the second derivative of p**7/540 - 4*p**6/405 + 11*p**5/540 - p**4/54 - p**3/2 + 3*p. Let t(m) be the second derivative of a(m). Factor t(x).
2*(x - 1)**2*(7*x - 2)/9
Let n = 1085/396 - 22/9. Let j = 5/11 + n. Let -9/4*o**2 + 0*o**3 + 0 - 3/2*o + j*o**4 = 0. What is o?
-1, 0, 2
Let s(l) = -l**2 - 4*l + 10. Let r be s(-5). Let i(m) be the third derivative of -1/10*m**r + 0 + 2*m**2 + 0*m**3 - 1/12*m**4 + 0*m. Factor i(c).
-2*c*(3*c + 1)
Let p(b) = 3*b**2 + b. Let q be p(1). Let f be 6/q - (-9)/(-6). Solve -1/4 + f*x + 1/4*x**2 = 0 for x.
-1, 1
Let j(r) be the third derivative of 2*r**7/315 + r**6/30 - 35*r**2. Factor j(v).
4*v**3*(v + 3)/3
Suppose 0*a - 6 = -3*a. Let y(v) be the first derivative of 2/3*v**3 + 2*v + 2 + a*v**2. Solve y(g) = 0.
-1
Let b(q) = -q**4 + 7*q**3 - 6*q**2. Let y(s) = 3*s**4 - 22*s**3 + 18*s**2. Let v(n) = -21*b(n) - 6*y(n). Determine m so that v(m) = 0.
0, 2, 3
Suppose 4 = s - 2*d + 12, 3*d = s + 12. Let z = s + 3. Let o(f) = -f**2. Let l(y) = 12*y**2 - 12*y + 3. Let n(q) = z*o(q) + l(q). Suppose n(k) = 0. Calculate k.
1/3, 1
Let p(t) be the second derivative of t**4/18 - t**2/3 - 5*t. Let p(r) = 0. Calculate r.
-1, 1
Let a be (-11 - -10) + 3/(1 - -2). Let o(y) be the third derivative of -1/80*y**5 + 1/32*y**4 + y**2 - 1/80*y**6 + 0*y**3 + 0*y + a. Factor o(m).
-3*m*(m + 1)*(2*m - 1)/4
Factor -1/3 + 2/3*v - 1/3*v**2.
-(v - 1)**2/3
Suppose 3*x - 4*r + 10 = 0, -r + 12 = 4*x - 0*r. Factor -1 - 1/2*n + 1/2*n**x.
(n - 2)*(n + 1)/2
Let h(f) = f**3 + 15*f**2 - 16*f + 1. Let c be h(-16). Let x(s) be the first derivative of s + 1/3*s**3 - s**2 - c. Factor x(r).
(r - 1)**2
Let o(f) be the first derivative of -3*f**5/80 - 5*f**4/48 - f**3/24 + f**2/8 - 3*f + 4. Let n(b) be the first derivative of o(b). Let n(s) = 0. What is s?
-1, 1/3
Let i(l) be the second derivative of 2*l**2 - 17/10*l**5 - 11/3*l**3 + l + 1/3*l**6 + 7/2*l**4 + 0. Suppose i(p) = 0. What is p?
2/5, 1
Let g be 9 + 0 + -4 + -2. Factor 0*u - 1/3*u**g + 0 - 1/3*u**2.
-u**2*(u + 1)/3
Solve 5 - 76*b**3 - 85*b**3 - 5*b**2 + 171*b**3 - 10*b = 0.
-1, 1/2, 1
Let u(z) = -z**5 + z**4. Let f(i) = -12*i**5 - 2*i**4 + 44*i**3 - 48*i**2 + 18*i. Let l(x) = 2*f(x) - 28*u(x). Find v, given that l(v) = 0.
0, 1, 3
Let f(k) = k**2 - k - 1. Let y(v) = 3*v**5 + 6*v**4 - 3*v**3 + 12*v**2 - 18*v - 18. Let i(c) = -18*f(c) + y(c). Factor i(r).
3*r**2*(r - 1)*(r + 1)*(r + 2)
Let g(c) = c**2 - 4*c - 29. Let d be g(-4). Factor 15/2*o**4 + 0 - d*o - 3/2*o**5 + 21/2*o**2 - 27/2*o**3.
-3*o*(o - 2)*(o - 1)**3/2
Determine o so that 2/5*o**2 + 0 + 4/5*o = 0.
-2, 0
Let t = 169 - 167. Factor 1/3*n**2 + 3 + t*n.
(n + 3)**2/3
Let z = -20 - -24. Let w(r) be the second derivative of 2/21*r**3 + 1/105*r**6 + 0*r**2 + 0 + 2/35*r**5 - 2*r + 5/42*r**z. Suppose w(q) = 0. Calculate q.
