*d**2 + 0*d. Factor w(m).
-(m - 1)**2/3
Suppose 36 = 11*z - 2*z. Let w(m) be the first derivative of -2/25*m**5 + 5 - 4/15*m**3 + 0*m**2 + 0*m + 3/10*m**z. Factor w(r).
-2*r**2*(r - 2)*(r - 1)/5
Let s = 6127/2 + -3063. Factor s*y**3 + 8*y - 4*y**2 + 0.
y*(y - 4)**2/2
Let w = -11507 - -34523/3. Factor 0 + w*y - 1/3*y**2.
-y*(y - 2)/3
Find k, given that 2/7*k**3 + 2/7*k**2 - 2/7*k - 2/7 = 0.
-1, 1
Suppose -11 = 31*h - 104. Let 18/7*d**4 + 92/7*d**2 - 60/7*d**h - 2/7*d**5 - 66/7*d + 18/7 = 0. Calculate d.
1, 3
Suppose 0 = -76*h + 71*h. Let v(m) be the second derivative of m + h*m**2 - 1/14*m**3 + 0 - 1/28*m**4. Find i, given that v(i) = 0.
-1, 0
Determine u, given that 123 + 9 + 44*u**2 + 8*u**2 - 5*u**3 + 78 + 148*u**2 + 415*u = 0.
-1, 42
Suppose 0*k + 52 = k + n, 4*n - 161 = -3*k. Let i = 49 - k. Factor 2/9*s**4 - 2/9*s**i + 0*s**3 + 0*s + 0.
2*s**2*(s - 1)*(s + 1)/9
Suppose 0 = t + i - 8, -t + 3*i + 6 = 2*t. Suppose -13 - 7*u - 8 + t - 4*u**2 - 9*u = 0. Calculate u.
-2
Let u(q) = -q**3 - 8*q**2 - 11*q - 8. Let d be u(-7). Suppose -4*a - 12 + d = 0. Find n, given that -15/7*n**a + 9/7*n**4 + 3/7*n**3 - 3/7*n + 6/7 = 0.
-1, 2/3, 1
Factor -10/9*b**2 + 4/3*b + 0 + 2/9*b**3.
2*b*(b - 3)*(b - 2)/9
Let u(o) be the first derivative of -5*o**2 + 1/40*o**6 + 1/20*o**5 - 2 - 1/4*o**4 + 0*o + 0*o**3. Let j(q) be the second derivative of u(q). Factor j(b).
3*b*(b - 1)*(b + 2)
Let g be (11 + -1)*(-4)/(-10). Suppose g*i - 2*i = 8. Factor 16*u**2 - u**5 - 15*u**2 + i*u**3 - u**4 + u**3 - 4*u**3.
-u**2*(u - 1)*(u + 1)**2
Let c = 373/5 + -2233/30. Let x(f) be the third derivative of 0 + 0*f - 1/16*f**4 + c*f**3 + 1/120*f**5 - 8*f**2. Factor x(d).
(d - 2)*(d - 1)/2
Let a(y) = y**3 + 24*y**2 + 24*y + 26. Let c be a(-23). Factor -376*h**3 + 3*h**2 + 380*h**c - 7*h**2.
4*h**2*(h - 1)
Let u(q) be the third derivative of -q**6/540 - q**5/10 - 9*q**4/4 - 23*q**3/6 - 38*q**2. Let c(i) be the first derivative of u(i). Factor c(r).
-2*(r + 9)**2/3
Let h(o) be the second derivative of 0*o**3 + 0 + 1/10*o**5 - 11*o - 2/21*o**7 + 0*o**2 + 0*o**4 + 1/15*o**6. Factor h(s).
-2*s**3*(s - 1)*(2*s + 1)
Factor 232 - 38*p**2 + 26*p + 34*p - 52 + 43*p**2.
5*(p + 6)**2
Let d be (-3)/(-9) - (60/(-16) - -4). Let t(r) be the second derivative of -d*r**4 + 0*r**2 + 0 - r - 1/6*r**3. Let t(a) = 0. What is a?
-1, 0
Let z be (-24)/(((4*3)/(-4))/2). Determine v so that -z*v + 4*v**4 + 12*v**2 - 16 + 20*v**3 - 2*v**3 - 2*v**3 = 0.
-2, -1, 1
Let y = -2214/143 + 206/13. Let 3/11*c**3 + 8/11*c**4 + 0 - 7/11*c**2 + 2/11*c - y*c**5 = 0. Calculate c.
-1, 0, 1/2, 2
Let w(t) = -t**4 - t**2 - 3*t - 1. Let m(y) = 108*y**4 + 695*y**3 + 1208*y**2 + 754*y + 133. Let s(b) = -m(b) - 3*w(b). Solve s(u) = 0 for u.
