u = -29 - -61. Factor -16*n**2 - 1 + 18*n - 1 - u*n**2 + 32*n**3.
2*(n - 1)*(4*n - 1)**2
Let z(y) be the second derivative of y**5/5 - y**4/3 - 4*y. Suppose z(v) = 0. Calculate v.
0, 1
Let q(b) = 3*b - 6. Let n be q(4). Suppose 2*o = -o + n. Factor 1/5*m + 0*m**o - 1/5*m**3 + 0.
-m*(m - 1)*(m + 1)/5
Let h(v) = 7*v**3 - 5*v**2 - 5. Let o(n) = 3*n**3 - 2*n**2 - 2. Let k = -1 - -7. Suppose k*u = u - 50. Let r(a) = u*o(a) + 4*h(a). Factor r(d).
-2*d**3
Let k(t) be the first derivative of t**5/25 + t**4/20 + 4. Factor k(p).
p**3*(p + 1)/5
Factor -5*l**2 + 5*l + 2*l - l + 4*l.
-5*l*(l - 2)
Suppose -863*v + 290*v**2 + 183*v**3 + 223*v + 160 + 178*v**3 - 396*v**3 = 0. What is v?
2/7, 4
Factor -1/2*w**2 - 121/2 + 11*w.
-(w - 11)**2/2
Let q(m) be the first derivative of 0*m + 8 + 8/21*m**3 - 4/21*m**6 + 4/5*m**5 - m**4 + 0*m**2. Find r such that q(r) = 0.
0, 1/2, 1, 2
Suppose t = -5*d - 2*t + 35, 3*d - 4*t = -8. Let z(m) be the first derivative of -3/10*m**5 + 1/2*m - m**3 - 2 + m**d + 0*m**2. What is c in z(c) = 0?
-1/3, 1
Let y(n) be the first derivative of n**6/540 - n**5/90 + n**4/36 + 7*n**3/3 - 7. Let p(a) be the third derivative of y(a). Factor p(r).
2*(r - 1)**2/3
Let f = -17 - -9. Let d be f/(-6)*(-3)/(-8). Factor -i**2 + 0 - d*i**3 - 1/2*i.
-i*(i + 1)**2/2
Let y(t) be the third derivative of -t**10/75600 - t**9/15120 - t**8/10080 + t**5/60 - 6*t**2. Let f(j) be the third derivative of y(j). Factor f(h).
-2*h**2*(h + 1)**2
Let k(r) = r**3 + r**2 - 3*r + 4. Let d(v) = -v**3 - 2*v**2 + 2*v - 3. Let m(x) = -3*d(x) - 4*k(x). Let h be m(3). Factor 1/2 + 0*o**h - 1/2*o**4 + o - o**3.
-(o - 1)*(o + 1)**3/2
Let t(c) = 6*c**2 - 18*c + 15. Let m(b) be the second derivative of -5*b**4/12 + 17*b**3/6 - 7*b**2 - 10*b. Let s(n) = -3*m(n) - 2*t(n). Factor s(p).
3*(p - 4)*(p - 1)
Suppose 2*a + 3*a = -3*g + 20, 0 = -a + 4. Let r(j) be the third derivative of g*j**3 + 1/60*j**4 - 1/150*j**5 - 2*j**2 + 0 + 0*j. Factor r(n).
-2*n*(n - 1)/5
Let t(k) = k + 1. Let d be t(2). Suppose -4*r**2 + 4*r**d + 3*r**5 + 4*r**4 + 0*r**2 - 7*r**5 + 0*r**3 = 0. What is r?
-1, 0, 1
Let x(b) be the third derivative of b**10/529200 - b**8/70560 - b**5/15 - 3*b**2. Let w(p) be the third derivative of x(p). Suppose w(g) = 0. What is g?
-1, 0, 1
Let m(o) be the first derivative of 14*o**6/3 - 8*o**5/5 - 14*o**4 + 16*o**3/3 + 14*o**2 - 8*o + 27. Determine p, given that m(p) = 0.
-1, 2/7, 1
Let l(d) = -d**2 - 5*d - 2. Let z be l(-4). Factor 2*o**3 + 0*o**4 - z*o**4 - 2*o + 2*o.
-2*o**3*(o - 1)
Let h(t) = -2*t - 6. Let z be h(-4). Let -3*i**2 - 3*i**2 - i**3 + 7*i**z = 0. Calculate i.
0, 1
Let f(t) be the third derivative of -t**7/70 - 3*t**6/20 - 9*t**5/20 - t**4/2 + 12*t**2. Factor f(l).
-3*l*(l + 1)**2*(l + 4)
Let w = 46/495 + 4/45. Solve 4/11*y**4 + 2/11*y**5 + 0*y + w*y**3 + 0*y**2 + 0 = 0.