-2, -1, 0
Solve 9*x**2 + 0 + 3/2*x**3 + 27/2*x = 0.
-3, 0
Suppose 3*g = 10 - 1. Determine o, given that -2*o - 2*o**g - o - 4*o**2 + 8*o**2 + o = 0.
0, 1
Suppose 3 = -2*c - 2*j + 13, -c + j = 1. Let s(i) be the first derivative of 1/3*i**3 + 1/12*i**6 - 3 - 1/4*i**c + 0*i + 0*i**4 - 1/5*i**5. Factor s(a).
a*(a - 1)**3*(a + 1)/2
Let g(f) = f**3 + f**2 + f. Let q(n) = -n**4 + 6*n**3 + 5*n**2 + 2*n. Let p(r) = -4*g(r) + q(r). Factor p(w).
-w*(w - 2)*(w - 1)*(w + 1)
Suppose 0 = -3*f - 2*f + 10. Suppose 4 = -0*m + 2*m. Factor -16*y**3 + 5*y**4 - 7*y**5 - f*y**5 - 26*y**4 - 4*y**m.
-y**2*(y + 1)*(3*y + 2)**2
Let n(v) be the first derivative of -1 + 3/5*v**2 - 4/5*v - 2/15*v**3. Solve n(q) = 0.
1, 2
Let h(i) = -147*i**4 + 173*i**3 - 61*i**2 + 11*i - 3. Let w(y) = -293*y**4 + 347*y**3 - 121*y**2 + 23*y - 7. Let v(t) = 14*h(t) - 6*w(t). Factor v(s).
-4*s*(3*s - 1)*(5*s - 2)**2
Let v(f) be the third derivative of f**6/240 + f**5/60 - f**4/48 - f**3/6 - 6*f**2. Find i such that v(i) = 0.
-2, -1, 1
Let j(r) be the first derivative of -4*r**5/5 + 8*r**3/3 - 4*r + 1. Determine t, given that j(t) = 0.
-1, 1
Factor 0 + 6/7*a**2 - 4/7*a + 4/7*a**3.
2*a*(a + 2)*(2*a - 1)/7
Solve -15/7*l**2 - 1/7 - 13/7*l**3 - l - 4/7*l**4 = 0.
-1, -1/4
Let v(c) be the second derivative of -c**5/20 + c**4/6 - 7*c. Factor v(n).
-n**2*(n - 2)
Let k(l) = l**2 + 16*l + 8. Suppose 4*m - 8*m = 12. Let s(c) = -8*c - 4. Let q(r) = m*k(r) - 5*s(r). Factor q(v).
-(v + 2)*(3*v + 2)
Let d(w) = -3*w**2 + 10*w - 14. Let u(b) = 4*b**2 - 11*b + 13. Let s(k) = -3*d(k) - 2*u(k). Suppose s(t) = 0. What is t?
4
Let c = 2 + 0. Let x(a) be the second derivative of -1/3*a**2 - c*a - 1/18*a**3 + 1/12*a**4 + 0. Suppose x(p) = 0. Calculate p.
-2/3, 1
Let c(j) = -4 - j + 2*j + 5. Let y(h) be the second derivative of -h**4/12 - h**3/2 - h**2 - 2*h. Let v(n) = -c(n) - y(n). Factor v(t).
(t + 1)**2
Let z(i) = -i**2 - 2*i. Let s(b) = b**2 + 10*b + 9. Let n(r) = -r - 1. Let m(f) = -18*n(f) - 2*s(f). Let p(l) = -3*m(l) + 4*z(l). Let p(u) = 0. Calculate u.
0, 1
Let n(l) be the third derivative of -l**7/420 + l**5/120 - 72*l**2. Find a, given that n(a) = 0.
-1, 0, 1
Let r(p) = p + 2. Let m be r(0). Factor 0*k + 0*k**m - 2*k**2 - 3*k + 5*k.
-2*k*(k - 1)
Let n(f) = 8*f**5 - 38*f**4 - 18*f**3 - 14. Let r(x) = -3*x**5 + 13*x**4 + 6*x**3 + 5. Let h(a) = -5*n(a) - 14*r(a). Solve h(i) = 0.
-3, -1, 0
Let n(a) be the third derivative of a**5/30 - 2*a**4/3 + 16*a**3/3 - 5*a**2. Find b such that n(b) = 0.
4
Suppose 84*g + 68*g**2 + 71*g**2 - 141*g**2 - 882 = 0. What is g?
21
Suppose -h = -4*q - 70, -6*q - 64 = -3*q + 5*h. Let k be 50/q - (-7 - -4). Factor 0 + 0*a + k*a**3 + 2/9*a**5 + 0*a**2 - 4/9*a**4.