-13/3, -1, -2/7
Let q be (-26)/(-39)*(0 + 1 + 2). Let b = 159/8 - 1399/72. Let -2/9 + 2/3*u**q + b*u = 0. Calculate u.
-1, 1/3
Let y(d) be the second derivative of -2*d**6/15 + 14*d**5/5 - 25*d**4/3 + 8*d**3 - 2*d - 59. What is l in y(l) = 0?
0, 1, 12
Let v(p) = -2 - 25*p**2 - 18 - 8*p**3 + 60*p + 13*p**3. Let u(q) = -q. Let b(i) = -20*u(i) - v(i). Factor b(z).
-5*(z - 2)**2*(z - 1)
Let w(i) be the first derivative of 14 + 1/16*i**4 + 1/24*i**6 + 0*i + 0*i**2 + 1/10*i**5 + 0*i**3. Factor w(b).
b**3*(b + 1)**2/4
Let j(i) be the second derivative of -7*i**6/90 - 6*i**5/5 - 83*i**4/36 - i**3 - 24*i. What is s in j(s) = 0?
-9, -1, -2/7, 0
Let f(l) be the second derivative of -l**5/15 - 5*l**4/3 - 50*l**3/3 - 5*l**2 - 35*l. Let n(k) be the first derivative of f(k). Factor n(c).
-4*(c + 5)**2
Let f(o) be the second derivative of -o**6/60 - o**5/15 - 5*o**2 + 8*o. Let g(t) be the first derivative of f(t). Factor g(w).
-2*w**2*(w + 2)
Factor -1/5*x**3 + 1/5*x + 1/5*x**4 + 2/5 - 3/5*x**2.
(x - 2)*(x - 1)*(x + 1)**2/5
Let b(y) be the third derivative of 1/3*y**3 - 1/15*y**6 - 1/10*y**5 + 4/105*y**7 + 0 + 1/6*y**4 + 0*y + 12*y**2. Factor b(u).
2*(u - 1)**2*(2*u + 1)**2
Let r(a) = 4*a**2 - 2*a + 3. Let g(z) = -29*z**2 + 54*z**2 - 26*z**2 - 3*z + 4*z - 1. Let i(u) = -3*g(u) - r(u). Factor i(n).
-n*(n + 1)
Let w be (-20)/(-6)*98/2450. What is a in -2/15*a**3 + 0 + w*a**2 + 2/15*a - 2/15*a**4 = 0?
-1, 0, 1
Let y(v) = -10*v - 36. Let d be y(-4). Let n(t) be the first derivative of -2 + 0*t**d + 0*t + 2/3*t**3 - 2/5*t**5 + 0*t**2. Let n(i) = 0. What is i?
-1, 0, 1
Let h(w) be the second derivative of 0 + 1/4*w**3 + 5*w + 0*w**2 - 1/8*w**4. Factor h(v).
-3*v*(v - 1)/2
What is z in -1/8*z**3 - 289/2 - 136*z + 67/8*z**2 = 0?
-1, 34
Let m(n) be the third derivative of n**8/3360 - n**7/175 + 3*n**6/80 - 9*n**5/100 + 311*n**2. Let m(a) = 0. What is a?
0, 3, 6
Suppose 0 = 2*w - 4*n + 8, 0 = 3*w + n - 4*n + 21. Let b be (-4 - (-27)/6)*(0 - w). Suppose 6*y**4 + 9/2*y**b + 1/2*y - y**3 - 2*y**2 + 0 = 0. Calculate y.
-1, 0, 1/3
Suppose 2/19*y**3 + 0 - 2/19*y**2 + 2/19*y**4 - 2/19*y = 0. What is y?
-1, 0, 1
Suppose -g = -4*p + 10, 2*p - 2*g - 6 = -4. Let a(z) be the third derivative of 1/15*z**5 + 4*z**2 - 4/3*z**p + 0*z + 0 - 1/6*z**4. Factor a(k).
4*(k - 2)*(k + 1)
Let l(n) be the second derivative of -5*n**7/42 + 3*n**6/5 - 7*n**5/20 - n**4/2 + 110*n. Solve l(b) = 0.
-2/5, 0, 1, 3
Let i be (1/(-20))/(-5 + 9). Let l = 47/80 - i. Let 3/5*u**2 - l*u**3 + 1/5*u**4 + 0 - 1/5*u = 0. What is u?
0, 1
Let h(m) = -12*m**3 - 36*m**2 - 36*m + 66. Let x(k) = k**3 + k**2 - k + 1. Let u(r) = -h(r) - 9*x(r). Factor u(q).
3*(q - 1)*(q + 5)**2
Factor 7 - 63*b**3 + 59*b**3 - 8*b**2 + 16*b + 25.
