**3. Factor m(s).
3*(s + 1)**2*(3*s + 2)
Let c(f) be the second derivative of 9*f + 0 + 1/18*f**5 + 0*f**2 + 1/27*f**4 + 0*f**3. Factor c(z).
2*z**2*(5*z + 2)/9
Let i(b) be the second derivative of -b**9/22680 + b**8/5040 - b**7/3780 - 7*b**4/12 - 3*b. Let s(m) be the third derivative of i(m). Let s(r) = 0. What is r?
0, 1
Suppose 25 = 2*y + 5*d, -3 = -y + 4*d - 23. Let z be (y - (-3)/9) + 1. Solve -1/3*v**2 + 4/3*v - z = 0 for v.
2
Solve 15/4*z**3 + 9/4*z + 3/4 - 27/4*z**2 = 0 for z.
-1/5, 1
Let y(w) = 2*w**3 - w**3 + 12 + 2*w**2 - 12*w**2 - 2*w**3 + w. Let x be y(-10). Suppose 3*o**2 + 4 + 3*o**3 - 5*o**x - 4 = 0. What is o?
0, 2/3
Let m(u) be the first derivative of 16/15*u + 2/75*u**5 + 7/30*u**4 - 6 + 4/5*u**3 + 4/3*u**2. Solve m(k) = 0 for k.
-2, -1
Let p(d) = -d**3 + 12*d**2 - 9*d + 1. Let y be p(11). Let m = 33 - y. Factor -2*o**2 + 5*o + 7*o - 2 - o**2 - m.
-3*(o - 2)**2
Let m be ((-1)/(8/(-92)))/2. Let z(x) be the first derivative of 13/3*x**3 + 3/2*x**6 + 1 + 0*x - x**2 + 3/5*x**5 - m*x**4. Find t, given that z(t) = 0.
-2, 0, 1/3, 1
Suppose -38 = -4*b - 2*h - h, -2*h = -4. Find n, given that 5*n**3 - 4*n - b*n**5 + 5*n + 5*n**3 - 11*n**2 + 10*n**4 + 1 - 3*n**3 = 0.
-1, -1/4, 1/2, 1
Suppose -20 = 30*i - 34*i. Factor -5/3*u**4 - 1/3 - 10/3*u**2 - 5/3*u - 1/3*u**i - 10/3*u**3.
-(u + 1)**5/3
Suppose 2*j = -0*j - 4*s - 18, 4*j + 2*s = -12. Let r be (j - -1)*(-2)/4. Suppose -2/9*g**4 - 2/3*g**3 + r - 2/9*g - 2/3*g**2 = 0. Calculate g.
-1, 0
Let l(x) be the second derivative of -1/15*x**6 + 0 + 0*x**3 - 3/10*x**5 - 1/3*x**4 - 5*x + 0*x**2. Determine v so that l(v) = 0.
-2, -1, 0
Let u be 6/(-12)*(-2)/(-23). Let s = 51/115 + u. Determine b, given that 2/5*b**3 - s*b**2 - 2/5*b + 2/5 = 0.
-1, 1
Let k(n) be the first derivative of n**7/252 - n**6/60 + n**5/120 + n**4/24 - n**3/18 + 4*n + 6. Let g(m) be the first derivative of k(m). Factor g(q).
q*(q - 2)*(q - 1)**2*(q + 1)/6
Let y(w) be the first derivative of 2*w**5/25 + w**4/10 - 4*w**3/15 - 13. Factor y(b).
2*b**2*(b - 1)*(b + 2)/5
Factor 9/8*c**3 + 0 + 1/8*c**2 + 11/8*c**4 + 1/2*c**5 - 1/8*c.
c*(c + 1)**3*(4*c - 1)/8
Let t(l) be the second derivative of 0*l**4 + l + 1/10*l**5 + 0*l**2 + 0 + 0*l**3. Suppose t(y) = 0. What is y?
0
Let o(r) = 26*r**5 + 2*r**4 - 20*r**3 + 8*r**2 - 8*r + 8. Let c(d) = 9*d**5 + d**4 - 7*d**3 + 3*d**2 - 3*d + 3. Let p(j) = 8*c(j) - 3*o(j). Factor p(h).
-2*h**3*(h - 1)*(3*h + 2)
Factor -3*c**5 + 4*c**4 + c**5 - 5*c**3 + 3*c**3.
-2*c**3*(c - 1)**2
Factor 2/11*q**2 + 0*q - 8/11.
