19*f**3 + 4*f**4.
4*f*(f + 1)**2*(f + 2)
Let c = 39 + -39. Let j(h) be the third derivative of -1/24*h**4 + c - 1/30*h**5 + 0*h**3 + 0*h - 1/120*h**6 + h**2. Factor j(v).
-v*(v + 1)**2
Let q(n) = 2*n - 2. Let f be q(4). Suppose 3*u - 2*u = -5*v - 15, -f = 4*u + 2*v. Determine x, given that u - x**2 - 2/5*x = 0.
-2/5, 0
Let z(n) be the first derivative of -2*n**6/3 + 6*n**5/5 - 2*n**3/3 - 6. Solve z(g) = 0.
-1/2, 0, 1
Let 1/4*h**2 + 0 + 0*h = 0. What is h?
0
Let z(y) be the first derivative of y**8/112 + y**7/40 - y**6/15 - y**5/10 - y**3/3 + 4. Let h(a) be the third derivative of z(a). Factor h(w).
3*w*(w - 1)*(w + 2)*(5*w + 2)
Suppose 2*y + 1 + 0 = -3*m, 5*m + 3*y = 0. Factor -4*u**3 - 4*u**3 - 2*u**2 + 6*u**m.
-2*u**2*(u + 1)
Factor -17*t + 26*t**3 - t + t**5 - 2*t**2 - 7*t**4 + 3*t + 9 - 12*t**3.
(t - 3)**2*(t - 1)**2*(t + 1)
Factor 0 + 2/9*m**3 + 0*m - 2/3*m**2.
2*m**2*(m - 3)/9
Factor -3*k**2 + 0*k + 3/2*k**4 + 0*k**3 + 3/2.
3*(k - 1)**2*(k + 1)**2/2
Suppose 0 = -4*w - 3*m + 21, 2*m - 9 = -w - 0*w. Let -r**2 - 4*r**w + 9*r**2 + r**4 - 4*r**2 = 0. What is r?
0, 2
Let l be 1/(2*(-20)/(-24)). Factor 1/5*x**3 + 3/5*x**2 + 1/5 + l*x.
(x + 1)**3/5
Let v(l) be the first derivative of 1/6*l**3 + 0*l**2 + 0*l + 2. Factor v(j).
j**2/2
Let a(v) be the second derivative of 7*v**4/6 + 2*v**3/3 - 14*v. Find x, given that a(x) = 0.
-2/7, 0
Let f(n) be the first derivative of -n**6/2 - 12*n**5/5 - 9*n**4/2 - 4*n**3 - 3*n**2/2 + 20. What is z in f(z) = 0?
-1, 0
Let s(u) be the third derivative of -7*u**6/360 + u**5/12 - u**4/8 + u**3/18 - 7*u**2. Factor s(v).
-(v - 1)**2*(7*v - 1)/3
Let u(m) be the second derivative of -m**7/280 + m**6/60 - 2*m**3/3 - 8*m. Let h(p) be the second derivative of u(p). Factor h(d).
-3*d**2*(d - 2)
Let a(f) be the first derivative of f**4 - 16*f**3/3 - 34. Factor a(t).
4*t**2*(t - 4)
Let m(f) be the third derivative of -f**7/1155 + f**6/165 - f**5/66 + f**4/66 - 8*f**2. Determine u, given that m(u) = 0.
0, 1, 2
Let t(l) be the second derivative of -l**9/52920 + l**8/11760 - l**4/2 + l. Let b(h) be the third derivative of t(h). Let b(y) = 0. What is y?
0, 2
Let d(t) be the second derivative of 1/12*t**4 + 1/30*t**6 + 0*t**2 - 1/168*t**7 - 3*t - 1/24*t**3 - 3/40*t**5 + 0. Factor d(m).
-m*(m - 1)**4/4
Let d(s) be the third derivative of -s**6/30 + 3*s**5/5 - 9*s**4/2 + 18*s**3 + 11*s**2. Factor d(f).
-4*(f - 3)**3
Factor -69*n**4 + 66*n**4 + 2*n**3 + n**3 + n**5 - n**2.
n**2*(n - 1)**3
Let u(a) = a + 11. Let y be u(-8). Factor -1 - 2*p + 0 - y*p**2 - 3 + 5*p**2.
2*(p - 2)*(p + 1)
Let j(u) be the second derivative of u**10/15120 + u**9/3780 - u**7/630 - u**6/360 + u**4/2 + 2*u. Let y(z) be the third derivative of j(z). Factor y(h).
2*h*(h - 1)*(h + 1)**3
Let w be -2*(2 - 10/4). Suppose w = -4*b + 9. Solve -3*h**b + 2*h + 6*h**2 - 4*h**2 - 1 = 0 for h.
