*6/80 - l**5/40 - 4*l**3/3 - 3. Let r(k) be the third derivative of f(k). Factor r(q).
-3*q*(q + 1)*(q + 2)/2
Let i = 66 + -33. Let y be i/22*(-1 + 2). Factor 9/2*o**2 + 0 + 3/2*o**4 - y*o - 9/2*o**3.
3*o*(o - 1)**3/2
Let i(t) = 5*t**3 - 16*t**2 + 13*t - 4. Let x(l) = -24*l**3 + 80*l**2 - 66*l + 21. Let n = 24 - 57. Let f(u) = n*i(u) - 6*x(u). Suppose f(c) = 0. Calculate c.
2/7, 1
Let j = -58 - -61. Solve 0 - 4/5*b**2 + 49/5*b**5 + 0*b - 21/5*b**4 - 24/5*b**j = 0.
-2/7, 0, 1
Determine w so that 27*w + 25*w**2 + 17*w**2 + 6*w**4 + 27*w**3 + 0*w**2 + 6 = 0.
-2, -1, -1/2
Factor 4*o**2 - 8*o + o**2 - o**2.
4*o*(o - 2)
Let i(q) be the second derivative of q**10/45360 - q**8/10080 - 7*q**4/12 - 2*q. Let m(c) be the third derivative of i(c). Factor m(b).
2*b**3*(b - 1)*(b + 1)/3
Factor -11*s - s**2 + 10*s**2 - 5*s - 5*s**2.
4*s*(s - 4)
Let x(l) = l**3 - 7*l**2 - 6*l - 9. Let s be x(8). Suppose 2*m - s*m = 0. Determine q, given that 0 - 4/5*q**4 - 2/5*q**3 + m*q - 2/5*q**5 + 0*q**2 = 0.
-1, 0
Let i(s) be the second derivative of s**4/48 + s**3/24 + 18*s. Determine g so that i(g) = 0.
-1, 0
Let h(b) be the first derivative of -2*b**3/21 + 4*b**2/7 - 12. Find w, given that h(w) = 0.
0, 4
Suppose 0 = 5*i - 13 - 12. Let y(t) be the third derivative of 0*t**3 + 2*t**2 + 0 + 1/48*t**4 + 1/240*t**i + 0*t. Factor y(x).
x*(x + 2)/4
Suppose -4*z - 6 = -7*z. Suppose -5*v = w + 2*w + 3, -z*w - 3*v = 1. Factor -w*y**2 - 2*y**2 + 8*y**2 + y**3.
y**2*(y + 2)
Suppose 0 = -0*j - 3*j + 12. Let b(s) be the second derivative of 0 + 2*s + 1/18*s**j + 1/3*s**2 + 2/9*s**3. Suppose b(g) = 0. What is g?
-1
Factor -i - 1/3*i**2 + 0.
-i*(i + 3)/3
Let m(u) = -2*u**3 - u**2 + 1. Let t(v) = v**2 - 3*v - 1. Let q be t(3). Let y be m(q). Factor 6*o + 4*o**2 - y - 2 - 6*o**2.
-2*(o - 2)*(o - 1)
Let r(g) = 3*g**2 - 9*g + 6. Let l = 24 - 15. Let h be 57/l + 2/(-6). Let f(j) = 3*j**2 - 9*j + 6. Let v(k) = h*f(k) - 7*r(k). Factor v(s).
-3*(s - 2)*(s - 1)
Let n(g) be the second derivative of 1/21*g**3 - 2*g + 0 - 1/42*g**4 + 2/7*g**2. Let n(o) = 0. Calculate o.
-1, 2
Suppose 4*j = -5*g - 3, 1 = 3*g + 4*j - 2. Let q be 3/((-5 + 2)/g). Determine f, given that -4*f - 3*f**4 + 2*f**2 - f**5 + q*f + f**4 + 2*f**5 = 0.
-1, 0, 1
Let y(x) = x**2 + 9*x + 7. Let u(w) = -5*w**2 - 46*w - 34. Let l(n) = -2*u(n) - 11*y(n). Let o be l(-4). Factor 0 + 0*m - 2/7*m**4 + 4/7*m**o - 2/7*m**2.
-2*m**2*(m - 1)**2/7
Let n(t) be the third derivative of -t**10/604800 - t**9/241920 + t**8/40320 + t**5/20 - t**2. Let q(o) be the third derivative of n(o). Factor q(f).
-f**2*(f - 1)*(f + 2)/4
Let o(f) = -f - 5. Let h be o(-5). Factor h - 1/4*k - 1/4*k**2.
-k*(k + 1)/4
Suppose -2*i**3 + 10/9*i**2 + 2*i - 14/9*i**4 + 4/9 = 0. Calculate i.