-1, 0
Factor 0 - 8/3*m**2 - 2/3*m**3 + 0*m.
-2*m**2*(m + 4)/3
Let b(u) = u**4 - u**3 - u**2. Let v = -2 - -1. Let s(r) = -19*r**4 - 14*r**3 + 17*r**2 + 13*r + 2. Let n(l) = v*b(l) + s(l). Solve n(z) = 0.
-1, -2/5, -1/4, 1
Factor 4/5*n**2 + 2/5 - 6/5*n.
2*(n - 1)*(2*n - 1)/5
Suppose -25*j = 5*j - 60. Factor -2 - 5/2*o**j + 4*o + 1/2*o**3.
(o - 2)**2*(o - 1)/2
Let o(r) be the first derivative of 2*r**5/5 + 5*r**4/2 + 6*r**3 + 7*r**2 + 4*r + 7. Suppose o(w) = 0. What is w?
-2, -1
Let w(j) = 6*j + 6. Let t(a) = -a**2 - 7*a - 6. Let n(h) = -3*t(h) - 4*w(h). Suppose n(f) = 0. What is f?
-1, 2
Let w(z) be the first derivative of 9*z**4/20 + 11*z**3/5 + 12*z**2/5 - 12*z/5 - 20. Factor w(f).
3*(f + 2)**2*(3*f - 1)/5
Suppose -4*n - 14 = 2, 3*l = -n - 124. Let s be 2/(-5) + (-26)/l. Find k such that 0 - s*k + 1/2*k**2 - 1/4*k**3 = 0.
0, 1
Let f(i) be the second derivative of -i**7/147 + i**5/35 - i**3/21 - 5*i. Factor f(x).
-2*x*(x - 1)**2*(x + 1)**2/7
Let d be -5 + 2 - 657/(-216). Let p(v) be the second derivative of -d*v**3 + 0 + 1/48*v**4 + 3*v + 0*v**2. Factor p(x).
x*(x - 1)/4
Let d(s) be the second derivative of s**7/84 + s**6/30 + s**5/40 - 9*s. Suppose d(i) = 0. What is i?
-1, 0
Let v(z) be the first derivative of 4*z**3/15 - 6*z**2/5 - 16*z/5 - 8. Factor v(u).
4*(u - 4)*(u + 1)/5
Factor 6*m**3 + 1/2*m**4 + 49/2 - 42*m + 11*m**2.
(m - 1)**2*(m + 7)**2/2
Let d(h) be the second derivative of -h**5/30 - h**4/18 + 5*h. Factor d(l).
-2*l**2*(l + 1)/3
Suppose -y + 5*y - 5*i = 14, -5*y - 4*i + 38 = 0. Let u(z) = -z + 12. Let l be u(y). What is t in l*t + 1 + 49/4*t**5 - 21/4*t**4 - 73/4*t**3 + 17/4*t**2 = 0?
-1, -2/7, 1
Let c(k) = -k**2 + 2*k + 3. Let z(b) = b**2 - 2*b - 4. Suppose -2*f = -5*f. Suppose f = -2*p + p + 5. Let g(a) = p*c(a) + 4*z(a). Factor g(v).
-(v - 1)**2
Suppose -2*d = 4*d. Let h(i) be the first derivative of 1/18*i**6 + 2 + 0*i - 1/15*i**5 + d*i**2 + 1/9*i**3 - 1/12*i**4. Factor h(s).
s**2*(s - 1)**2*(s + 1)/3
Suppose 4*m = 2*q, -5*m = -6*q + q. Let p(x) be the first derivative of 1 - 1/6*x**4 + 0*x - 2/9*x**3 + m*x**2. Factor p(n).
-2*n**2*(n + 1)/3
Let u be 3 - ((-3)/(-4) + -3). Let p = 23/4 - u. Factor 1/2*f**3 + p*f**2 - 1/2*f - 1/2.
(f - 1)*(f + 1)**2/2
Suppose d + d + 3*t - 8 = 0, t = d - 4. Factor -f - f**2 - 3 + 3 + f**3 + 0 + f**d.
f*(f - 1)*(f + 1)**2
Let l(s) be the second derivative of s**8/20160 + s**7/7560 - s**6/2160 - s**5/360 - s**4/12 - s. Let y(q) be the third derivative of l(q). Factor y(a).
(a - 1)*(a + 1)**2/3
Let w = 21 + -59/3. Find x such that 4/3*x**2 - w + 2/3*x**3 - 2/3*x = 0.
-2, -1, 1
Suppose -l + 6*l = 15. Factor -5*q**l + q**3 - 3*q**5 - 7*q**5 + 14*q**4.
