z + 1)**2
Let c(k) be the first derivative of -k**3 - 6*k**2 - 12*k + 11. Factor c(r).
-3*(r + 2)**2
Let g(i) be the first derivative of i**6/2 + 3*i**5/5 - 9*i**4/4 - 5*i**3 - 3*i**2 - 17. Factor g(p).
3*p*(p - 2)*(p + 1)**3
Find x, given that -3*x**2 + 2*x**2 + 14*x - 144 + 10*x = 0.
12
Let k(y) be the second derivative of 0*y**3 + 1/10*y**2 + 0 - 2*y - 1/60*y**4. Determine f, given that k(f) = 0.
-1, 1
Let y = 8 - 0. Let j be 1/y*10*4. Suppose 2*u**3 + 0 + 2*u**4 + 2/3*u**2 + 2/3*u**j + 0*u = 0. Calculate u.
-1, 0
Let l = 15 + -13. Factor -m**2 + 4*m**4 + 4*m**3 - m**2 + l*m**2.
4*m**3*(m + 1)
Let l = 20 + -16. Factor 2*o**l + 0*o**2 - 5*o**3 + 2*o**2 + o**3.
2*o**2*(o - 1)**2
What is n in -n**2 - 16 - 19 + 36 = 0?
-1, 1
Let u(x) be the second derivative of x**4/36 - x**3/18 - x**2/3 + 7*x. Factor u(h).
(h - 2)*(h + 1)/3
Suppose -4*u + 5*s = -5, -4*u + 2*u - s - 1 = 0. Suppose -6 = -3*d - u. Factor 0*m**d - 2/3*m**3 + 1/3 + 2/3*m - 1/3*m**4.
-(m - 1)*(m + 1)**3/3
Factor 1/4*j**2 - 1/4*j - 1/2.
(j - 2)*(j + 1)/4
Let v(s) be the first derivative of 3*s**4 + 23*s**3/3 + 5*s**2 - s + 3. Determine z so that v(z) = 0.
-1, 1/12
Let k(i) be the third derivative of -i**7/315 - i**6/90 - i**5/90 + 8*i**2 + i. Factor k(a).
-2*a**2*(a + 1)**2/3
Let d(w) be the first derivative of -5*w**6/6 - w**5 + 15*w**4/4 + 25*w**3/3 + 5*w**2 - 34. Find y, given that d(y) = 0.
-1, 0, 2
Let m(d) be the second derivative of -d**6/30 - d**5/2 - 2*d**4 + 5*d**3/3 + 25*d**2/2 - 16*d. Factor m(a).
-(a - 1)*(a + 1)*(a + 5)**2
Suppose -c - 12 = -2*u - 2*u, 3*c - 4*u = -4. Find a such that 0*a**c + 0*a**2 + 2/7*a**3 + 0 - 2/7*a**5 + 0*a = 0.
-1, 0, 1
Determine p, given that 10/11*p**2 - 14/11*p**3 + 4/11*p + 0 = 0.
-2/7, 0, 1
Let t(q) be the first derivative of 3*q**4/4 + 8*q**3/3 + 7*q**2/2 + 2*q + 1. Suppose t(n) = 0. What is n?
-1, -2/3
Let k = -103/3 + 311/9. Let v(i) be the first derivative of -k*i**3 - 3 + 1/3*i**2 + 0*i. Factor v(q).
-2*q*(q - 1)/3
Let -2/3*c**4 - 2/3*c**3 + 2/3*c**2 + 0 + 2/3*c = 0. What is c?
-1, 0, 1
Let z be 6/(-48) + -13*3/(-120). Factor 0*j**2 + 1/5*j + 0 - z*j**3.
-j*(j - 1)*(j + 1)/5
Let i(w) = 5*w**2 + 4*w - 19. Let f(d) = -6*d**2 - 3*d + 18. Let o(u) = 6*f(u) + 7*i(u). Factor o(y).
-(y - 5)**2
Find d, given that -27/5*d - 18/5*d**2 - 12/5 - 3/5*d**3 = 0.
-4, -1
Find k, given that 6*k + 4*k**2 + 3*k - 3*k = 0.
-3/2, 0
Let g(u) = u**3 + 4*u**2 - u - 1. Let i = -5 + 1. Let t be g(i). Suppose 0*w + 0*w**2 - 1/3*w**t + 0 = 0. What is w?
0
Let u(n) = 10*n**2 - 11*n + 27. Let y(k) = -9*k**2 + 12*k - 27. Suppose -3*b + 21 + 12 = -5*h, 2*h = -6. Let j(l) = b*u(l) + 7*y(l). Factor j(p).
-3*(p - 3)**2
Factor 34/11*s + 2/11*s**3 - 16/11 - 20/11*s**2.
2*(s - 8)*(s - 1)**2/11
Determine b so that 12/5*b**2 + 2/5 - 8/5*b + 2/5*b**4 - 8/5*b**3 = 0.