2*a**3*(a - 1)**2/9
Let z(k) be the third derivative of -1/784*k**8 + 0*k**3 + 3/490*k**7 + 0*k**4 + 1/140*k**5 - 6*k**2 + 0 + 0*k - 3/280*k**6. Solve z(o) = 0 for o.
0, 1
Let n be 1*(0 - (0 - 2)). Let a(y) be the third derivative of 0*y - 1/540*y**6 + y**n - 1/36*y**4 + 0 + 1/90*y**5 + 1/27*y**3. Solve a(v) = 0.
1
Let n(t) = 8*t**5 - 6*t**4 - 14*t**3 - 12*t**2 - 12*t - 12. Let x(o) = o**5 - o**4 - o**3 - o**2 - o - 1. Let z(d) = -n(d) + 12*x(d). Let z(u) = 0. What is u?
0, 1/2, 1
Let u(j) = -j**3 - 6*j**2 + j + 8. Let d be u(-6). Let z be 56/(-21) - (-1 - d). Factor z*a**3 - 2/3*a**2 + 0 + 1/3*a.
a*(a - 1)**2/3
Factor 78*k**4 - 87 - 112*k**2 - 36*k**3 + 23 - 82*k**4 - 144*k.
-4*(k + 1)*(k + 2)**2*(k + 4)
Suppose -20 = 5*l, 2*l = g + 4 - 16. What is f in 26/3*f**3 + g*f**4 + 8/3*f + 2/3*f**5 + 8*f**2 + 0 = 0?
-2, -1, 0
Let -16/7 - 2/7*p**2 - 12/7*p = 0. Calculate p.
-4, -2
Let y(v) be the third derivative of -v**5/360 - 7*v**4/36 - 49*v**3/9 - 43*v**2. Factor y(o).
-(o + 14)**2/6
Let u(d) = 2*d**2 - d - 7. Let j be u(5). Factor f**3 - j - 4*f**2 + 42 + 7*f**3 - 6*f - 2*f**5.
-2*(f - 1)**3*(f + 1)*(f + 2)
Let b(s) be the third derivative of -s**6/420 + s**5/210 - 7*s**2. What is x in b(x) = 0?
0, 1
Suppose 11 + 25 = l. Let x be ((-16)/l)/(6/(-9)). Factor -4/3*d**4 + 4/3*d**2 + 0 + 2/3*d**5 + 0*d**3 - x*d.
2*d*(d - 1)**3*(d + 1)/3
Suppose 0 = 4*y - 4, 4*y - 4 = 12*x - 13*x. Factor x*g + 0 + 1/4*g**2 + g**4 - 5/4*g**3.
g**2*(g - 1)*(4*g - 1)/4
Let o = -1/6 + 1/2. Let q(n) be the first derivative of -o*n**3 - 1/6*n**2 - 1/15*n**5 + 2 + 0*n - 1/4*n**4. Factor q(t).
-t*(t + 1)**3/3
Let w(q) = -q**3 - 2*q**2 - q + 2. Let m be w(-2). Suppose 3*n = -2*n - 3*s + 27, -s = -3*n + 5. Factor 2*a**m + 9/2*a**2 - 1/2 + 11/2*a**n + 1/2*a.
(a + 1)**3*(4*a - 1)/2
Let b(t) be the third derivative of t**7/840 + t**6/240 - t**5/60 - t**4/48 + t**3/8 + 5*t**2 - 6. Let b(y) = 0. What is y?
-3, -1, 1
Let b(u) be the second derivative of -4*u + 1/12*u**4 + 1/3*u**3 + 0 + 0*u**2. Factor b(j).
j*(j + 2)
Let r(t) be the third derivative of t**6/360 + t**5/36 + t**4/24 - t**3/2 + 16*t**2. Factor r(v).
(v - 1)*(v + 3)**2/3
Let y = 51 - 93. Let i = y - -128/3. Factor 0*t**2 - 2/3*t + 0 - i*t**5 + 4/3*t**3 + 0*t**4.
-2*t*(t - 1)**2*(t + 1)**2/3
Let b(h) = -12*h**2 - 12*h - 5. Let f(y) = -12*y**2 - 12*y - 6. Let w(u) = 3*b(u) - 2*f(u). Determine g, given that w(g) = 0.
-1/2
Let z(n) be the second derivative of -1/10*n**6 - 3/2*n**2 - 3/5*n**5 - n - 3/2*n**4 + 0 - 2*n**3. Factor z(i).
-3*(i + 1)**4
Let i be 2*(8 + (-2 - 0)). Factor 2 + i*h**3 - h**2 - 4 - 8*h - h**2.
2*(h - 1)*(2*h + 1)*(3*h + 1)
Let v be (3/(45/6))/1. Let -v*n**5 + 2/5*n**2 + 0 + 0*n - 2/5*n**4 + 2/5*n**3 = 0. Calculate n.
-1, 0, 1
Let s(c) be the second derivative of -5*c