1
Let m(h) be the first derivative of h**3/4 + 33*h**2/4 + 363*h/4 + 24. Factor m(r).
3*(r + 11)**2/4
Let f(a) = 6*a**2 + 22*a + 20. Let h(m) = -m**2 + m. Let u(g) = -f(g) - 2*h(g). Let u(q) = 0. Calculate q.
-5, -1
Let p(i) be the first derivative of -i**4/44 + 7*i**3/33 - 3*i**2/11 - 30. What is f in p(f) = 0?
0, 1, 6
Let f(u) be the first derivative of u**8/336 - u**7/105 + u**6/120 - 5*u**2/2 - 6. Let b(k) be the second derivative of f(k). Find d such that b(d) = 0.
0, 1
Suppose -2*g = -4 - 0. Let p be (g/(-1))/((-1)/2). Find j such that -2*j**p - 2*j**2 - 3*j**5 + 0*j**4 + j**3 + 2*j**5 + 4*j**2 = 0.
-2, -1, 0, 1
Let q(j) be the third derivative of -2*j**2 - 1/30*j**5 + 0*j + 1/48*j**4 + 1/40*j**6 - 1/105*j**7 + 0*j**3 + 1/672*j**8 + 0. Determine p, given that q(p) = 0.
0, 1
Let b(x) be the first derivative of -x**4/12 + 2*x - 5. Let q(j) be the first derivative of b(j). Let q(t) = 0. Calculate t.
0
Suppose -5 = -4*n - w, 0 = -3*n + w + 9. Let s be 1/3 - 14/(-3). Factor -4*r - 2 - 3*r**n + s*r**2 - 4*r**2.
-2*(r + 1)**2
Let m be 2/(-4)*1/(-2). Let c(u) be the second derivative of u - 1/10*u**5 + 0 + 1/60*u**6 - 1/3*u**3 + 1/4*u**4 + m*u**2. Solve c(s) = 0.
1
Determine n, given that 36*n**4 + 48*n**3 + 12*n**3 + 28*n**2 + 0*n + 4*n = 0.
-1, -1/3, 0
Let f(r) be the first derivative of -3*r**3 - 4 - 1/2*r**4 - 9*r**2 - 1/30*r**5 + r. Let x(d) be the first derivative of f(d). Solve x(z) = 0.
-3
Let v(l) = -20*l + 342. Let f be v(17). Factor -1/7*h**3 + 1/7*h + 1/7 - 1/7*h**f.
-(h - 1)*(h + 1)**2/7
Factor 0*z - 1/3*z**3 + 0*z**2 - 1/2*z**4 + 0 - 1/6*z**5.
-z**3*(z + 1)*(z + 2)/6
Suppose -19*y - 4 = -21*y. Let h be (4/(-24))/(y/(-4)). Factor -1/3*u**2 + 0 - h*u**3 + 0*u.
-u**2*(u + 1)/3
Let h(x) be the third derivative of x**8/23520 - x**6/2520 - x**4/6 + 5*x**2. Let z(k) be the second derivative of h(k). Let z(d) = 0. Calculate d.
-1, 0, 1
Suppose -24*t + 19*t + 75 = 0. Let p(y) = -y**3 + y + 6. Let x be p(0). Factor t*k**3 + x*k**4 - 2 - k - 2*k**3 - k**4 + 9*k**2.
(k + 1)**3*(5*k - 2)
Solve 3/11*r**2 + 0 + 1/11*r**3 + 2/11*r = 0.
-2, -1, 0
Let w = 1 + 11. Let h be 4/w + 10/42. Factor -10/7*l**3 + h + 10/7*l - 4/7*l**2.
-2*(l - 1)*(l + 1)*(5*l + 2)/7
Let b = 51/25 - -19/25. Let 4/5*k**4 + b*k - 4/5 - 12/5*k**2 - 2/5*k**3 = 0. What is k?
-2, 1/2, 1
Let q = -33 + 28. Let z(l) = -l**3 - l**2 - 2*l. Suppose k - 5*k - 8 = 0. Let o(s) = 3*s**3 + 3*s**2 + 4*s. Let f(n) = k*o(n) + q*z(n). Factor f(w).
-w*(w - 1)*(w + 2)
Let -1/4*p**2 + 0 - 1/4*p = 0. Calculate p.
-1, 0
Factor -3/7*o**4 - o**3 + 1/7*o**5 + 8/7 + o**2 + 18/7*o.
(o - 4)*(o - 2)*(o + 1)**3/7
Find j, given that j**4 + 6*j**4 - 2*j**4 + 10*j + 25*j**2 + 20*j**3 + 0*j**2 = 0.