1
Let x(u) be the third derivative of u**8/30240 - u**7/3780 + u**6/1620 - 7*u**4/24 - 2*u**2. Let h(l) be the second derivative of x(l). Factor h(t).
2*t*(t - 2)*(t - 1)/9
Let v(h) be the second derivative of -h**5/4 + 25*h**4/12 - 35*h**3/6 + 15*h**2/2 + 17*h. Factor v(y).
-5*(y - 3)*(y - 1)**2
Let i(d) = 3*d**2 - 8*d + 7. Let z be i(2). Let w(x) be the second derivative of -z*x + 0*x**3 + 0*x**2 - 1/15*x**5 + 1/18*x**4 + 0. What is n in w(n) = 0?
0, 1/2
Let z = 631 + -1159/2. Let q = -50 + z. What is h in q*h - 3/2*h**2 + 3 = 0?
-1, 2
Suppose -l - 3*i = 15, 5*l + 13 = -2*i + 3. Suppose 5*m - 4*m = l. Suppose 2*a + m*a**2 - a**2 - a**2 = 0. Calculate a.
0, 1
Suppose 6/7*q**3 + 4/7*q**2 + 0 - 2/7*q = 0. What is q?
-1, 0, 1/3
Let f = -74 - -134. Suppose 5*k = 5*m - f, -m + 5*k + 10 = -10. Factor m*p + 2*p**2 - 10*p - 8*p**4 - 6*p**3.
-2*p**2*(p + 1)*(4*p - 1)
Factor 4*k**4 - 39*k - 17*k**3 - 19*k + 18*k - 15*k**3 + 68*k**2.
4*k*(k - 5)*(k - 2)*(k - 1)
Suppose -4*u - h + 36 = -0*u, -4*u = -h - 44. Let n be 5/u*(-16)/(-10). Factor 0*m - 2/5*m**3 - n*m**2 + 0.
-2*m**2*(m + 2)/5
Let s(q) be the third derivative of q**6/300 - q**5/75 - q**4/60 + 2*q**3/15 - 28*q**2. Determine z so that s(z) = 0.
-1, 1, 2
Let b(f) be the first derivative of -1/6*f**4 - 1 + 0*f**2 + 4/9*f**3 + 0*f - 2/15*f**5. What is y in b(y) = 0?
-2, 0, 1
Factor -z - 1/2 - 1/2*z**2.
-(z + 1)**2/2
Determine d so that -2/7 + 11/7*d**2 + 9/7*d = 0.
-1, 2/11
Let o(v) be the third derivative of 0*v + 0*v**4 - 2*v**2 + 0*v**3 + 0 - 1/672*v**8 + 1/240*v**6 - 1/420*v**7 + 1/120*v**5. Factor o(m).
-m**2*(m - 1)*(m + 1)**2/2
Let t(v) be the first derivative of -v**7/168 - v**6/120 + v**5/20 + v**4/12 + v - 5. Let o(q) be the first derivative of t(q). Let o(u) = 0. Calculate u.
-2, -1, 0, 2
Factor 8/9*i**3 + 2/9*i**5 - 10/9*i + 4/9 - 8/9*i**4 + 4/9*i**2.
2*(i - 2)*(i - 1)**3*(i + 1)/9
Let v be (1 + 1)/(4/6). Suppose -2*u + 39 = 3*u + v*m, -2*u - 3*m = -21. Factor -20*w**2 - 3*w - u*w**4 + 10*w**5 + 4 - 8*w**3 + w + 22*w**4.
2*(w - 1)*(w + 1)**3*(5*w - 2)
Let t(l) be the first derivative of -l**4/8 + 3*l**2/4 + l + 1. Let w(u) be the first derivative of t(u). What is z in w(z) = 0?
-1, 1
Let u(i) be the second derivative of 0*i**3 + 0 + 1/8*i**2 - i - 1/48*i**4. Factor u(q).
-(q - 1)*(q + 1)/4
Let m(c) = -c**2 - 6*c - 3. Let i be m(-5). Let 4*a - 24*a**3 - 12*a**4 - 5*a**2 - a**2 - i*a**4 = 0. What is a?
-1, 0, 2/7
Let o(r) be the second derivative of -4*r - 1/20*r**5 + 0 - 1/12*r**4 + 1/2*r**2 + 1/6*r**3. Factor o(t).
-(t - 1)*(t + 1)**2
Let j(u) = -u + 9. Let l be j(9). Let h(v) be the third derivative of 1/20*v**5 - 4*v**2 - v**3 + 1/70*v**7 + 0 + 3/40*v**6 + l*v - 3/8*v**4. Solve h(f) = 0.
-2, -1, 1
Factor 194*b**2 + 13 + 78*b**4 + 150*b**3 - 62*b**2 + 51*b + 15*b**5 - 7.