-1, -2/7, 1
Let 2*f**2 + 1/2*f**3 + 1 + 5/2*f = 0. What is f?
-2, -1
Suppose 4*a + 0*a = -2*a. Let f(n) be the second derivative of -3*n - 1/48*n**4 + a*n**2 + 0*n**3 + 0. Suppose f(h) = 0. Calculate h.
0
Let q(h) = h**3 + 3*h. Let d(g) be the third derivative of -g**4/24 - 3*g**2. Let z(b) = 6*d(b) + 2*q(b). Let z(a) = 0. What is a?
0
Let y = -13 - -25. Let n be (4/(-6))/((-16)/y). Let -n*q**3 + 0 + 1/4*q**4 + 0*q + 1/4*q**2 = 0. Calculate q.
0, 1
Let u = 2605/9 + -289. Let y = -2/45 + u. Find o such that y*o + 2/5*o**2 - 2/5 - 2/5*o**3 = 0.
-1, 1
Factor -2/3*u + 1/3 + 1/3*u**2.
(u - 1)**2/3
Let d(j) be the first derivative of 1 - 2/7*j + 0*j**2 + 4/21*j**3 + 0*j**4 - 2/35*j**5. Factor d(g).
-2*(g - 1)**2*(g + 1)**2/7
Let i(u) be the first derivative of -5*u**4/4 + 10*u**3/3 - 5*u**2/2 + 33. Factor i(f).
-5*f*(f - 1)**2
Let 0 - 8/7*i**3 + 4/7*i + 0*i**4 + 0*i**2 + 4/7*i**5 = 0. Calculate i.
-1, 0, 1
Let c(h) be the first derivative of -1/30*h**5 - 1/6*h**4 + 0*h - 5/18*h**3 - 1/6*h**2 - 3. Let c(z) = 0. What is z?
-2, -1, 0
Let f(i) = 7*i + 7. Let p be f(-3). Let s be 4/14 - 4/p. What is m in -6/7*m**3 - s*m**2 - 4/7 + 2*m = 0?
-2, 1/3, 1
Let y = -9 + 12. Factor 16*j + 40*j**2 + 12*j**4 - 84*j**y - 6*j**4 + 40*j**4 - 8*j**5.
-2*j*(j - 2)**3*(4*j + 1)
Let n(j) be the second derivative of j**9/432 + j**8/840 + j**3/2 + 2*j. Let r(t) be the second derivative of n(t). Factor r(c).
c**4*(7*c + 2)
Let r = -3 - -5. Suppose 8 = -2*m + 3*m - 5*g, 5*g + 14 = 3*m. Let -2/7*l**5 + 0*l**r + 0*l**4 + 0*l + 2/7*l**m + 0 = 0. Calculate l.
-1, 0, 1
Let g(h) be the third derivative of h**5/15 + h**4/12 + h**3/6 + 3*h**2. Let d be g(-1). Find q such that 0*q**3 + 2*q**d - q**3 + q**4 = 0.
-1, 0
Let z(f) = -13*f**2 + f + 7. Let j = -9 + 2. Let i(k) = -6*k**2 + 3. Let l(t) = j*i(t) + 3*z(t). Factor l(n).
3*n*(n + 1)
Let i(d) be the second derivative of -49*d**4/3 + 28*d**3/3 - 2*d**2 - 13*d. Solve i(m) = 0.
1/7
Let i(b) be the second derivative of 1/40*b**5 - 5*b + 0*b**2 + 0 - 1/120*b**6 + 0*b**3 + 0*b**4. Let i(j) = 0. What is j?
0, 2
Let a be 2/(-2) + ((-105)/9)/(-5). Solve -a*v**3 - 8/3 - 16/3*v - 1/6*v**4 - 4*v**2 = 0 for v.
-2
Solve 2/3*y - 2*y**3 - 4/3 + 8/3*y**2 = 0.
-2/3, 1
Let n(d) be the first derivative of -56/9*d**3 - 3/5*d**5 - 8/3*d**4 - 2 - 8*d**2 - 1/18*d**6 - 16/3*d. Factor n(x).
-(x + 1)*(x + 2)**4/3
Suppose -11 = -2*v + i, 3*i + 20 = 5. Let x = v + 0. Let y(j) = -2*j**3 - j. Let k(h) = -h**3. Let n(u) = x*k(u) - y(u). Solve n(m) = 0 for m.
-1, 0, 1
Let j(s) be the second derivative of -5*s**4/12 - 5*s**3 - 25*s**2/2 - s. Let j(c) = 0. What is c?
-5, -1
Find z such that -6*z**2 - 162 - 3*z - z**3 - 9*z + 154 = 0.
-2
Let j(t) be the first derivative of -t**6/420 - t**5/84 - t**4/42 + 4*t**3/3 + 3. Let h(q) be the third derivative of j(q). Factor h(y).