-2*q**3*(q - 1)*(5*q - 2)
Let u(a) be the first derivative of 3*a**6/5 - 7*a**5/10 - a**4/3 - 2*a + 1. Let l(q) be the first derivative of u(q). Let l(d) = 0. What is d?
-2/9, 0, 1
Let w(t) be the first derivative of -1/6*t**2 - 1/9*t**3 + 1/12*t**4 + 3 + 0*t + 1/15*t**5. Factor w(d).
d*(d - 1)*(d + 1)**2/3
Let s = -4 - -8. Suppose -s*m - h + 11 = 0, -2*m - 2*h = -m - 1. Factor 4*k**2 + 2*k + 2*k**m - 2 + 2 + 0.
2*k*(k + 1)**2
Factor 4*c**3 - 4*c**5 + 4*c - 8*c**4 + 20*c**2 - 12*c**2 - 4*c**3.
-4*c*(c - 1)*(c + 1)**3
Suppose -2*f = -12 + 4. Suppose -4/9*b**f + 0*b**3 + 0 - 2/9*b**5 + 4/9*b**2 + 2/9*b = 0. What is b?
-1, 0, 1
Let z(c) = 12*c**2 + 8. Let t(b) be the second derivative of b**4/12 + b**2/2 + b. Let o(q) = -3*q - 17. Let m be o(-9). Let a(f) = m*t(f) - z(f). Factor a(u).
-2*(u - 1)*(u + 1)
Let m(t) be the third derivative of t**7/1575 + t**6/900 - t**5/450 - t**4/180 - 14*t**2. Find u, given that m(u) = 0.
-1, 0, 1
Let h(p) = 5*p**2 - 1. Let r be h(1). Factor 0*t + 4*t**4 + 3*t - r*t**3 + t - 4*t**2 + 0*t.
4*t*(t - 1)**2*(t + 1)
Let l(p) be the third derivative of p**7/840 - p**6/120 + p**5/48 - p**4/48 - 15*p**2. Determine q, given that l(q) = 0.
0, 1, 2
Let n(b) = b**2 - b + 12. Let z be n(6). Let k be (-5 - 1)/(z/(-28)). Factor 0*p**2 + 0 + 0*p + 3/4*p**5 + 3/2*p**k + 3/4*p**3.
3*p**3*(p + 1)**2/4
Suppose -4*u = 2*c - 4, 10 = 4*u - 2*u - 3*c. Find l such that 1/7*l**u - 2/7*l + 0 = 0.
0, 2
Let w(v) be the first derivative of -v**4/6 - 2*v**3/9 - 1. Factor w(j).
-2*j**2*(j + 1)/3
Let p(x) be the third derivative of -x**8/30240 + x**6/1080 - x**5/270 + 5*x**4/24 - 3*x**2. Let q(i) be the second derivative of p(i). Factor q(v).
-2*(v - 1)**2*(v + 2)/9
Suppose z - 4*z = o - 1, -4*o + z + 17 = 0. Let y(m) be the first derivative of 0*m + 1/8*m**2 + 3 + 0*m**3 - 1/16*m**o. Factor y(n).
-n*(n - 1)*(n + 1)/4
Let h be ((-4)/6)/(8/(-12)). Solve 8*g**4 - h - 4*g**2 - 6*g**4 - 2 + 5 = 0.
-1, 1
Suppose 0 = n - 1 - 1. Suppose d + l = 2*d, -n*d - 2*l + 8 = 0. Determine r so that -3*r**d + 1 - 4*r + r**2 - 3 = 0.
-1
Let -2/3*q**2 + 2/3 + 2/9*q - 2/9*q**3 = 0. What is q?
-3, -1, 1
Let j(l) = -l**5 - 9*l**4 - 3*l**3 - l**2 + 2. Let n(i) = i**5 - i**4 + i**3 + 1. Let u(g) = -3*j(g) + 6*n(g). Factor u(c).
3*c**2*(c + 1)**2*(3*c + 1)
Let i = -8 - -12. Determine r, given that 8*r**3 + 5*r**4 + 0*r - 5*r**4 - 4*r - i*r**5 = 0.
-1, 0, 1
Let b(i) be the second derivative of i**5/90 + i**4/54 - 2*i**3/27 + 6*i. Find o, given that b(o) = 0.
-2, 0, 1
Suppose t + 4 = 3*t. Suppose -b - 12 - 1 = -5*g, 2*b = -t*g + 10. Solve -2*f**3 + 6*f**3 - 2 + 4 - b*f**4 - 4*f = 0 for f.
-1, 1
Let c(g) = g**3 - 3*g**2 - 10*g + 4. Let l be c(5). Let k(a) be the first derivative of 1/24*a**6 + 0*a + 0*a**2 + 0*a**3 + 2 - 1/16*a**l + 