2*(q - 2)*(q + 2)/11
Suppose 5*a - a = -8. Let z be (-1)/(-2) + (-3)/a. Determine l so that -2/5*l**z + 2/5 + 0*l = 0.
-1, 1
Factor -1/3*s**3 - 1/3 + 1/3*s**2 + 1/3*s.
-(s - 1)**2*(s + 1)/3
Let n(v) = -4*v**2 + 4*v + 3 - 12 + 3. Let m(i) = -i**2 + i - 2. Let j(o) = -7*m(o) + 2*n(o). Factor j(t).
-(t - 2)*(t + 1)
Factor 5*n**2 - 2*n**5 + 0*n**3 + 2*n**3 + 3*n**2 - 10*n**2 + 2*n**4.
-2*n**2*(n - 1)**2*(n + 1)
Let q = -709/5 + 142. Factor 0 - 4/5*d**3 + d**2 + q*d**4 - 2/5*d.
d*(d - 2)*(d - 1)**2/5
Let k = 1/300 + 2393/2100. Suppose 0 = -r + 5*l - 4 + 2, 0 = 4*r - 3*l - 9. Factor k*m**2 + 0 + 6/7*m**r + 2/7*m.
2*m*(m + 1)*(3*m + 1)/7
Let p(h) be the first derivative of -h**4/14 + 26*h**3/7 - 507*h**2/7 + 4394*h/7 + 33. Find f, given that p(f) = 0.
13
Let k be 10/(-30)*6/(-4). Find u, given that 0 - 1/2*u + k*u**2 = 0.
0, 1
Let g(j) be the third derivative of -j**7/385 + j**6/132 - j**5/165 + 21*j**2. Factor g(h).
-2*h**2*(h - 1)*(3*h - 2)/11
What is n in 113/4*n**3 + 18*n**4 + 21/4*n + 4*n**5 + 1/2 + 19*n**2 = 0?
-2, -1, -1/4
Let p be (18/8)/3*(-4)/(-6). Factor 1/4*d**4 - 1/4*d + p + 1/4*d**3 - 3/4*d**2.
(d - 1)**2*(d + 1)*(d + 2)/4
Let d(k) = k**3 - k**2 + k - 1. Let i(z) = z**3 - 9*z**2 + 13*z - 5. Let j(g) = 5*d(g) - i(g). Factor j(b).
4*b*(b - 1)*(b + 2)
Let g(z) be the second derivative of z**7/231 + z**6/33 + 9*z**5/110 + 7*z**4/66 + 2*z**3/33 + z. Factor g(v).
2*v*(v + 1)**3*(v + 2)/11
Let i(k) be the third derivative of 19/420*k**6 + 2/21*k**3 + 1/84*k**4 + 0 - 1/14*k**5 - 1/105*k**7 + 2*k**2 + 0*k. Find b such that i(b) = 0.
-2/7, 1
Let m be (-1)/2 + (-52)/(-96). Let v(f) be the second derivative of 1/4*f**2 + 2*f - 1/6*f**3 + m*f**4 + 0. Find k, given that v(k) = 0.
1
Let j(z) be the first derivative of -z**6 + 4*z**5/5 + 7*z**4/2 + 4*z**3/3 - 58. Let j(f) = 0. What is f?
-1, -1/3, 0, 2
Let f(b) be the second derivative of 3/35*b**5 + 13/42*b**3 + 6*b + 23/84*b**4 + 0 + 1/7*b**2. Solve f(y) = 0.
-1, -2/3, -1/4
Let v(d) be the second derivative of -5/6*d**4 + 3*d + 0 - 4*d**2 + 1/10*d**5 + 8/3*d**3. Suppose v(l) = 0. Calculate l.
1, 2
Let p(x) = x**3 + 4*x**2 + 3*x + 3. Let r be p(-3). Let -5*h + h**2 + 2 + 3*h**3 - h**4 + 2*h**2 + 0*h**r - 2*h**3 = 0. Calculate h.
-2, 1
Let n(y) be the second derivative of -y**6/135 + 9*y. Let n(s) = 0. What is s?
0
Let z = -12 + 4. Let f = -3 - z. Suppose -4*n**5 + 3*n**5 + n**f - 2*n**5 + 2*n**4 = 0. Calculate n.
0, 1
Let a = 9 - 13. Let v be (-1)/(-5)*(-5)/a. Let 1/4*o**2 + 1/4*o + 0 - 1/4*o**4 - v*o**3 = 0. What is o?