3*(b + 1)**3*(b + 2)*(5*b + 1)
Let l = 106 + -103. Factor 0 + 2/3*u**5 + 0*u**2 + 0*u**4 + 2/3*u - 4/3*u**l.
2*u*(u - 1)**2*(u + 1)**2/3
Let n(z) = z**2 - 1. Let x(i) = -5*i**3 + i**2 + 5*i - 1. Let p(r) = 6*n(r) - x(r). Factor p(w).
5*(w - 1)*(w + 1)**2
Factor 0*m**2 + 5*m**2 - 7*m**2 + 0*m**2.
-2*m**2
Let h(k) = -1. Let f(w) = -w**2 - w + 1. Let r(x) = -f(x) - h(x). Let a be r(1). Factor 4*m**4 + 12*m**2 - 2*m**4 + 8*m + 1 + 6*m**3 + 1 + a*m**3.
2*(m + 1)**4
Let q(p) be the second derivative of -p**5/20 + p**4/5 - 3*p**3/10 + p**2/5 - 12*p. Let q(x) = 0. Calculate x.
2/5, 1
Let s(i) = -4*i**3 + 28*i**2 - 21*i. Let w(o) = 36*o**3 - 252*o**2 + 188*o. Let c(r) = 28*s(r) + 3*w(r). Factor c(x).
-4*x*(x - 6)*(x - 1)
Let d be (-3 - 9/(-3)) + -3. Let z be 5/(-45) + (-1)/d. Solve -2/9 + 2/9*b**2 - 2/9*b + z*b**3 = 0 for b.
-1, 1
Suppose 0*t + 48 = 4*t. Suppose -2*s - 2*s = -t. Determine z so that 2/5*z + 7/5*z**4 + 0 - 11/5*z**s - 7/5*z**2 + 9/5*z**5 = 0.
-1, 0, 2/9, 1
Suppose -2*z + 3 + 5 = 0. Factor -2/3*r**2 + 0 + 0*r + 1/3*r**3 + 1/3*r**z.
r**2*(r - 1)*(r + 2)/3
Let l be -3*6/(-9)*-2. Let x(w) = 6*w**3 + 3*w**2 - 3*w. Let y(z) = -z**4 - 7*z**3 - 3*z**2 + 3*z. Let r(c) = l*x(c) - 3*y(c). Factor r(d).
3*d*(d - 1)**2*(d + 1)
Suppose 2*a + m - 33 = 2*m, 4*m = -3*a + 33. Let n = 19 - a. Factor 0 - 1/2*q**3 - 1/4*q**n - 1/4*q**2 + 0*q.
-q**2*(q + 1)**2/4
Let -2/9*m + 0 + 1/3*m**2 - 1/9*m**3 = 0. What is m?
0, 1, 2
Suppose m + 0*m = -3*o + 48, -m + 23 = -2*o. Let n = m - 31. Factor 2*r**n + 1/2 + 2*r.
(2*r + 1)**2/2
Let y(z) = -10*z**4 + 10*z**3 - 2*z**2 + 6*z + 28. Let k(m) = -3*m**4 + 3*m**3 - m**2 + 2*m + 9. Let l(d) = 16*k(d) - 5*y(d). What is p in l(p) = 0?
-1, 1, 2
Let i(h) be the first derivative of -h**6/33 + 6*h**5/55 + h**4/22 - 14*h**3/33 + 8*h/11 - 11. Determine k so that i(k) = 0.
-1, 1, 2
Let s = -3473/4 - -875. Let r(d) be the first derivative of 18*d**3 - 18*d**2 + 8*d - s*d**4 + 1. Factor r(z).
-(3*z - 2)**3
Factor o**2 + 5*o**3 + 0*o**2 - o**2 - 5*o**5.
-5*o**3*(o - 1)*(o + 1)
Let v be 9/(-15) + 112/(-55) - -3. Factor -2/11 - 4/11*i**3 + 2/11*i**5 - 2/11*i**4 + 2/11*i + v*i**2.
2*(i - 1)**3*(i + 1)**2/11
Suppose v = -a + 2, -v = -2*a + 2*v + 14. Let y(d) = 2*d - 2. Let i be y(2). Factor -2*c - c**2 - 2*c**a + c**2 + 2*c**3 + 2*c**i.
-2*c*(c - 1)**2*(c + 1)
Determine a, given that 2/3*a + 0 - 2/9*a**4 + 2/9*a**3 + 10/9*a**2 = 0.
-1, 0, 3
Let w = -1024/21 - -148/3. Let b(y) be the second derivative of 4/3*y**3 - 31/42*y**4 - w*y**2 - 9/10*y**5 + y + 0. Determine o, given that b(o) = 0.
-1, 2/9, 2/7
Let p be 7*2*(-2)/(-4). Solve -3*l**2 + p*l**2 - l**2 = 0.
0
Let p be 3/10*((-15)/1