e the first derivative of 4*s**3/3 + s**2 - s - 2. Let d be w(1). Factor 2*f**3 - 4*f**d - f**3 + f**5 - 2*f**4.
-f**3*(f + 1)*(3*f - 1)
Let y(w) be the third derivative of w**4/24 + 3*w**3/2 - 12*w**2. Let l be y(-9). Factor 0 + 4/3*j**4 + 2/3*j**5 - 2/3*j - 4/3*j**2 + l*j**3.
2*j*(j - 1)*(j + 1)**3/3
Solve -24/13*p**4 + 0 + 18/13*p**5 + 2/13*p + 8/13*p**2 - 4/13*p**3 = 0.
-1/3, 0, 1
Let s = -10 + 17. Let u be 221/91 - (-4)/s. Solve -1/4*h**4 + 1/4*h**2 + 0 + 1/4*h - 1/4*h**u = 0 for h.
-1, 0, 1
Let w be 50/18 + 2/9. Let s(l) be the first derivative of 0*l + 2/5*l**2 - 34/15*l**w + 18/5*l**4 - 2. Factor s(g).
2*g*(4*g - 1)*(9*g - 2)/5
Suppose d + 5 + 2 = 2*x, -3*x + 3*d + 12 = 0. Factor 1 - 7/2*t + 7/2*t**x - t**2.
(t - 1)*(t + 1)*(7*t - 2)/2
Factor 0 - 1/2*n**4 + 3*n**3 + 4*n - 6*n**2.
-n*(n - 2)**3/2
Let k(o) be the first derivative of -3*o**4/4 + 5*o**3 - 12*o**2 + 12*o - 11. Find q such that k(q) = 0.
1, 2
Let m = 11 - 8. Let q(i) be the first derivative of -1/2*i**2 - 1/12*i**m - i + 1. Suppose q(r) = 0. Calculate r.
-2
Let p(j) be the third derivative of j**5/165 + 7*j**4/132 + j**3/11 + 3*j**2. Factor p(a).
2*(a + 3)*(2*a + 1)/11
Suppose 0 = -9*g + 5*g - 144. Let v be (g/28)/(4/(-14)). Let -1/2*r**2 + 3*r - v = 0. Calculate r.
3
Let d be 152/36 + 4/(-18). Let m(y) be the second derivative of 0 + y - 1/4*y**d - 3/2*y**2 + y**3. Find u such that m(u) = 0.
1
Let g(o) be the third derivative of o**9/20160 + o**8/2240 - o**5/15 - 6*o**2. Let f(s) be the third derivative of g(s). Factor f(t).
3*t**2*(t + 3)
Let y(p) be the first derivative of p**6/24 - p**5/10 - p**4/4 + p**3/6 + 3*p**2/8 - 11. Suppose y(i) = 0. What is i?
-1, 0, 1, 3
Let w(b) be the second derivative of b**6/6 - b**5/2 + 5*b**4/12 - 33*b. Suppose w(m) = 0. Calculate m.
0, 1
Let l(w) be the third derivative of -w**8/784 + w**7/245 - w**5/70 + w**4/56 + 5*w**2. Find b, given that l(b) = 0.
-1, 0, 1
Suppose 15*x**3 - 12*x**4 - 12*x**2 - 59*x**3 + 44*x + 472 - 448 = 0. What is x?
-3, -1, -2/3, 1
Let c be -2 - 4/((-32)/20) - -1. Factor 9/4*q**2 - 3/4 - c*q.
3*(q - 1)*(3*q + 1)/4
Let s(u) be the first derivative of u**7/315 + u**6/60 + u**5/30 + u**4/36 - u**2 - 2. Let z(p) be the second derivative of s(p). What is b in z(b) = 0?
-1, 0
Let t(z) = -11*z - 6. Let u be t(9). Let i be (6/8)/(u/(-40)). Factor -2/7*y**2 + 2/7*y**4 + 0 - 2/7*y**5 + 0*y + i*y**3.
-2*y**2*(y - 1)**2*(y + 1)/7
Suppose -2 = -5*l + 4*p + 8, p = 0. Let k(a) = -a**2 + 6*a + 3. Let h be k(6). Determine r, given that -4*r**l + 5*r**3 - 2*r - 3*r + 7*r - 3*r**h = 0.
0, 1
Suppose -146*v + 132*v = -70. Suppose 0*m**2 - 25/9*m**3 + 2/9 + 7/9*m - 4/3*m**v - 32/9*m**4 = 0. What is m?
-1, -2/3, -1/2, 1/2
Let s(l) be the second derivative of -l**4/24 + l**3/6 - l. Find a, given that s(a) = 0.