-2, -1, 0
Let i(r) = -11*r**2 + 9*r + 16. Let v(k) = 5*k**2 - 5*k - 8. Let y(h) = 4*i(h) + 9*v(h). Let g be y(10). Factor 1/2*m**2 + 2*m + g.
(m + 2)**2/2
Let v(b) be the second derivative of 49*b**6/6 + 175*b**5/4 + 110*b**4/3 + 10*b**3 - 52*b. Determine k, given that v(k) = 0.
-3, -2/7, 0
Determine a so that 16/3*a**2 + 20/3*a + 4/3*a**3 + 8/3 = 0.
-2, -1
Let t(o) = -6*o**3 - 16*o**2 - 19*o - 9. Let v(w) = -3*w**3 - 8*w**2 - 9*w - 4. Let f(g) = -4*t(g) + 10*v(g). Factor f(i).
-2*(i + 1)**2*(3*i + 2)
Suppose n = 5*t - 23, 2*n + 2*t = 5 + 9. Factor 0*c**n + 2*c**2 + 0*c**2 - 2.
2*(c - 1)*(c + 1)
Let f(o) = 5*o**2 - 5*o + 8. Let p(a) = -3*a**2 + 3*a - 5. Let v be (-4*(-6)/(-3))/(-1). Let b(s) = v*p(s) + 5*f(s). Determine g so that b(g) = 0.
0, 1
Let i(v) be the third derivative of -1/120*v**6 + 3/2*v**3 + 0*v + 0 + 7/60*v**5 + 5*v**2 - 5/8*v**4. Factor i(x).
-(x - 3)**2*(x - 1)
Factor -6/7*h**3 + 12/7 + 2/7*h**4 - 6/7*h**2 + 2*h.
2*(h - 3)*(h - 2)*(h + 1)**2/7
Let l(n) = -n**3 + n**2 + n - 1. Let v(c) = -5*c**3 + 4*c**2 + 7*c - 6. Let r(x) = -6*l(x) + v(x). Factor r(d).
d*(d - 1)**2
Let c = -4 + 4. What is a in -4/7*a + c - 2/7*a**2 = 0?
-2, 0
Let s(o) be the third derivative of 0*o**3 + 6*o**2 - 1/340*o**6 + 0 + 1/102*o**4 - 1/102*o**5 + 0*o. Factor s(n).
-2*n*(n + 2)*(3*n - 1)/17
Suppose 4*x - 2*x = -0*x. Factor x + l**2 + l**4 + 1/4*l + 1/4*l**5 + 3/2*l**3.
l*(l + 1)**4/4
Let y(v) be the first derivative of 5 - 3/8*v**6 + 3/2*v**5 - 37/16*v**4 - 1/2*v**2 + 5/3*v**3 + 0*v. What is a in y(a) = 0?
0, 2/3, 1
Suppose 4*k - 8 = -0*k. Factor -2*u**k + 3 - 3.
-2*u**2
Let w be (14/49)/((-12)/(-54)). Solve 0*v**2 + 6/7*v**3 + 0*v - 3/7*v**4 + 0 - w*v**5 = 0.
-1, 0, 2/3
Let g(m) be the third derivative of -2*m**2 + 1/150*m**5 + 0 + 0*m - 1/60*m**4 + 1/300*m**6 - 1/15*m**3. Factor g(z).
2*(z - 1)*(z + 1)**2/5
Let g(t) = t**3 + t + 2. Let d be g(-1). Let z(r) be the first derivative of 1 - 2/3*r**3 + 0*r**2 + d*r + 1/5*r**5 + 1/4*r**4. Factor z(n).
n**2*(n - 1)*(n + 2)
Let a be -4 + 2 + (-526)/(-232). Let x = a - 1/58. Factor 1/2*k + 1/4 + x*k**2.
(k + 1)**2/4
Let m(z) be the second derivative of -z**7/420 - z**6/180 + z**5/30 + z**3 - 4*z. Let i(k) be the second derivative of m(k). Find y, given that i(y) = 0.
-2, 0, 1
Let t be -1*((1 - 4) + 0). Suppose 0*a + 4*a + t*y - 6 = 0, 4 = 3*a + 2*y. Suppose -1/4*h**4 + a - 3/4*h**2 - 1/4*h - 3/4*h**3 = 0. What is h?
-1, 0
Suppose 5*z - 22 = -3*x, -x = 2*z - 4*z. Let v be (-1)/(-6) + (-1)/(-30). Factor -2/5*g - v*g**z - 1/5.
-(g + 1)**2/5
Let x(p) be the first derivative of 33*p**4/28 - 9*p**3/7 - 3*p**2/7 - 16. Factor x(a).
3*a*(a - 1)*(11*a + 2)/7
Let o(p) = -194*p**3 + 203*p**2 - 17*p - 29. Let t(s) = -969*s**3 + 1014*