-2*(y + 1)*(3*y + 2)/7
Let a(k) be the second derivative of -k**4/18 + k**3/3 - 8*k. Factor a(f).
-2*f*(f - 3)/3
Factor g**2 + g**2 - 4*g + 8*g + 6 - 4.
2*(g + 1)**2
Let q(x) be the third derivative of -x**7/630 + x**6/360 + x**5/180 - x**4/72 - x**2. Factor q(p).
-p*(p - 1)**2*(p + 1)/3
Let t(n) = n**2 - n - 1. Let m(d) = 10*d**2 - d + 5. Let s(f) = -m(f) - 5*t(f). Find v such that s(v) = 0.
0, 2/5
Suppose -10*z + 9*z - 12 = -3*b, 22 = -z + 5*b. Suppose 3/4*s**5 - 3/2*s - 15/4*s**2 + 0 + 3/4*s**4 - 9/4*s**z = 0. Calculate s.
-1, 0, 2
Let s(r) be the third derivative of r**7/105 - r**6/20 + r**5/15 + 8*r**2. Factor s(h).
2*h**2*(h - 2)*(h - 1)
Suppose w + 4*s + 0 = -15, -10 = -3*w - s. Let j be -1 + w + 12/(-12). Factor 0 - 2/5*h + 6/5*h**2 + 2/5*h**4 - 6/5*h**j.
2*h*(h - 1)**3/5
Let i(p) be the first derivative of -p**3/3 + p**2/2 + p + 3. Let o(z) = z**3 - 2*z - 6. Let m(a) = 2*i(a) - o(a). Factor m(k).
-(k - 2)*(k + 2)**2
Let c(r) be the third derivative of -49*r**6/40 + 7*r**5/5 - r**4/2 - 11*r**2. Factor c(s).
-3*s*(7*s - 2)**2
Let u(n) = n**3 + n**2 - 4. Let f = 9 - 8. Let z(k) be the second derivative of k**2/2 + k. Let w(t) = f*u(t) + 4*z(t). Find p, given that w(p) = 0.
-1, 0
Let s(k) be the second derivative of -k**7/189 + k**6/135 + k**5/30 - k**4/54 - 2*k**3/27 - k. Determine h so that s(h) = 0.
-1, 0, 1, 2
Let d be 18/(-12)*(-2)/1. Suppose 9 - 3*j - 2*j + d*j**2 - 7*j + 3 = 0. Calculate j.
2
Let x(y) = 4*y**3 - 6*y**2 + 2. Let g(a) = 9*a**3 - 13*a**2 + a + 3. Let k(w) = 2*g(w) - 5*x(w). Solve k(c) = 0.
-1, 1, 2
Let h be (27/30)/((-3)/(-5)). Let q(z) = z**3 + 5*z**2 + z + 7. Let g be q(-5). Factor 0*n - 3*n**3 + 0 - 3/2*n**4 - h*n**g.
-3*n**2*(n + 1)**2/2
Let i = -8 + 11. Factor 8*f**5 - 10*f**5 - i*f**4 + 5*f**4.
-2*f**4*(f - 1)
Let u(o) be the third derivative of 0*o**3 + 0 - 1/45*o**5 - 1/144*o**6 + 6*o**2 - 1/36*o**4 + 0*o - 1/1260*o**7. Suppose u(n) = 0. What is n?
-2, -1, 0
Let p(d) = d + 2. Let u be p(-2). Suppose y + y = u. Factor x**4 + 0*x + y*x**2 + 1/2*x**5 + 0*x**3 + 0.
x**4*(x + 2)/2
Factor 1/7 + 1/7*n**3 - 1/7*n**2 - 1/7*n.
(n - 1)**2*(n + 1)/7
Suppose 4*o = -0*o + 12. Let a(x) = 3*x**3 + 1 - x**4 - x**2 + x - x**3 - o*x**3. Let t(w) = -4*w**4 - 2*w**3 + 2*w + 2. Let r(l) = -2*a(l) + t(l). Factor r(c).
-2*c**2*(c - 1)*(c + 1)
Let w = -4444/141 - -5/282. Let k = w - -32. Find h, given that 1/2 + 0*h - k*h**2 = 0.
-1, 1
Let g(y) = 6*y + 4. Let j(f) = f**2 - 19*f - 13. Let k(x) = -14*g(x) - 4*j(x). Determine s, given that k(s) = 0.
-1
Suppose 0 = 3*c - 2*c - 4. Factor m**c - 2*m + 0*m - 4 + 0*m**3 + 2*m**3 + 3.
(m - 1)*(m + 1)**3
Let i(q) be the first derivative of -2*q**5 + 7*q**4/6 + 16*q**3/45 - 4*q**2/15 - 