0, 2
Let -3*n**2 - n**2 - 4*n + 33*n**3 - 15*n**3 - 14*n**3 + 4*n**4 = 0. Calculate n.
-1, 0, 1
Let u(h) be the first derivative of h**4/54 - 2*h**3/27 + 5*h - 5. Let l(b) be the first derivative of u(b). Solve l(f) = 0.
0, 2
Factor -20*y**2 + 105/2*y**3 + 0 - 10*y.
5*y*(3*y - 2)*(7*y + 2)/2
Let p = 17 + -14. Factor 3*x**2 - 1 - 2*x**p + x - 2*x**2 + x**3.
-(x - 1)**2*(x + 1)
Suppose -2 + 12 = 5*y. Let p = 10/21 + 6/7. Factor -2/3*t**2 - y*t - p.
-2*(t + 1)*(t + 2)/3
Let f = 16 - 5. Solve -56*m**3 + 45*m**4 + 2 - 2*m**5 - 6*m**5 + 44*m**2 - f*m**4 - 16*m = 0 for m.
1/4, 1
Let t(j) = -5*j**2 - 8. Let u(m) be the second derivative of 0*m**3 - 1/4*m**4 - 5/2*m**2 - 2*m + 0. Let f(c) = -5*t(c) + 8*u(c). Factor f(b).
b**2
Let 27*g - g**2 - 27*g = 0. Calculate g.
0
Let h(c) = -1. Let i(x) = 6*x**2 - 4*x - 6. Suppose 4 = 2*y + 2. Let m(g) = y*i(g) - 6*h(g). Solve m(p) = 0.
0, 2/3
Let c(r) be the third derivative of -r**7/2940 + r**5/420 - r**3/2 - 2*r**2. Let t(l) be the first derivative of c(l). Factor t(f).
-2*f*(f - 1)*(f + 1)/7
Let v(d) be the second derivative of -2*d**6/35 - d**5/7 - 2*d**4/21 - 9*d. Factor v(r).
-4*r**2*(r + 1)*(3*r + 2)/7
Let m(v) be the first derivative of 1 - 1/6*v**3 + 0*v**2 + 1/2*v. Factor m(r).
-(r - 1)*(r + 1)/2
Let i(d) = -d**3 - 10*d**2 - 12*d - 7. Let y be i(-8). Let v = -35 - y. Suppose -3/2*a**v - a**3 - 1/2*a**5 + a**2 + 3/2*a + 1/2 = 0. Calculate a.
-1, 1
Determine s, given that -1/9*s**4 - 4/9*s - 4/9*s**3 - 2/3*s**2 - 1/9 = 0.
-1
Let x(n) = 3*n - 8. Let a be 8/(-6)*(-69)/23. Let g be x(a). Determine j, given that -7/3*j**3 + 0 + j**g - 1/3*j + 5/3*j**2 = 0.
0, 1/3, 1
Let d be (4/(-18))/((-4)/3). Let y(z) be the second derivative of 0 + z + d*z**4 - 1/15*z**6 - 1/10*z**5 + 0*z**2 + 1/3*z**3. What is w in y(w) = 0?
-1, 0, 1
Let q = 2/65 - -53/390. Let y(n) be the first derivative of -2 + 1/2*n + 1/2*n**2 + q*n**3. Suppose y(p) = 0. Calculate p.
-1
Let h(w) = -2*w**2 - 9*w + 6. Let c(b) = -b**2. Let l(d) = 5*c(d) - h(d). Find n such that l(n) = 0.
1, 2
Let p be 2/(-1 - 9/(-6)). Let u(n) be the first derivative of -3/7*n**2 + 4/7*n + 1/14*n**p + 0*n**3 - 2. Factor u(z).
2*(z - 1)**2*(z + 2)/7
Factor -49 + 29 - 40*s - 13*s**2 - 2*s**2.
-5*(s + 2)*(3*s + 2)
Let m be (32/40)/(4/10). Let t(n) be the first derivative of 2 - m*n**3 - 2*n - 3*n**2 - 1/2*n**4. Solve t(v) = 0.
-1
Let l = 19 - 19. Suppose -8 = -5*j + 2. Let -2/7*k**j + 2/7*k**4 + 0*k**3 + 0 + l*k = 0. Calculate k.
-1, 0, 1
Let s(h) = -2*h**4 + 4*h**3 + 6*h**2 - 15*h - 1. Let u(l) = -l**4 + 2*l**3 + 3*l**2 - 8*l. Let x(b) = 4*s(b) - 7*u(b). Factor x(m).