-1, 0, 1
Factor 0 + 1/6*v**4 + 0*v - 1/3*v**3 + 1/6*v**2.
v**2*(v - 1)**2/6
Let r(v) be the second derivative of 3*v**5/20 - 3*v**4/2 + 5*v**3/2 + 29*v. Solve r(h) = 0.
0, 1, 5
Let z(v) be the first derivative of 6*v**5/35 - 3*v**4/7 - 10*v**3/7 + 18*v**2/7 + 46. Determine b, given that z(b) = 0.
-2, 0, 1, 3
Let b(x) be the second derivative of x**7/42 + x**6/30 - 3*x**5/20 - x**4/12 + x**3/3 - 15*x. Factor b(f).
f*(f - 1)**2*(f + 1)*(f + 2)
Let x(l) be the third derivative of l**8/504 + l**7/63 + l**6/20 + 7*l**5/90 + l**4/18 + 12*l**2. Let x(f) = 0. What is f?
-2, -1, 0
Let z(y) = -y**3 - 5*y**2 - 4*y + 3. Let s be z(-4). Suppose -4 = -s*q + 2*x - 4*x, 3*q + 3*x = 0. Factor q*j**2 + 7*j**3 + j**2 - 3*j**2.
j**2*(7*j + 2)
Let r be -1 + (27/84)/((-3)/(-12)). Solve -r*i**4 - 2/7*i - 6/7*i**3 - 6/7*i**2 + 0 = 0 for i.
-1, 0
Let m(b) be the first derivative of -2*b + 4 - 1/2*b**2 + 1/3*b**3. Factor m(k).
(k - 2)*(k + 1)
Let t(f) be the second derivative of f**4/78 - 3*f**3/13 + 8*f**2/13 - 11*f - 2. Factor t(q).
2*(q - 8)*(q - 1)/13
Let s(c) be the third derivative of -1/360*c**6 - 1/180*c**5 - 2*c**2 + 1/18*c**3 + 0*c + 0 + 1/72*c**4. Factor s(i).
-(i - 1)*(i + 1)**2/3
Let w(b) be the third derivative of b**5/80 - b**4/32 - b**3/4 + 8*b**2. Factor w(c).
3*(c - 2)*(c + 1)/4
Suppose -24 = -2*b - b. Let p be ((-15)/(-10))/(3/b). Suppose -6*z**3 - 6*z**2 + 3*z**2 - 2*z**5 + 6*z**p + 5*z**2 = 0. Calculate z.
0, 1
Let n(l) be the second derivative of 16*l**7/189 + 8*l**6/135 - 7*l**5/90 + l**4/54 - 19*l. Let n(p) = 0. Calculate p.
-1, 0, 1/4
Solve 10/7*y - 1/7*y**2 + 0 = 0 for y.
0, 10
Let s be 112/(-54)*-3 - 6. Suppose -2/9*m**4 + 2/9*m**2 - s*m**3 + 2/9*m + 0 = 0. What is m?
-1, 0, 1
Suppose 0*t - 3 = 3*t. Let v be t/(-1) - 2*-1. Factor a**2 - 3*a**5 - 4*a**4 + a**5 + v*a**2 + 2*a.
-2*a*(a - 1)*(a + 1)**3
Let h(c) be the second derivative of -1/28*c**4 + 1/7*c**3 + 0*c**2 + 0 - 5*c. Factor h(o).
-3*o*(o - 2)/7
Let w(o) be the third derivative of 1/168*o**8 + 0*o**3 - 1/60*o**6 + 0*o**5 + 0 + 0*o**4 + 0*o**7 - 2*o**2 + 0*o. Suppose w(u) = 0. What is u?
-1, 0, 1
Let a = -19/6 - -4/3. Let w = a + 5/2. Find t, given that w*t**2 + 0 + 0*t = 0.
0
Let c(r) be the second derivative of -r**6/180 + r**4/72 - 9*r. Factor c(i).
-i**2*(i - 1)*(i + 1)/6
Factor 0*d - 2/9*d**3 + 2/3*d**2 - 8/9.
-2*(d - 2)**2*(d + 1)/9
Let 7/2*g**2 + 6*g + 2 - 9/2*g**3 - 11/2*g**4 - 3/2*g**5 = 0. What is g?
-2, -1, -2/3, 1
Let s(d) = d - 16. Let r be s(16). Suppose 3*p + p - 20 = 0. Let 1/3*q**p - 2/3*q**3 + 0*q**4 + 1/3*q + 0*q**2 + r = 0. Calculate q.
-1, 0, 1
Let p = -8 + 13. Let d be ((-2)/p)/((-2)/10). Determine g so that -2*g**4 - 8*g**3 - 4*g