-4*(b - 2)*(b + 2)**2
Let d = 33 - 28. Suppose -2 = 4*r - d*r. Factor -3*n**2 + 2*n**r + n + 0*n**2.
-n*(n - 1)
Let x = -90 + 149. Suppose 0 = 3*j - 77 + x. Factor 4 + 3*i**2 - j*i - 1/2*i**3.
-(i - 2)**3/2
Factor 4/13*q + 30/13 - 2/13*q**2.
-2*(q - 5)*(q + 3)/13
Let s(w) be the second derivative of -w**8/13440 + w**7/840 - w**6/120 + w**5/30 + 5*w**4/6 + 19*w. Let d(b) be the third derivative of s(b). Factor d(x).
-(x - 2)**3/2
Let h(c) = 291*c + 1746. Let u be h(-6). Suppose p + 3 = 3*d - 0, -1 = -2*d + p. Factor 0*x + 2/5*x**d - 2/5*x**4 + u*x**3 + 0.
-2*x**2*(x - 1)*(x + 1)/5
Let b(d) = 3*d**3 - 2*d**2 - 7*d + 3. Let q(k) = -2*k**3 + k**2 + 5*k - 2. Let x(v) = -5*b(v) - 7*q(v). Let f(z) be the first derivative of x(z). Factor f(s).
-3*s*(s - 2)
Let g(n) be the first derivative of n**6/240 - n**4/48 - 7*n**2/2 + 1. Let h(u) be the second derivative of g(u). Determine r so that h(r) = 0.
-1, 0, 1
Let -39/2*h + 1521/4 + 1/4*h**2 = 0. What is h?
39
Let p(q) be the second derivative of -22*q + 1/6*q**3 - 1/30*q**6 + 0 + 0*q**2 + 1/12*q**4 - 1/20*q**5. Determine z, given that p(z) = 0.
-1, 0, 1
Let x(l) be the third derivative of l**8/10080 - l**6/360 - l**5/90 - 5*l**4/12 - 14*l**2. Let v(c) be the second derivative of x(c). What is i in v(i) = 0?
-1, 2
Let n(b) = b**3 - 2*b**2 - 5*b + 6. Suppose -4*h + 15 = 4*y - 17, -17 = y - 4*h. Let v be n(y). What is k in 10/7*k**3 - 4/7*k + v + 6/7*k**2 = 0?
-1, 0, 2/5
Let i(d) = 53*d**2 + d. Let k be i(-1). Let t be 4 + (k/(-8) - -3). Factor -t*s - 1/4 - 1/4*s**2.
-(s + 1)**2/4
Suppose -3*r = -158 + 146. Let o(c) be the first derivative of 1/4*c + 1/12*c**3 + 1/4*c**2 + r. Factor o(h).
(h + 1)**2/4
Factor -20*g**2 + 2251*g**3 - 27*g + 2*g - 2256*g**3 - 10.
-5*(g + 1)**2*(g + 2)
Let u(a) = -2*a**3 + a**2 + a + 1. Let j be u(-1). Factor 1 - 2*v**j + 0*v**2 + 16*v**2 - 11*v**2 - 8*v**2.
-(v + 1)**2*(2*v - 1)
Let d(o) be the third derivative of o**7/350 - 3*o**6/100 + 13*o**5/100 - 3*o**4/10 + 2*o**3/5 - 67*o**2 - o. Factor d(m).
3*(m - 2)**2*(m - 1)**2/5
Suppose -3*p - p - 5*d - 11 = 0, 0 = 2*p - d - 5. Let g be (-1)/(p - 3/2). Factor -g*f**2 + 2*f**4 + 7*f**5 - 6*f**3 - 5*f**3 + 4*f**3.
f**2*(f - 1)*(f + 1)*(7*f + 2)
Let u(b) be the second derivative of 1/60*b**4 - 2/5*b**2 - 2/15*b**3 + 0 + 1/100*b**5 + 5*b. Factor u(a).
(a - 2)*(a + 1)*(a + 2)/5
Let g(b) = 2*b**2 + 153*b + 121. Let p(c) = 2*c**2 + 146*c + 120. Let q(j) = 4*g(j) - 5*p(j). Factor q(z).
-2*(z + 1)*(z + 58)
Let d(n) = -31*n**2 + 124*n. Let j be d(4). Let h(p) be the first derivative of 2/9*p**3 - 1/15*p**5 + j*p**2 + 0*p - 1 + 1/12*p**4. Factor h(s).
-s**2*(s - 2)*(s + 1)/3
Factor 8/5*s**2 + 0 - 18/5*s.
2*s*(4*s - 9)/5
Let t(i) be the third derivative of -i**8/1680 - i**7/42 + i**6/600 + i**5/12 - 342*i**2. Suppose t(n) = 0. What is n?
-25, -1, 0