-(m - 2)**2*(m + 1)**2
Suppose -2*t = -t - 4. Suppose -2*m - 8 = 2*y - 7*y, 5*y + t*m = 14. Find s, given that 0 + 0*s + s**y - 1/2*s**3 = 0.
0, 2
Let t(q) be the third derivative of q**6/30 - q**4/2 - 4*q**3/3 + 10*q**2. Factor t(w).
4*(w - 2)*(w + 1)**2
Let t(i) be the third derivative of i**7/1365 - i**6/780 - i**5/390 + i**4/156 - 10*i**2. Determine a so that t(a) = 0.
-1, 0, 1
Let i(k) be the third derivative of k**8/3192 - k**6/570 + k**4/228 - 13*k**2. Find w such that i(w) = 0.
-1, 0, 1
Let m(u) be the second derivative of -u**7/105 - u**6/60 + u**5/30 + u**4/12 + 3*u**2/2 + 3*u. Let d(l) be the first derivative of m(l). Factor d(v).
-2*v*(v - 1)*(v + 1)**2
Let m(b) be the third derivative of -11*b**5/4 + 85*b**4/24 - 5*b**3/3 - 6*b**2. Find n such that m(n) = 0.
2/11, 1/3
Suppose 5*c = -3*l - 14, l - 4*c - 16 = 2. Suppose 0 = 5*z - l*z. Solve z + 6/7*m**3 - 10/7*m**4 + 0*m + 4/7*m**2 = 0 for m.
-2/5, 0, 1
Let p be (-36640)/(-126) - (-4)/(-18). Let s = p - 290. Factor -4/7*d**3 + 2/7*d**4 + 2/7*d + 2/7 - s*d**2 + 2/7*d**5.
2*(d - 1)**2*(d + 1)**3/7
Let z(j) be the third derivative of 21*j**6/200 + j**5/75 - j**4/30 + 11*j**2. Factor z(n).
n*(7*n + 2)*(9*n - 2)/5
Let r(b) be the first derivative of 9*b**4/8 - 2*b**3 - 15*b**2/4 + 3*b + 42. Find c, given that r(c) = 0.
-1, 1/3, 2
Let w(k) = -6*k**4 + 3*k**3 + 2*k**2 - k + 2. Let i(r) = -7*r**4 + 4*r**3 + r**2 - r + 3. Let y(z) = 2*i(z) - 3*w(z). Factor y(g).
g*(g - 1)*(g + 1)*(4*g - 1)
Let r(k) be the second derivative of k**4/42 + 2*k**3/7 - k**2 + 59*k. Let r(c) = 0. What is c?
-7, 1
Let b(d) = -d**2 - 4*d + 9. Let v be b(-5). Let y(t) be the second derivative of 0*t**2 - 1/15*t**5 + 2*t - 1/18*t**v + 0 + 0*t**3. Let y(z) = 0. What is z?
-1/2, 0
Let w(b) be the second derivative of b**7/11340 - b**6/3240 - b**4/4 - b. Let o(c) be the third derivative of w(c). Find v, given that o(v) = 0.
0, 1
Solve 12*w + 3*w**2 + 10*w - 9*w - w + 12 = 0 for w.
-2
Factor 1/6*d**3 + 0 - 1/6*d**2 - 1/3*d.
d*(d - 2)*(d + 1)/6
Factor 1/2 + 5/4*n + 1/2*n**2.
(n + 2)*(2*n + 1)/4
Let g = 327 + -5211/16. Let k(v) be the first derivative of -g*v**4 + 3/4*v**5 + 2 + 3*v**2 - 3*v - 1/4*v**3 - 1/8*v**6. Find d such that k(d) = 0.
-1, 1, 2
Let j(k) be the third derivative of 0*k**4 + 3*k**2 - 1/120*k**5 + 0*k + 1/160*k**6 + 0*k**3 + 1/168*k**7 + 0. Factor j(l).
l**2*(l + 1)*(5*l - 2)/4
Let h(k) be the third derivative of k**6/24 + 9*k**5/20 - k**4 + 2*k**3/3 - 8*k**2. Let f(w) be the first derivative of h(w). Suppose f(g) = 0. Calculate g.
-4, 2/5
Let 8*z + 20*z**5 + 88*z**4 + 4*z + 9*z + 132*z**3 - 5*z + 80*z**2 = 0. Calculate z.
-2, -1, -2/5, 0
Let v = -51 - -55. Let a(b) be the second derivative of v*b + 1/30*b**4 + 0*b**2 + 0*b**3 - 3/50*b**5 - 1/105*b**7 + 1/25*b**6 + 0. Factor a(u).
-2*u**2*(u - 1)**3/5
Let j(l) be the first derivative of -1/24*l**4 + 1/9*l*